3tl|aca, Nein @ack arV12121 Duplicate whist Cornell University Library 3 1924 031 243 268 olin.anx Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031243268 DUPLICATE WHIST. DUPLICATE WHIST, BY JOHN T. MITCHELL, (An Entirely New Edition.) Containing full explanation of the various methods of duplicate play now in vogue, individual schedules up to sixty-four and instructions for formulating team schedules up to any number. WITH APPENDICES: MODERN LEADS AND INFERENCES. DRAFT OF PROGRAM FOR CONGRESS. DRAFT OF BY-LAWS FOR WHIST CLUB. THE LA^Al^S OF ^VHIST AND DUPLICATE WHIST. (As Adopted by the AMERICAN WHIST LEAGUE.) KALAMAZOO, MICH. Ihling Bros. & Everard, 1897. Copyright, BY Ihling Bros. & Everard, A. D. 1896. TO THE AMERICAN WHIST LEAGUE (in particular) AND TO \/VHIST PLAYERS THE WORLD OVER (in general) THIS BOOK IS RESPECTFULLY DEDICATED BY THE AUTHOR. ERRATA. Owing to a raisuiiderstandingf with the author on the subject of proof reading, some errata have been allowed to pass into the final print, and it is for the purpose of calling attention to them that we now claim the reader for a few brief lines. Page 14, line 19. Read "Corresponding Secretary" for "President " Mr. Schwarz was President in 1895-6. Page 57. The E. player at Table 8 in Game 24 should be 19, not 29. The S. player at Table 6 in Game 31 should be 34, not 44. Page 68. The figures in the Eight Table Schedule under the last two headings are transposed; i. e., the last column should be read under the "Passed to" heading, and the next to the last column under the "Received from" heading. Page 86. In the first line of foot note, "A, K or ' should be inserted before "K, Q." If the reader will kindly make these corrections in his copy of the book, he will confer a favor upon THE PUBLISHERS, Ihling Bros. & Everard. Kalamazoo, Mich., Jan. ^, 1897. CONTENTS. Introductory . . . . . . 9 Historical . . . . . . . . . . 13 Inter-Club Duplicate Whist . . . . 18 Progressive Duplicate Whist . . 29 Single Table Duplicate . . . . . . 38 Individual Schedules . . . . il) Whitfeld Progressive Duplicate . . 67 Ladies and Gentlemen's Schedules . . . . 69 Team Schedules . . . . . . T4 Appendix I. Leads and Inferences of Modern Whist . . SI Appendix II. Program for Congress or Annual Meeting 113 Appendix III. By-Laws and House Rules for Whist Club 121 Appendix IV. Laws of Whist and Duplicate Whist as adopted by the American Whist League 139 Index . . . . . . . . . . 157 INTRODUCTORY. There has been more or less controversy as to the origin of Duplicate Whist. Mr. Barnet Phillips of the New York Times informed me that it was played in Berlin and Paris as far back as 1840, but it seems to have been dropped for want of a simple method of play, and has only been revived within the last decade, owing to the invention of systems which make it as easy to practise as straight whist. It is for the' purpose of describing the various systems now in vogue that the writer has undertaken a revision of his first treatise on the subject, believ- ing that an up-to-date text book on Duplicate Whist is a real need of the whist fraternity. It is claimed that Duplicate Whist gives hap- hazard play a significance which it does not deserve, because in certain instances more tricks can be made by playing irregularly than by following the rules; but if noninformatory tactics are followed all through an evening's play, it will be found that they lose far more tricks than they gain, and Duplicate Whist is the very thing that will prove it. If giving both sets of opponents the same cards, with the same trump and the lead in the same position, does not put both sides on an equal footing then there is nothing that can do so, and if "duplicate" is not a true test of 10 Mitchell's duplicate whist. skill, it must be acknowledged that whist, itself, is not a scientific game, but a mere succession of chance plays, which may prove fortunate or unfortunate according- to the cards held by one's opponents. Some people go to the other extreme, and claim that there is enough science in straight whist to off- set any luck that poor players may have in holding cards, but the records of those clubs who have kept track of the scores of both straight and duplicate whist prove that this claim is illfounded; in fact, it is generally found that the players who make a good score at "duplicate" are poor scorers at "straight," and that is the main reason why duplicate whist is the favorite game among the better class of players. When the first edition of " Duplicate Whist " appeared, the game it advocated was attacked with great virulence by certain of the more conservative writers of that day. It was branded a "delusion" and a "fad," and it was asserted that like most other delusions and fads it would have but an ephemeral existence. The writer, however, had an abiding faith in the future of the game he was trying to make the whist fraternity adopt as their standard, and time has proved him a better prophet than his critics, for to-day "it is the only method employed in testing the merits of rival teams or clubs," just as he said it would be. A little longer time is required to play a given number of hands at duplicate than at straight whist. INTRODUCTORY. 11 but the resulting' gain oi* loss is so much more con- clusive as to the skill of the players that the extra time consumed must be considered well expended. Every whist player knows that when the high cards are ag'ainst him it is impossible for him to take a majority of the tricks; and while there may be some- thing in keeping down the opponent's majority, it is nothing compared with the certainty that before the close of the g'ame the chances will be evened up, and both sides given equal opportunities. This certainly adds zest to the contest, and makes every player bend all his energies to the game, knowing full well that if he lets opportunities slip there is no way to recover them, for there is practically no luck in duplicate whist, and therefore no g"oing behind the returns. The systems of play as laid down by the author- ities are not interfered with, except as regards play- ing to the score, which would be manifestly out of place when the object is to take the greatest number of tricks with every hand. Each player is free to follow his favorite "master," and the result of the game, provided he makes no mistakes and has worthy opponents, will surely prove whether he has found the true principles of the "king of games," or has been following false lights only to find himself floun- dering in the mire of defeat. With these introductory remarks the duplicate game is commended to all true lovers of whist. In all clubs and coteries where whist is played for its 12 Mitchell's duplicate whist. own sake, "duplicate" is now the only game played, "straight" being confined to those clubs that allow playing for stakes, where a game is required which gives the mediocre player a show for his money. HISTORICAL. 13 HISTORICAL. Cavendish, in his "Card Table Talk," says: — "In the latter part of the winter of 1857, during an after-dinner conversation, it was remarked by some of the party that whist is a. mere matter of chance, since no amount of ingenuity can make a king win an ace, and so on. This produced an argument as to the merits of the game ; and as two of the disputants obstinately main- tained the original position, it was proposed to test their powers by matching them against two excellent players in the room. "To this match, strange to say, the bad players agreed, and a date was fixed. Before the day arrived, it was proposed to play the match in double, another rubber of two good against two bad players being formed in an adjoining room, and the hands being played over again, the good players having the cards previously held by the bad ones, and vice versa, the order of the play being, of course, in every other respect preserved. The difficulty now was to find two players sufficiently bad for the purpose ; but two men were found, on con- dition of having odds laid them at starting, which was accordingly done. "On the appointed day, a table was formed in room A, and, as soon as the first hand was played, the cards were re-sorted and con- veyed into room B. There the hand was played over again, the good players in room B having the cards that the bad players had in room A. At the end of the hand, the result was noted for compari- son, independently of the score, which was conducted in the usual way. Thirty-three hands were played in each room. In room A, the good players held very good cards, and won four rubbers out of six ; in points, a balance of eighteen. In room B, the good players had, of course, the bad cards. They played seven rubbers with the 14 Mitchell's duplicate whist. same number of hands that in the other room had played six, and they won three out of the seven, losing seven points on the balance. The difference, therefore, was eleven points, or nearly one point a rubber in favor of skill. "A comparison of tricks only showed some curious results. In seven of the hands the score by cards in each room was the same. In eighteen hands the balance of the score by cards was in favor of the superior players ; in eight hands in favor of the inferior. In one of these hands the bad players won two by cards at one table, and three by cards at the other. ' ' The most important result is, that at both tables the superior players gained a majority of tricks. In room A, they won on the balance nineteen by tricks ; in Room B, they won two by tricks. ' ' It will be observed that this experiment does not altogether eliminate luck, as bad play sometimes succeeds. But by far the greater part of luck, namely, that due to the superiority of winning cards, is by the plan described quite got rid of." In reply to an inquijry made by Mr. Theodore Schwarz, then P*©£^«»tjof the American Whist Leag'ue, Cavendish gave the names of the players •who participated in the game above described, as per the following letter : August 17TH, 1893. Jlfy Dear Schwarz : — You wanted to know the names of the first duplicate whist players. The date has already been given in "Whist." I have heard from my brother and he states as follows : DANIEI. JONES. CHINERY. TABLE I. LEWIS. EDWARD WILSON. BULLOCK. MATTHIAS EOYCE TABLE 2 HENRY JONES. 15 Daniel Jones is my brother. Chinery was afterwards editor of The Times. John D. Lewis was afterwards M. P. for Davenport. Boyce is known in whist circles as " Mogul." Henry Jones. G. W. P., in "American Whist Illustrated," says: — "The play of trumps at the outset from five or more does not, in a majority of cases, win more tricks for the player than will their proper husbandry and use. If you will play twenty or fifty hands in duplicate, you may ascertain this fact." Neither of these writers, however, gives the modus operandi of duplicate play, nor was it intended by them that the duplicate method should be gener- ally practised, — probably because they were unac- quainted with any simple manner of playing it. 16 Mitchell's duplicate whist. In the spring- of 1888 the following- parag-raph appeared in the London Field: "A match at whist was played in Glasgow between teams of the Carleton and Wanderer's Clubs, April 16, when a new system of duplicate play, the invention of Mr. James Allison, was tested. The cards at the commencement of each hand were dealt in the usual manner, but in the course of play they were not formed into tricks. Each player kept his thirteen cards before him till the finish of the hand, and after playing to each trick he placed his card either longwise or shortwise, to show by which side the trick had been won. This arrangement prevailed at two tables, the hands being simultaneously played. The hands, as soon as finished, were gathered up by each player and placed, backs up, on the table, the dealer leaving the trump card, face up, on top of his pack. The players then changed tables and replayed the hand, the players being reversed. A deal was only necessary every two hands, and but little more time, after some prac- tice, was taken than in playing one hand in the usual way." This system has been adopted b}- most of the duplicate whist pla3'ers in this country, except that the players are reversed prior to the commencement- of the game, the players of one four sitting north and south at the first table and east and west at the second table, while the players of the other four sit east and west at the first table and north and south HISTORICAL. 17 at the second, and the hands are passed from one table to the other by means of trays or boards* specially prepared fof holding- the cards. Instead of desig-nating- the winner of a trick by placing- the card long-wise or shortwise, sometimes chips or counters are used, and as each trick is won a chip is taken, and the number of chips held at the end of the hand shows the number of tricks taken by each side. It may be remarked that in sing-le table or two table duplicate, the hands may be replayed exactly as in straig-ht whist, the cards being- thrown into the center of the table and g-athered into tricks. *Until the invention of the Kalamazoo Tray the playing of duplicate whist was considered a more or less tedious affair, especially when it was deemed advisable to preserve a record of the play, and, in fact, it is questionable if duplicate whist would ever have become the popular game it is to-day, but for that invention. ^^ 18 Mitchell's duplicate whist. INTERCLUB DUPLICATE WHIST. This is the name now g-iven to that form of the game in which the replay of the hands is not accom- plished at the same table nor by the same players who played the originals, but by co-partners at another table, in fact, the team -of- four game. Two players of one four sit north-south at the first table, and the other two sit east-west at the second table, while two players of the opposing four sit east-west at the first table and the other two north -south at the second. When the duplicate hand has been played, both fours have held all the hands at both tables, and each should have taken thirteen tricks for every hand, the points gained and lost being the difference between that number and the number actually taken. The original scores should not be divulged until after the duplicate hands have been played, and the strictest silence should prevail until the game is finished, as any conversation heard at the other table is liable to influence the play. Twenty-four hands (twelve original deals at each table) can be played in about two hours and a half, and should afford ample test of the merits of opposing fours. In case of a large number of players in one assembly the hands may be passed from table to INTERCLUB DUPLICATE WHIST. 19 table so that all the players may play the same deals and an "average" struck for the north-south and east-west hands. This gives a basis from which to reckon the individual gains and losses to the respective halves of each team-of-four. In this connection, it may be remarked that if in playing a match game it should be found that each club has an incomplete team {i. e., a pair without co-partners), the odd team need not be left out: the club that has the extra team sitting north -south at the last table adds the east-west average to its total score, while the club whose extra team sits east-west at the last table adds the north -south average to its score. This is as fair for one side as the other, and allows all the players present to participate in the game. In seating the players of opposing clubs it has become a custom to place the first team of the visiting club north -south at the first table, east- west at the second, and so on down the line. This custom may be formulated into the following general rule : Players of the visiting club shall sit north-south at the odd numbered tables, east-west at the even; and players of the home club shall sit east-west at the odd numbered tables, north-south at the even. When the match is played on neutral ground, positions may be decided by lot or agreement. If a match is between a large number of players on each side, it will be found advisable not to change 20 Mitchell's duplicate whist. partners or opponents (except on the progressive principle, which will hereafter be explained), but if the match is between single teams-of-four, players may change positions after every four deals according to the following schedule, in which the numbers 1, 2, 3 and 4 represent the players of the visiting club, and the numbers 5, 6, 7 and S the players of the home club. FIRST TABLE. NORTH. SOUTH. EAST. WEST 1 and 2 against 5 and 6 1 2 a 7 8 1 3 ii 7 5 1 3 a 6 8 1 4 " 5 8 1 \ 4 SECOND TABLE 6 7 NORTH. SOUTH. EAST. WEST 7 and s against 3 and 4 5 6 3 4 8 6 2 4 5 7 2 4 6 7 2 3 5 8 2 3 If the match is for forty-eight hands, the follow- ing schedule should be used for the second twenty- four, the players, of course, retaining the same numbers: INTERCLUB DUPLICATE WHIST. 21 FIRST TABLE. NORTH. SOUTH. EAST. WEST. and 2 against 6 and 5 2 8 7 3 5 7 3 8 6 4 8 5 4 7 6 SECOND TABLE. NORTH. SOUTH, EAST. WEST. 8 and 7 ag-ainst 3 and 4 6 5 U 3 4 6 8 «( 2 4 7 a "2 4 7 6 ^^ 2 3 8 .5 It 2 3 After the entire i fame has been pla yed it will be found that each player has played against every other player the same number of times, has played through him and up to him the same number of times, and has played with every other man on his own team the same number of times. These are the schedules adopted by the Amer- ican Whist League, with some slight modifications suggested by actual practice since their adoption, and will be found to equalize the opposition to a nicety, and not allow the " personal equation " to figure unduly in the placing of teams against each other. 22 MITCHELL'S DUPLICATE WHIST. SCHEDULE SCORE CARD. Versus CLUB NO. I, CLUB NO z. I 5 a 3 4 \'\ - - 7 8 Dai rE Table i. — NORTH. DEAL. N S E W SCORE. TOTAL. O. K. EAST. 2 5 6 ._ 2 3 4 5 6 7 8 ■■ 7 8 9 lO II 12 t 3 7 5 13 14 15 i6 '■ 6 8 •■ ' 17 i8 19 20 4 5 8 21 ■■ 6 7 23 24 Total, INTERCLUB DUPLICATE WHIST. SCHEDULE SCORE CARD. 23 Versus CLUB NO. I. CLUB NO. z. I 5 6 7 8 2 3 4 Datr Table 2— NORTH. DEAL. N S E w SCORE. TOTAL. O, K. EAST. I 7 8 3 4 3 4 5 6 6 --- - --- 7 8 9 lo 8 6 2 4 II 12 13 14 15 i6 7 1 i 17 i8 6 7 2 3 19 20 21 5^ 8 23 Total 24 Mitchell's duplicate whist. schedule score card. Versus CLUB NO. I. CLUB NO. 2. 5 6 7 8 2 3 4 ' Dai Table i. — NORTH. DEAL. N S E W SCORE. TOTAL. 0. K EAST. 25 26 27 28 I . 2 6 5 --- .... 29 3° 3' 32 8 7 .... 33 34 35 36 3 5 7 ... 37 38 39 40 8 6 ... ..... 41 42 43 44 4 8 5 . _ 45 46 47 48 7 6 . Total, . INTERCLUB DUPLICATB WHIST. SCHEDULE SCORE CARD. 25 Versus CLUB NO I. CLUB NO. z. T 5 6 7 8 2 3 4 ' Date, Table 2. — NORTH. DEAL. N S E W SCORE. TOTAL. 0. K. EAST. 25 26 27 8 7 3 4 - 28 __ 29 30 6 5^ ,, 31 32 33 34 35 36 6 8 4 --- 37 38 7 5 ;; 39 40 - - - 41 42 43 Ad. 7 6 2 45 46 47 48 8 5 Total,... 26 Mitchell's duplicate whist. Only one score card is required at each table — the north man keeping- the score and the east man O. K.-ingit. The interclub game may be used to advantage within clubs for tournaments between individuals, pairs or fours. It has been the style of game played at the Chicago Whist Club almost since its very organization, and as this club is where the writer has gained most of his experience in such matters, the game which it has adopted naturally suggests itsfelf to him as the best that has been so far devised. From eighty to one hundred players have taken part in the weekly tourney of the Chicago Whist Club for more than four years, and there is no demand for a change of style yet. When everybody wanted to play in the individual game, the players had to be divided into sections, in order to accommodate the schedules which it was necessary to play by; and when there were entries for pairs, teams-of-four and individuals all at the same time, all were allowed to play according to their inclinations, but the game was always interclub duplicate whist, with the exception of a few months at the starf, before this satisfactory game had developed. Except when the number of players exceeds ninety-six, the number of deals per game may be limited to twenty-four, which are as many as can be comfortably played in one evening. When there are more than forty-eight players in the game, and less INTERCLUB DUPLICATE WHIST. 27 than ninety-six, one hand may be dealt at each table except the last, at which as many may be dealt as are necessary to cotnplete the twenty-four. When there are more than twenty-four players in the game and not more than forty-eigfht, two hands may be dealt at each table. Over twenty-four, thirty-two or less, three hands to a table; and so on, adjusting- the number of hands to a table according to the number of players in the game, and making the last table deal as many as are necessary to bring the total up to twenty-four. If it is desired to play for an individual record, it will be necessary to play under the once-with-and- twice-against schedules. This will make the number of games in a tournament just one less than the number of players in it. The gains and losses are computed by the comparison of scores with the average for the north-south or east-west hands as the case may be, and may be reckoned by tricks or games, as may be decided by the committee in charge of the game. If the number of players in an individual record tournament is very large, and the time limited, two games of twelve hands each, or three games of eight hands each may be played in one evening; and if the total number of tables exceeds the number of hands in a game, the tournament may be divided into sections to suit the occasion. For example, in a sixty-four individual tournament, in which it was 28 Mitchell's duplicate whist. decided to play games of eight hands, there would be two sections, and playing three games per sitting, it would take twenty-one sittings to complete the tournament. Each section would play different hands, and each would have its own average. If it is desired to play for a pair record, the once-against schedules are all that is required, and the number of games in a tournament is one less than the number of pairs. If the time is limited the number of hands in a game may be reduced in the same way as in the individual tourney. The once-against schedules apply also to team- of-four tournaments and as it takes four players to make a unit this is the quickest kind of a tournament. Ninety-six players in a team-of-four tournament would complete a schedule in twenty-three weeks, in a pair tournament it would take them forty-seven weeks and in an individual tournament a year and forty-three weeks, playing one game per week. If it is decided to play more than one game at a sitting, the deals per game may be reduced in the manner described, although it must be borne in mind that the fewer the deals the less satisfactory is the test obtained. For annual meetings, congresses, etc., where it is possible to have two or more sittings per day for five or six days at a stretch, the schedules may be used to great advantage, and the number of hands to be played against each club, pair or indi- vidual can be regulated according to the length of time at the disposal of the players. PROGRESSIVE DUPLICATE WHIST. PROGRESSIVE DUPLICATE ^VHIST. The form of the progressive g'ame introduced by the writer into the Chicago Whist Club in 1892 was adopted by the American Whist League for the pre- liminary play for the Hamilton Trophy at the Con- gress of 1893 and has been a feature of all succeeding Congresses. The number of hands to be played are divided equally among the number of tables, and the quota at each table is played before any progression takes place. When a set has been played the east and west players move to the next higher numbered table, while the hands are passed to the next lower numbered table and another set is played. Then the east and west players move again in the same direc- tion as before, and the hands are passed in the oppo- site direction as before, and so on until a complete round of the tables has been made. The hands are passed from the first to the last table, while the east- west players move from the last table to the first. At the conclusion of the game every east and west pair has played against every north and south pair and every pair has played all the hands. The gain or losS to each team is computed by the average for the respective hands, which is figured by dividing the aggregate score by the number of tables. The above directions apply only to games in which the number of tables is odd. If the number of tables is even, after the east and west players have made half the circuit they strike the same hands that 30 MITCHELL'S DUPLICATE WHIST. they started with. This difficulty has been very cleverly overcome by the invention of Professor A. Hadlock, of Kalamazoo, Mich., whose method is as follows : Divide the total number of hands to be played into two equal parts, and finish one half before starting the other. When the east and west players get half way around in the progression they remain for another hand or set of hands at the table at which they find them- selves, and then pass on to the next table. This makes them finish the first half with one table yet to play. When the second half of the game begins, the east and west players move back to the table next following the one at which they played the double set and proceed as before. When they get half way around the second time they find themselves at the table at which they did not play at all the first time, and as that is where they now play a double set of hands before passing to the next table, when they get around the second time they have played an equal number of hands at each table Prof. Hadlock's game will apply to any number of even tables, and in the case of four tables, it may be remarked, there is no change of positions between the first and second halves of the game, as at the third change the east and west players finish the first half and are seated at the proper tables for commencing the second. If the number of tables is an even number not divisible by three (such as 4, 8, 10, 14, etc.,) there is another way, the invention of the writer, to get around the difficulty, which is as follows: Start the game exactly as described in the directions for odd tables, but divide the quota to be played at each table into two equal portions, and let the east and west players move after every half set of hands has been played, and go the round of the tables twice. The hands, how- ever, only make the round once and are played in exact succession by the north and south players, who play the unplayed half of the first set against the next comers; then the first half of the next set, and so on. If the number of tables is so great that only one deal can be started at each table, neither of the above PROGRESSIVE FOURS. 31 methods of gfetting" around the even table difficulty can be adopted, in which case the skipping-one-table game invented' by Mr. E. T. Baker, of Brooklyn, comes into play. This is as foUov^s: After the east and west players have gone half way around they skip one table and continue the progression. This brings them to the table at which they started with one hand to play, and they play that hand against their original opponents. There are tvi^o progressive "four" games. One, also the invention of the writer, is applicable to any number of tables which divided by two brings an odd result, such as six, ten, fourteen, etc. In this game half the north and south players move and half the east and west players sit still. The fbur players move as a unit, or remain seated as a unit, the north- south players at the odd numbered tables and the east and west at the even being the sitting fours, while the east and west at the odd and the north and south at the even are the moving fours. The hands are passed back and forth between the odd num- bered tables and the next higher, and between the even numbered tables and the next lower (thus com- pleting a match between the two fours at contiguous tables), and are then passed in blocks of two to the next lower two tables while the moving fours go to the next higher two tables. At the conclusion of the game all the moving fours have played all the sitting fours, and they have both played all the hands. In order to facilitate the movement of the boards in this game the tables should be arranged in parallel 32 Mitchell's duplicate whist. rows, so that 1 and 2, 3 and 4, 5 and 6, etc., are alongside each other, and the last two tables are contiguous to the first two tables. Take, for instance, fourteen tables ; the arrangement would be as follows : 14-13 I I CD I If the game is between two clubs it may be divided into two independent halves, each half containing an odd number of tables. The players of one club sit north and south in one half and east and west in the other, and after each half has played a round of so many hands (one or two to a table as the time permits) the boards are passed to the other half for the re-play. If the number of tables engaged is so large that there is not time to play the minimum number of hands (one original deal at each table in each half), the hands may be dealt by a neutral committee prior to the commencement of the game, and duplicated so that identical hands may be played in each division. If the number of tables divided by two is even, the quota of hands to be played against each four may be halved, and the moving fours go the round of the tables twice, according to directions in the pair game. This would not do, however, in the case of twelve or PRO(»RESSI\'E FOURS. 33 twenty-four tables, as the halves of these numbers divide evenly by three. The other progressive "four" g-ame is the inven- tion of Mr. E. C. Howell, of Boston, and was called in the programme of the fifth American whist congress, held at Minneapolis in 1895, "Howell's Modifi- cation of the John T. Mitchell Progressive Sys- tem." It provides for the playing of every four against every other four and also for complete matches between them. In the writer's pair game no attempt is made to have the east and west co-partners of any north-south team play the same hands in duplicate against the north and south co-partners of the east-west team that started them. This is accomplished in the Howell method by the following process: "The players move as in Mitch- ell's system, but the trays are carried, not to the next table, but from the middle to the head, with the others in natural order. With onh* three tables in play the two systems are identical. With five tables Howell moves the trays up two tables, with seven tables, three; with nine tables, four, and so on." When the number of players engaged make an even number of tables an extra table is put in, and during the play there are always two tables which are idle, but the hands are passed back and forth just the same as though the tables were fully occupied. The effect of this scheme is to bring about the overplay of the same deals by the same teams, and 34 MITCHELL'S DUPLICATE WHIST. the score is usually counted by matches won instead of tricks gained. In case of a tie the tricks decide. Schedules showing- movement of trays under Howell system : 4-5 Tables. 6-7 Tables. 8-9 Tables. lo-ii Tables. 12-13 Tables. 3 to I 4 to I .5 to I 6 to I 7 to I 4 to 2 5 to 2 6 to 2 7 to 2 8 to 2 5 to 3 6 to 3 7 to 3 8 to 3 9 to 3 I to 4 7 to 4 8 to 4 9 to 4 10 to 4 2 to 5 I to 5 9 to 5 10 to 5 II to 5 2 to 6 I to 6 II to 6 12 to 6 3 to 7 2 to 7 T to 7 13 to 7 3 to 8 2 to 8 I to 8 4 to 9 3 4 5 to to to 9 10 II 2 to 9 3 to 10 4 to II 5 to 12 6 to 13 14-15 Tables. i6- -17 Tables. il 3-ig Tables. 20-21 Table 8 to I 9 to I 10 to I 11 to I 9 to 2 10 to 2 II to 2 12 to 2 10 to 3 II to 3 12 to 3 13 to 3 II to 4 12 to 4 13 to 4 14 to 4 12 to 5 13 to 5 14 to 5 15 to 5 13 to 6 14 to 6 15 to 6 16 to 6 14 to 7 15 to 7 16 to 7 17 to 7 15 to 8 l6 to 8 17 to 8 18 to 8 I to 9 17 to 9 18 to 9 19 to 9 2 to 10 I to 10 19 to 10 20 to 10 3 to II 2 to 11 I to II 21 to II 4 to 12 3 to 12 2 to 12 I to 12 5 to 13 4 to 13 3 to 13 2 to 13 6 to 14 5 to 14 4 to 14 3 to 14 7 to 15 6 to 7 to 8 to 15 16 17 5 to 6 to 7 to 8 to 9 to 15 16 17 18 19 4 to 15 5 to 16 6 to 17 7 to 18 8 to 19 9 to 20 10 to 21 PROGRESSIVE FOURS. 35 22-23 Tables. 24-25 Tables. 26-27 Tables. 28-29 Tables. 12 to I 13 to I 14 to I 15 to I 13 to 2 14 to 2 15 to 2 16 to 2 14 to 3 15 to 3 16 to 3 17 to 3 15 to 4 16 to 4 17 to 4 18 to 4 16 to 5 17 to 5 18 to 5 19 to 5 17 to 6 18 to 6 ig to 6 20 to 6 18 to 7 19 to 7 20 to 7 21 to 7 19 to 8 20 to 8 21 to 8 22 to 8 20 to 9 21 to 9 22 to 9 23 to 9 21 to 10 22 to 10 23 to 10 24 to 10 22 to II 23 to II 24 to II 25 to II 23 to 12 24 to 12 25 to 12 26 to 12 T to 13 25 to 13 26 to 13 27 to 13 2 to 14 T to 14 27 to 14 28 to 14 3 to 15 2 to 15 I to 15 29 to IS 4 to 16 3 to 16 2 to 16 I to 16 5 to 17 4 to 17 3 '0 17 2 to 17 6 to 18 5 to i8 4 to 18 3 to 18 7 to 19 6 to 19 5 to 19 4 to 19 8 to 20 7 to 20 6 to 20 5 to 20 9 to 21 8 to 21 7 to 21 6 to 21 10 to 22 9 to 22 8 to 22 7 to 22 11 to 23 10 to 23 9 to 23 . 8 to 23 11 to 24 10 to 24 9 to 24 12 to 25 .• II to 25 10 to 25 12 to 26 II to 26 13 to 27 12 to 27 13 to 28 14 to 29 36 Mitchell's duplicate whist. LADIES AND GENTLEMEN'S PROGRESSIVE. When both sexes participate in the game, and one sex is not opposed to the other, the ladies may sit north and east, the g-entlemen west and south ; and if the gentlemen move in one direction while the boards are passed in the other, each lady will meet every gentleman, either as partner or opponent. "When there is time for a number of sittings, both the ladies and gentlemen may change opponents at successive games, using the individual schedules for multiples of four, and the pair schedules for other numbers, as guides in seating themselves at the com- mencement of each game. If one sex is opposed to the other, and the number of tables engaged divided by two brings an odd result, such as 6, 10, 14, 18, etc., the game in which the sitting fours and moving fours oppose each other may be played, the ladies, of course, being the sitting fcvurs. TWO TABLE PROGRESSIVE. 37 TWO TABLE PROGRESSIVE. When there are only two tables in a game, and it is desired to establish a pair record, it can be done, in a measure, by placing the teams so that each shall be in succession the co-partner of the other. The following schedule illustrates the movement of the teams : TABLE I, TABLE 2. N & S. E. 4 W. N. & S. E. & W. Deals 1 to 8 12 3 4 Deals 9 to 16 13 4 2 Deals 17 to 24 1 4 2 3 Each team figures its gain or loss by comparison with the pair that sits the same way at the other table. 38 Mitchell's duplicate whist. SINGLE TABLE DUPLICATE. By providing- a pack of cards and a tray for every original deal, vi^hist in duplicate can be played by four people. The cards are placed in the proper position in the tray after the hands are played, and v\rhen the ag-reed number of deals have been played, either the trays are turned quarter wa.j round, or the players change seats as may be deemed most expedient, and the players play the hands formerly held by their opponents. The score is counted exactly as in the interclub game, the difference between thirteen and the number of tricks actually taken showing the gain or loss. If the players are of such calibre that memory plays an important part in the play off, the second half of the game may be postponed until a future sitting, and another game begun. At the second sitting the first game may be played off and a third game begun; at the third sitting the second game played off and the fourth begun, and so on. This, of course, requires two sets of packs and trays. It will be found harder to remember the cards if the players change partners after every four, six or eight hands, and this will further add interest to the N. S. E. w. 1 2 3 4 1 3 i 2 1 4 2 3 SINGLE TABLE DUPLICATE. 39 g"ame by affording- an individual record. Players may chang-e partners and positions by the following- schedule : Deals 1 to 4, 6 or 8 Deals 5 to 8, 7 to 12 or 9 to 16 Deals 9 to 12, 13 to 18 or 17 to 24. . . , Players should not try to memorize the location of cards so as to take advantag^e of their mnemonic ability in the play off. It may help them to win mnemonic gfames, but it will not improve their whist playing-; in fact, experience has proven that players who cultivate their memories for this style of g-ame become firm believers in "shots" and irreg-ular plays, and when they come to take part in a team-of-four or prog-ressive pair g-ame, in which the faculty they have so assiduously cultivated is of absolutely no use, they find themselves at considerable disadvantage. 40 Mitchell's duplicate whist. INDIVIDUAL SCHEDULES. The following paper is from the pen of Mr. W. H. Whitfeld, of Cambridg-e, England, who needs no introduction to the whist players of America. His biography appeared in "Whist" of February, 1894, and many double dummy whist problems and other contributions by him have adorned the pages of that journal both before and since that date: Some eighteen months ago the problem of the arrangement of whist players for a tournament was brought to my notice by Mr. Schwarz and Mr. Mitchell. Since I have had no experience in dupli- cate whist, and have never entered for any form of whist tournament, 1 was little concerned with the question considered practically ; to me it was only an interesting mathematical puzzle. It is from this point of view that I will make some remarks on the question, explain- ing briefly how a solution was arrived at for the different cases. In all the methods of arrangement (except that for 48 players) the main principle is the same. The arrangement for successive days is formed from that for the first day by the players moving in cyclical order. No. I's seat on the first day will be occupied by No. 2 on the second day ; No. 2's seat will be occupied by No. 3 ; No. 3's seat will be occupied by No. 4, and so on. One player alone remains in the same seat, which he retains throughout the tournament. This player I have denoted by the highest number. No. 36 in the case of 36 players ; this makes the solutions appear neater than making him No. I. The arrangement for the third day is formed from the second in a similar manner. When the members reach the top they begin again with No. i ; e. g., in the case of 36 players, No. 35 being succeeded by No. i. INDIVIDUAL SCHEDUr,E. 41 How it is ensured that all the required conditions are fulfilled is best shown by taking an example. I will take the case, of 36 players the solution of which is one of the most symmetrical. At the first table on the first day the two players, Nos. i and 34, are in partnership ; these two numbers differ by 33. On the second day their seats will be occupied by Nos. 2 and 35, which also differ by 33. On the third day their seats will be occupied by Nos. 3 and i, which differ by 2 (= 35 — 33I. During the tournament all numbers that differ by 2 or by the complementary number 33 will come into partnership in the places of Nos. i and 34 at the first table. Similarly all the numbers which differ by 4 or by its complementary number, 31, will come into partnership in the places of Nos. 2 and 33 at the next table. At the nine tables there are eighteen partnerships, 17 of which, it should be noted, are represented in the difference of the numbers of each pair of partners by the numbers 1-17 (or their complements), each occurring once only, the iSth partnership being that of the fixed player with each of the other players in turn. It is thus seen that during the 35 days each player will play once, and only once, with every other player as partner. In the same way, if we examine the cases of opposition, we shall find that the differences of the numbers belonging to players which are opposed to each other are represented by the numbers 1-17 (or their complements), each occurring twice. Thus it is ensured that in the course of the tournament any two given players will twice be opposed to each other. It will be noticed that in the solution for the case of 36 players there is a good deal of symmetry. No. i plays with his complement- ary number, No. 34. Their adversaries are found by doubling these numbers respectively, subtracting 35 when the number exceeds 35. Doubling these numbers again we get the first pair of partners at the second table. Doubling again we obtain their adversaries, and so on for six of the tables. The reason why a symmetrical arrange- ment is possible, satisfying the conditions, can be briefly sketched. If we take a number less than 35 and prime to it, and continually double it (in fact, instead of doubling, we might multiply it by any 42 Mitchell's duplicate whist. number prime to 35), subtracting 35 when the result exceeds 35, we get a series of numbers which, after a certain time, will repeat itself ; thus, for instance, we can obtain the series of 12, numbers i, 2, 4, 8, 16, 32, 29, 23, II, 22, 9, 18. Similarly, the 12 numbers, 3, 6, 12, 24, 13, 26, 17, 34, 33, 31, 27, 19, form a recurring series. These two series include all the numbers less than 35, except the multiples of 5 and 7. It may be remarked that the numbers of one series are complementary to the numbers of the other series. If, instead of 2, we had multiplied by 4, we should have obtained four series, each composed of six numbers. In general, however we proceed, we shall find the same number of term in each series. Now if we form one table of four numbers and multiply contin- ually each number of it by some multiplier so as to form successive tables, not only do the numbers occur in a definite series, but also the difference of any two numbers will occur in a definite order, since, when we multiply two numbers by a certain multiplier, the difference of the two numbers will also be multiplied by the same multiplier. The problem, therefore, reduces to one of choosing our initial table so that the four series of numbers derived from each of the numbers denoting the players may not overlap, and likewise that the series of numbers denoting the differences of partners and opponents may not clash. We avoid two derived numbers clashing by seeing that the initial numbers belong to different series, or that they belong to different parts of the same series, or, in some cases, we can manage it by making one an odd and the other an even term of the same series. In most cases in which the number of days is not a prime number this gives little trouble. To return to the case of 36 players, after we have arranged the tables for those numbers that compose our two series, there remain the multiples of 5 and 7. The multiples of 7, excluding 35 itself, make up a table by themselves, the differences of the numbers being, of course, also multiples of 7. The multiples of 5, together with 35 and the fixed number, 36, can without much difficulty be arranged into two tables, the work bemg just the same as arranging a tournament for eight players, 1-8, and then multiplying the numbers of all the movable players by 5. INDIVIDUAL SCHEDULE. 43 A similar method of solution can be applied to nearly all ques- tions in which we do not obtain a prime number by subtracting unity from the number of players ; but in other cases, except in the case of 12, it cannot be applied. The difficulty is that a table has to be formed consisting of the fixed number (36 in the above case), the highest of the movable numbers (35 itself, which belongs to no series), and two other numbers. Unless there are some numbers which, not being prime to the highest number do not belong to the ordinary series, we have to take two numbers from the series to make up our tables. This makes a discontinuity in our series which cannot, in most cases, be surmounted. In these cases there is no short road to success. To show the more tedious method that had to be employed, I will take the first problem that I attempted, that for 20 players. The difference of any two of the numbers 1-19 may be any of the numbers 1-9, or their complements, that is their defect from ig. My first task was to arrange the 27 quantities formed by taking the numbers 1-9 each three times over into four sets of six each and one set of three ; each set of six must be so related to each other as to be capable of representing the differences at one table, e. g., z, 3, 7, 8, 5, 10, would be such a set, and would represent the differences at the table formed of the numbers i, 4, 9, 11 ; the set of three is to represent the differences of the three players who play at the same table with the fixed player. Having arranged our sets, our next step is to decide which numbers in each set are to be the difference of partners. At each table there are three ways of arranging partners. Thus, at the table I, 4, 9, II, the partnerships can be represented by any of the three pairs of numbers 3, 2 or 8, 7 or 5, 10. At the five tables we have to arrange the partners so that differences in their numbers shall be represented by the nine numbers 1-9, each occurring once. In most cases it will be found that this is impossible. We must then proceed to arrange our sets differently until we find an arrangement with which it is possible. 44 Mitchell's duplicate whist. After this the labor comes. When we have determined the form of each table in terms of the differences of the numbers, it is like a Chinese puzzle fitting them to the numbers. When i, 4, 9, 11, does not fit in, we try 2, 5, 10, 12, which is the same table moved on a step ; then we move it a step more, afterwards reversing it so that it becomes i, 3, 8, 11, the differences occurring in reverse order. When we have 6tted that table in, we proceed to fit the next in if we can. When we fail, we have to alter the previous arrangement of tables again. When we succeed, we must proceed to fit in another table until (as is generally the final result) we have determined that there is no possible way of arranging the tables, and we have to recom- mence the problem absolutely from the beginning. A great number of failures were experienced and the problem took a long time working out. The cases of 8, 12 and i5 players are very simple and present no difficulty whatever ; solutions have been worked out independently by a large number of people. The method described above was applied by myself to the cases of 20, 24 and 28 players. The question of 32 players, since it had already been solved before my attention was called to the subject, I did not attempt. I do not know by what method it was arrived at. I should have thought it probably quite as hard as the three cases, 20, 24, 28. Neat solutions, more or less regular, are possible for 36, 40, 52, 56, 64, 100, and, probably, also for 76, 88, 92, 96, &c. A tournament for 48 players can be arranged by a method due to Professor Moore, by which if a solution can be found for a given number of players, a solution can be found for a number four times as great. With other numbers, the difficulty of solution would probably be so great, and the practical value so small, that it is not worth while attempting to find an arrangement. I enclose a system of working a tournament so that each pair may play against every other pair. I only send the scheme for 4, 6, 7, 8, 9 and 10 tables. (See page 67.) It is quite easy to make up similar schemes for 12, 15 or 16 tables (in fact, whenever the number INDIVIDUAL SCHEDULE. 45 of hands to be played is a prime number) In the case of 5 tables a scheme of the kind is impossible. An explanation of the system for the case of four tables follows ; The movement of the players is the same as usual — E. & W. move one way, N. & S. the other, till they get to the end. At one of the ends one pair sits fixed and immovable. When they get to the end the players change their points of the compass, N. & S. becoming E. & W., or vice versa. Seven deals have to he played at the four tables, consequently some of the trays are unused part of the time. At the first table No. i deal is played first; No. i deal is then passed to the 4th table. No. 4 deal is received from the 3d table, but it is not played at once; it is placed under trays 2 and 3, the 2d deal being played. The deals are played in consecutive order at each table, and from this reason errors can soon be discovered by the man in charge, who ought to check off the deal being played at each table after each change. If left to themselves entirely the players would confuse the hands, since all the players except one pair change tables. In ordinary progressive pairs the N. cS: S. pair remaining throughout at one table keep things right, since they know what deal comes next, which table it comes from, etc. W. H. Whitfeld. Formulas for 8, 12 and 16 were published in "Whist" of January, 1892, by Mr. A. G. Saflford, of Washing-ton, D. C, who was the first in the field with solutions of problems of this nature, but until Mr. W. H. Whitfeld came to the rescue in 1895, I was unable to obtain a formula for any number higher than 16, with the exception of 32. The latter I obtained in the following- manner. Mr. Safford had told me that if I numbered the players from 1 up, placing- 1 & 2 vs. 3 & 4, 5 & 6 vs. 7 & 8, 9 & 10 vs. 11 & 12, etc., at successive tables for the first game, and 46 MITCHELL'S DUPLICATE WHIST. for the second game placed them in numerical order down the north seats at the successive tables, back along- the south seats, down again along the east or west seats and back again to the first table along the west or east seats, and make the players take a similar course after every change, that I could work out a formula. I went to work on the idea, but after countless experiments, found that it would only work for 8, 16 and 32, and it is because I found it to work for 32 that Mr. Whitfeld has not given us a solution for this number. I will try to explain how I got the formula from Mr. Safford's instructions. For the opening game the players sit as follows : Table i. Table 2. Table 3- Table 4. Table 5. Table 6. Table 7- N, S. E.W. N. s. K. W. N. S. E. W N. S E. W. N. S. E. W. N, S E. W, N. S. a.. W. I- 2- 3- 41 5- 6- 7- 8 g-io-Lr-12 13-14-15-16 I7-I8-I9-20 21-22-23-24 25-26-27-28 For the second game they sit: 1-16-17-321 2-15-18-311 3-14-19-301 4-13-20-29] 5-12-21-281 6-11-22-271 7-10-23-26J 8- 9-24-25 Now if we take these numbers and make them follow the same course as the original numbers did, placing 1, 16, 17, 82, 2, 16, 18, 31 in the successive north seats, 3, 14, 19, 30, 4, 13, 20, 29 back along the south seats, 5, 12, 21, 28, 6, 11, 22, 27 down along the east seats and 7, 10, 23, 26, 8, 9, 24," 25 back along the west seats, and keep on moving the players in that order thirty-one times, we will find that the figures follow each other in the following order : I- 2-l6-29| 8-31-24-27123-22-11-19121- 6-15-20128-26-10-14113- 4-32-25] 7-18-12-30] 9- 3-17- 5 INDIVIDUAL SCHEDULE. 47 Now we want a formula in which the figures will run in rotation, and in order to bring' this about we substitute the next number for the numbers we find in the respective positions. That is, we put 3 in the 16th position, 4 in the 29th, 5 in the 8th, 6 in the 31st, 7 in the 24th, 8 in the 27th, 9 in the 23rd, 10 in the 22nd, 11 in the 11th, 12 in the 19th, 13 in the 21st, 14 in the 6th, 15 in the 15th, 16 in the 20th, 17 in the 28th, 18 in the 26th, 19 in the 10th, 20 in the 14th, 21 in the 13th, 22 in the 4th, 23 in the 32nd, 24 in the 25th, 25 in the 7th, 26 in the 18th, 27 in the 12th, 28 in the 30th, 29 in the 9th, 30 in the 3rd, 31 in the 17th and 32 in the 5th and our task is accomplished. I- 2-30-22I32-14-25- 5129-19-11-27121-20-15- 3|3l-26-i2-l6|l3-l0- 9- 7124-18- 8-17J 4-28- 6-23 48 Mitchell's duplicate whist. SCHEDULE FOR EIGHT PLAYERS. Once >A^ith and Tv^rice Against. IME. TABLE I. TABLE 2. N. S. E w. N. S. E. w I 2 7 3 8 6 5 4 2 3 8 4 2 7 6 5 3 4 2 5 3 8 7 6 4 5 3 6 4 2 8 7 5 6 4 7 5 3 2 8 6 7 5 8 6 4 3 2 7 8 6 2 7 5 4 3 SCHEDULE FOR TWELVE PLAYERS. Once With and Twice Against. IME. TABLE I TABLE 2 TABLE 3. N S. E. w. N. S. E. w. N. s. li. w. I ( 2 12 5 8 6 10 II 9 3 4 7 2 t 3 2 6 9 7 II 12 10 4 5 8 3 I 4 3 7 10 8 12 2 II 5 6 9 4 I 5 4 8 II 9 2 3 12 6 7 10 5 [ 6 5 9 12 lO 3 4 i 7 8 II 6 [ 7 6 lO 2 II 4 5 3 8 9 12 7 t a 7 II 3 12 5 6 4 9 10 2 8 ] 9 8 12 4 2 6 7 5 ID II 3 9 1 lO 9 2 5 3 7 8 6 II 12 4 10 [ II 10 3 6 4 8 9 7 12 2 5 II [ 12 II 4 7 5 9 10 8 2 3 6 INDIVIDUAL SCHEDULE. 49 SCHEDULE FOR SIXTEEN PLAYERS. Once ^Vith and Twice Against. iME. TABLE : TABLE 2. TABLE 3 TABLE . 4- N S. E. w. N. s. E. w. N s. E. W. N. s. E. w. I 2 II 9 i6 5 6 3 lO 4 14 13 8 15 7 12 2 3 12 10 2 6 7 4 II 5 15 14 9 16 8 13 3 4 13 II 3 7 8 5 12 6 16 15 10 2 9 14 4 5 14 12 4 8 9 6 13 7 2 16 II 3 10 15 5 6 15 13 5 9 10 7 14 8 3 2 12 4 II 16 6 7 i6 14 6 10 II 8 15 9 4 3 13 5 12 2 7 8 2 15 7 II 12 9 i6 ID 5 4 14 6 13 3 8 9 3 i6 8 12 13 lO 2 II 6 5 15 7 14 4 9 10 4 2 9 13 14 II 3 12 7 6 16 8 15 5 lO II 5 3 lO 14 15 12 4 13 8 7 2 9 16 6 II 12 6 4 II 15 i6 13 5 14 9 8 3 10 2 7 12 13 7 5 12 i6 2 M 6 15 10 9 4 II 3 8 13 14 8 6 13 2 3 15 7 i6 II 10 5 12 4 9 14 15 9 7 14 3 4 i6 8 2 12 II 6 13 5 10 15 i6 10 8 '5 4 5 2 9 3 13 12 7 14 6 II 50 Mitchell's duplicate whist. ro Tj- in \D t>. MMHHMWMHMHM MMHMHWHMIHMM t^oo CiO « mTf-mvo r--.co C7*o h n mThinio MMWN HMHHMHH • m\o ^-.00 c\0 w N m"T^ln^o r-voo o\0 m m-^ ^?= MMWHMMMMMM« ^ ^, ^;O«^^Tl-ln^O^-.0OO^OlHN^o^ln^DC*.00O^ « WW« MMMMMMHHMH ^ 2"coC\OMm'^in\oc-*Q0O\O'-iNfnTru-i\ot^ ^ MMN MWMMMMMIH H "■ MJHh-iMMMHWHlN M "d- in ^D i>. 00 _. _ < nS ^ H U H CO < tfl O £ Eb ^ K:cH-)■^ln'Cr^00O^O«m'^^n^O^-00O^ S .Sm'-'-'-'-''-'-'" " M l-l ^^^'j''Jl_l(M i_iui_IUl_l>_ll-ll_lbJ o W -■r)MCMm-.COCTvONrn-^in\Dt^00O\ W" HMMMMMMMHMM <■ MMMM'MMHHMMM g MNro'^iniot-^ooo\owNm'^invor^oocri o INDIVIDUAL SCHEDULE. 51 ^ MMMHWMMHHMNNNNN w w m ,-: t^oo O^O >-" N n-i'^N ro^ »n«0 r>.CO Gi O w N m >*• »r)>0 ^ Tj- N ro ■^ in\D r^oo o\ O M N PO n- in\o t-^00 o\ o M « ro i/i IN M '-' ■^ M M )H M M JH M W N N IN M O M IN m ■* ino t^OO Oi o IH IN fO '^ N PO Tt- u-iio i>.oo cn M M M M H H M M M W o N N N N CO n w ini£) j>.oo Cl O M IN fO ■^ »n>£> t>-CO O^ O M N ro -^ M ro Tf Oi < M M w M IH M M M M H N IN N N N < 0. s t^oo 0^ O M M rn ■"^ loyD t>00 C^l o H N ro -^ M ro Tt- u-no M H IH M M M IH M M M « N N IN W ^ vO t^co d o M N ro TT u~lvO ^»oo Oi O 1- (N fO T(- M PO -"f u-i ^ HI M M M H M M M IH M N N IN N « Oi ^ » H M m Ti- mvo I>.00 O O H N PO Tl- IN ro -^ ino C^OO a> o M n ffl < M W M W )H M M (N N N w w M M D O '3 ■^ "TO r>.oo a> o M N ro -^ N ^ rf m\0 ^sco 0^ O H M ro u i-i H M M M "H N N N N M H H H IH li. < 2 W rO -^ w rO ■^ lO'O I>.00 Oi O 1-1 N ro -^ irnO t^OO 0\ O M >< u IN N N w M M M M H M iH M M M h i z H S^ M N m Tt- u-no l>.CO a o M N m ■^ IN ro "^ iO\D I>.00 0> O u •o ro H M M M *-• M M •-• M f) N N (S N M ^ B CO B bj \o c^oo o^ O H N ro Tl- w m '^ m\D t>. O IH IN ro -^ uo I-I H M N ca N N N M H M W M H Si J m tn O M N m ■^ w rn Tl- ITHO J>.00 c^ M M ro -^ invo rs.00 o\ o 41 < M M N N N "H M H M M IH M M M M 2: IN ^ N N m ■^ iTHO t^CO Gi O M M N M H H M IH W M O H (S N W M (b S u .J ^ O O H N m Tj- lO'O t^OO o\ N ro Ti- N ro ■"^ io\o c^oo M M M M M N C^ N N N a pi w m ■- £ ■«3 H M M M M w H M '-' N N N N M o 03 zi IH N ro ■^ N m -r mo t^co o\ O l_l M ro "^ m\o r^oo o^ o M IN N IN M IH M »H M W IH M M w N N ro ■^ iO>0 t^OO 52 Mitchell's duplicate whist. schedule for twenty-eight players. Once With and Twice Against. GAME. TABLE I TABLE 2. TABLE 3. TABLE 4. «, &. J£^. w. N. b. E. W. N. ». t. w. «, a. t. w. I 2 24 25 18 7 17 10 19 22 21 II 16 3 5 9 2 3 25 26 19 8 18 II 20 23 22 12 17 4 6 10 3 4 26 27 20 9 19 12 21 24 23 13 18 5 7 II 4 5 27 28 21 10 20 13 22 25 24 14 19 6 8 12 5 6 28 2 22 II 21 14 23 26 25 15 20 7 9 13 6 7 2 3 23 12 22 15 24 27 26 16 21 8 10 14 7 8 3 4 24 13 23 16 25 28 27 17 22 9 II 15 8 9 4 5 25 14 24 17 26 2 28 18 23 10 12 16 9 10 5 6 26 15 25 18 27 3 2 19 24 II 13 17 lO II 6 7 27 16 26 ig 28 4 3 20 25 12 14 18 II 12 7 8 28 17 27 20 2 5 4 21 26 13 15 19 12 13 8 9 2 18 28 21 3 6 5 22 27 14 16 20 13 14 9 lO 3 19 2 22 4 7 6 23 28 15 17 21 14 15 lO II 4 20 3 23 5 8 7 24 2 16 18 22 15 i6 II 12 5 21 4 24 6 9 8 25 3 17 19 23 i6 17 12 13 6 22 5 25 7 10 9 26 4 18 20 24 17 i8 13 14 7 23 6 26 8 II 10 27 5 19 21 25 i8 19 M 15 8 24 7 27 9 12 II 28 6 20 22 26 19 20 15 16 9 25 8 28 10 13 12 2 7 21 23 27 20 21 i6 17 10 26 9 2 II 14 13 3 8 22 24 28 21 22 17 18 II 27 10 3 12 15 14 4 9 23 25 2 22 23 i8 19 12 28 II 4 13 16 15 5 10 24 26 3 23 24 19 20 13 2 12 5 14 17 16 6 II 25 27 4 24 25 20 21 14 3 13 6 15 18 17 7 12 26 28 5 25 26 21 22 15 4 14 7 16 19 18 8 13 27 2 6 26 27 22 23 16 5 15 8 17 20 19 9 14 28 3 7 27 28 23 24 17 6 16 9 18 21 20 10 15 2 4 8 INDIVIDUAL SCHEDULE. 53 SCHEDULE FOR TWENTY-EIGHT PLAYERS— Continued. TABLE 5. TABLE 6. TABLE 7. GAME N. S. K. \V. M. &. 1:,. w. „. &. e. w. 15 20 27 6 23 4 28 13 26 8 M 12 I 16 21 28 7 24 5 2 14 27 9 15 13 2 17 22 2 8 25 6 3 15 28 10 16 14 3 18 23 3 9 26 7 4 16 2 II 17 15 4 ig 24 4 10 27 8 5 17 3 12 18 16 5 20 25 5 II 28 9 6 18 4 13 19 17 6 21 26 6 12 2 10 7 19 5 14 20 18 7 22 27 7 13 3 11 8 20 6 15 21 19 8 23 28 8 14 4 12 9 21 7 16 22 20 9 24 ■>■ 9 15 5 13 10 22 8 17 23 21 10 25 3 10 16 6 14 II 23 9 18 24 22 II 26 4 II 17 7 15 12 24 10 19 25 23 12 27 5 12 18 8 16 13 25 II 20 26 24 13 28 6 13 ig 9 17 14 26 12 21 27 25 14 2 7 14 20 10 18 15 27 13 22 28 26 15 3 8 15 21 II 19 16 28 14 23 2 27 16 4 9 16 22 12 20 17 2 15 24 3 28 17 5 10 17 23 13 21 18 3 16 25 4 2 18 6 II 18 24 14 22 19 4 1:7 26 5 3 19 7 12 ig 25 15 23 20 5 18 27 6 + 20 8 13 20 26 16 24 21 6 19 28 7 5 21 9 14 21 27 17 25 22 7 20 2 8 6 22 10 15 22 28 18 26 23 8 21 3 9 7 23 II 16 23 2 19 27 24 9 22 4 10 8 24 12 17 24 3 20 28 25 10 23 5 II 9 25 13 18 25 4 21 2 26 II 24 6 12 10 26 14 19 26 5 22 3 27 12 25 7 13 II 27 54 Mitchell's duplicate whist. schedule for thirty-two players. Once With and Twice Ag^ainst. AME. TABLE I. TABLE 2. TABLE 3. TABLE 4. N. S. E. W. N. S. E. W. N S E. W. N. S. E. W, I I 2 30 22 32 14 25 5 29 19 II 27 21 20 15 3 2 I 3 31 23 2 ig 26 6 30 20 12 28 .22 21 16 4 3 I 4 32 24" 3 16 27 7 31 21 13 29 23 22 17 5 4 c 5 2 25 4 17 28 8 32 22 14 30 24 23 18 6 5 I 6 3 26 5 18 29 9 2 23 15 31 25 24 19 7 6 I 7 4 27 6 19 30 10 3 24 16 32 26 25 20 8 7 I 8 5 28 7 20 31 II 4 25 J7 2 27 26 21 9 8 I 9 6 29 8 21 32 12 5 26 18 3 28 27 22 10 9 I 10 7 30 9 22 2 13 6 27 19 4 29 28 23 II 10 I II 8 31 10 23 3 14 7 28 20 5 30 29 24 12 II I 12 9 32 II 24 4 15 8 29 21 6 31 30 25 13 12 I 13 10 2 12 25 5 16 9 30 22 7 32 31 26 14 13 I 14 II 3 13 26 6 17 10 31 23 8 2 32 27 15 14 I 15 12 4 14 27 7 18 II 32 24 9 3 2 28 16 IS I 16 13 5 15 28 8 19 12 2 25 10 4 3 29 17 i6 I 17 14 6 16 29 9 20 13 3 26 II 5 4 30 18 17 I 18 15 7 17 30 10 21 14 4 27 12 6 5 31 19 i8 I 19 16 8 18 31 II 22 15 5 28 13 7 6 32 20 19 I 20 17 9 19 32 12 23 16 6 29 14 8 7 2 21 20 I 21 18 10 20 2 13 24 17 7 30 15 9 8 3 22 21 I 22 19 II 21 3 14 25 18 8 31 16 10 9 4 23 22 I 23 20 12 22 4 15 26 19 9 32 17 II 10 5 24 23 I 24 21 13 23 5 16 27 20 10 2 18 12 II 6 25 24 I 25 22 14 24 6 17 28 21 II 3 ig 13 12 7 26 25 I 26 23 15 25 7 18 29 22 12 4 20 14 13 8 27 26 I 27 24 16 26 8 19 30 23 13 5 21 15 14 9 28 27 I 28 25 17 27 9 20 31 24 14 6 22 16 15 10 29 28 I 29 26 iS 28 10 21 32 25 15 7 23 17 16 II 30 29 I 30 27 19 29 II 22 2 26 16 8 24 18 17 12 31 3° I 31 28 20 30 12 23 3 27 17 9 25 19 i8 13 32 31 I 32 29 21 31 13 24 4 28 18 10 26 20 19 14 2 INDIVIDUAL SCHEDULE. 55 SCHEDULE FOR THIRTY-TWO PLAYERS.— Continued. TABLE 5. TABLE 6. TABLE 7. TABLE 8. GAME N. S. E. W. N. S. E. W. N. S. E. W. N. S. E. w. 31 26 12 16 13 10 9 7 24 18 8 17 4 28 6 23 I 32 27 13 17 14 II 10 8 25 19 9 18 5 29 7 24 2 2 28 14 18 15 12 II 9 26 20 10 19 6 30 8 25 3 3 29 15 19 16 13 12 10 27 21 II 20 7 31 9 26 4 4 30 16 20 17 14 13 II 2S 22 12 21 8 32 10 27 5 5 31 17 21 18 15 14 12 29 23 13 22 9 2 II 28 6 6 32 18 22 19 16 13 13 30 24 14 23 10 3 12 29 7 7 2 19 23 20 17 16 14 31 25 15 24 11 4 13 30 8 8 3 20 24 21 18 17 15 32 26 16 25 12 5 14 31 9 9 4 21 25 22 19 18 16 2 27 17 26 13 6 15 32 10 10 5 22 26 23 20 19 17 3 28 18 27 14 7 16 2 II II 6 23 27 24 21 20 18 4 29 ig 28 15 8 17 3 12 12 7 24 28 25 22 21 19 5 30 20 29 16 9 18 4 13 13 8 25 29 26 23 22 20 6 31 21 30 17 10 19 5 14 14 9 26 30 27 24 23 21 7 32 22 31 18 II 20 6 15 15 10 27 31 28 25 24 22 8 2 23 32 19 12 21 7 16 16 II 28 32 29 26 25 23 9 3 24 2 20 13 22 8 17 17 12 29 2 30 27 26 24 10 4 25 3 21 14 23 9 18 18 13 30 3 31 28 27 25 II 5 26 4 22 15 24 10 19 19 14 31 4 32 29 28 26 12 6 27 5 23 16 25 II 20 20 15 32 5 2 30 29 27 13 7 28 6 24 17 26 12 21 21 16 2 6 3 31 30 28 14 8 29 7 25 18 27 13 22 22 17 3 7 4 32 31 29 15 9 30 8 26 19 28 14 23 23 18 4 8 5 2 32 30 16 10 31 9 27 20 29 15 24 24 19 5 9 6 3 2 31 17 II 32 10 28 21 30 16 25 25 20 6 10 7 4 3 32 18 12 2 II 29 22 31 17 26 26 21 7 II 8 S 4 2 19 13 3 12 30 23 32 18 27 27 22 8 12 9 6 5 3 20 14 4 13 31 24 2 19 28 28 23 9 13 10 7 6 4 21 15 5 i4 32 25 3 20 29 29 24 10 14 II 8 7 5 22 16 6 15 2 26 4 21 30 30 25 II 15 12 9 8 6 23 17 7-16 3 27 5 22 31 56 Mitchell's duplicate whist. schedule for thirty-six players. Once With and Twice Against. GAME. TABLE I. TABLE 2. TABLE 3. TABLE 4- TABLE 5. K. 3. E. W. rl, S. E. W. H. S. E. W. N. S. E. w. N, S. E. W. 1 I 2 32 12 7 17 27 22 613 34 20 10 9 36 18 14 5 3 16 2 I 3 33 13 8 18 28 23 7 14 35 21 II 10 2 19 15 6 4 17 3 I 4 34 14 9 19 29 24 8 15 36 22 12 11 3 20 16 7 5 18 ♦ I 5 35 15 10 20 30 25 9 16 2 23 13 12 4 21 17 8 6 19 5 1 6 36 i6 11 21 31 26 10 ly 3 24 14 13 5 22 18 g 7 20 6 I 7 2 17 12 22 32 27 II 18 4 25 15 14 6 23 19 10 8 21 7 I 8 3 18 13 23 33 28 12 19 5 26 16 15 7 24 20 II g 22 S 1 9 4 19 14 24 34 29 13 20 6 27 17 16 8 25 21 12 10 23 9 I 10 5 20 15 25 35 30 14 21 728 18 17 9 26 22 13 II 24 10 I II 6 21 16 26 36 31 15 22 8 29 19 18 10 27 23 14 12 25 11 i 12 7 22 17 27 2 32 16 23 9 30 20 19 II 28 24 15 13 26 12 I 13 8 23 18 28 3 33 17 24 10 31 21 20 12 29 25 16 14 27 13 I 14 9 24 19 29 4 34 18 25 II 32 22 21 13 30 26 17 15 28 H I 15 10 25 20 30 5 35 ig 26 12 33 23 22 14 31 27 18 16 29 15 1 16 II 26 21 31 6 36 20 27 13 34 24 23 15 32 28 ig 17 30 i6 I 17 12 27 22 32 7 2 21 28 14 35 25 24 16 33 29 20 18 31 17 1 18 13 28 23 33 8 3 22 29 15 36 26 25 17 34 30 21 ig 32 l8 1 ig 14 29 24 34 9 4 23 30 16 2 27 26 18 35 31 22 20 33 19 1 20 15 30 25 35 10 5 24 31 17 3 28 27 19 36 32 23 21 34 20 I 21 16 31 26 36 II 6 25 32 IS 4 29 28 20 2 33 24 22 35 21 I 22 17 32 27 2 12 7 26 33 19 5 30 2g 21 3 34 25 23 36 22 I 23 18 33 28 3 13 8 27 34 20 6 31 30 22 4 35 26 24 2 23 I 24 19 34 29 4 14 9 2835 21 7 32 31 23 5 36 27 25 3 24 I 25 20 35 30 5 15 10 29 36 22 8 33 32 24 6 2 28 26 4 25 I 26 21 36 31 6 16 II 30 2 23 9 34 33 25 7 3 29 27 5 26 I 27 22 2 32 7 17 12 31 3 24 10 35 34 26 8 4 30 28 6 27 I 28 23 3 33 8 18 13 32 4 25 II 36 35 27 9 5 31 29 7 28 I 29 24 4 34 9 19 14 33 5 26 12 2 36 28 10 6 32 30 8 29 I 30 25 5 35 10 20 15 34 6 27 13 3 2 29 II 7 33 31 9 30 I 31 26 6 36 11 21 16 35 7 28 14 4 3 30 12 8 34 32 10 31 I 32 27 7 2 12 22 17 36 8 29 15 5 4 31 13 g 35 33 II 32 I 33 28 8 3 13 23 18 2 9 30 16 6 5 32 14 10 36 34 12 33 I 34 29 9 4 14 24 ig 3 10 31 17 7 6 33 15 II 2 35 13 34 I 35 30 10 5 15 25 20 4 II 32 18 8 7 34 16 12 3 36 14 35 I 36 31 11 6 16 26 21 5 12 33 19 9 8 35 17 13 4 2 15 INDIVIDUAL SCHEDULE. 57 SCHEDULE FOR THIRTY-SIX PLAYERS— Continued. TABLE 6. TABLE 7. TABLE 8. TABLE 9. GAM I w. s. ^. w. n. E>. £.. w. «. a. n. W. N. a. K. W. 15 4 21 33 24 30 8 II 35 19 31 23 29 25 28 26 I l5 5 22 34 25 31 9 12 36 20 32 24 30 26 29 27 2 17 6 23 35 26 32 10 13 2 21 33 25 31 27 30 28 3 18 7 24 36 27 33 II 14 3 22 34 26 32 28 31 29 4 19 8 25 2 28 34 12 15 4 23 35 27 33 29 32 30 5 20 9 26 3 29 35 13 16 5 24 3f 28 34 30 33 31 6 21 10 27 4 30 36 14 17 6 25 2 29 35 31 34 32 7 22 II 28 5 31 2 15 18 7 26 3 30 36 32 35 33 8 23 12 29 6 32 3 16 19 8 27 4 31 2 33 36 34 9 24 13 30 7 33 t 17 20 9 28 5 32 3 34 2 35 10 25 14 31 8 34 5 18 21 10 29 6 33 4 35 3 36 11 26 15 32 9 35 6 19 22 II 30 7 34 5 36 4 2 12 27 16 33 10 36 7 20 23 12 31 8 35 6 2 5 3 13 28 17 34 II 2 8 21 24 13 .32 9 36 7 3 6 4 14 29 18 35 12 3 9 22 25 14 33 10 2 8 4 7 5 15 30 19 36 '3 4 10 23 26 15 34 II 3 9 5 8 6 16 31 20 2 14 5 II 24 27 16 35 12 4 10 6 9 7 17 32 21 3 15 6 12 25 28 17 36 13 5 II 7 10 8 18 33 22 4 16 7 13 26 29 18 2 14 6 12 8 II 9 19 34 23 5 17 8 14 27 30 19 3 15 7 13 9 12 10 20 35 24 6 18 9 15 28 31 20 4 16 8 14 10 13 II 21 36 25 7 19 10 16 29 32 21 5 17 9 15 II 14 12 22 2 26 8 20 II 17 30 33 22 6 18 10 16 12 15 13 23 3 27 9 21 12 18 31 34 23 7 tf II 17 13 16 14 24 4 28 10 22 13 19 32 35 24 8 20 12 18 14 17 15 25 5 29 II 23 14 20 33 36 25 9 21 13 19 15 18 16 26 6 30 12 24 15 21 34 2 26 10 22 14 20 16 19 17 27 7 31 13 25 16 22 35 3 27 II 23 15 21 17 20 18 28 8 32 14 26 17 23 36 4 28 12 24 16 22 18 21 19 29 9 33 ,'5 27 18 24 2 5 29 13 25 17 23 19 22 20 30 10^ 3(f -16 28 19 25 3 6 30 14 26 18 24 20 23 21 31 II 35) 17 29 20 26 4 7 31 15 27 19 25 21 24 22 32 12 38 18 30 21 27 5 8 32 16 28 20 26 22 25 23 33 13 2 19 31 22 28 6 9 33 17 29 21 27 23 26 24 34 14 3 20 32 23 29 7 10 34 18 30 22 28 24 27 25 35 68 Mitchell's duplicate whist. SCHEDULE FOR FORTY PLAYERS. Once With and Twice Against 3AME. TABLE I, TABLE 2. TABLE 3. TABLE 4. TABLE 5. N. S. E. W. rl. s. n. W. n, a, n. W. r.. s. E. W. N. S. E. W. I I 2 15 28 18 12 4 13 10 7 3 27 6 24 22 34 < 20 21 23 9 2 I 3 16 29 19 13 5 14 II 8 4 28 7 25 23 35 21 22 24 ID 3 I 4 17 30 20 14 6 15 12 9 5 29 8 26 24 36 22 23 25 II ♦ I 5 18 31 21 15 7 16 13 10 6 30 9 27 25 37 23 24 26 12 5 I 6 19 32 22 l6 8 17 14 II 7 31 ID 28 26 38 24 25 27 13 6 I 7 20 33 23 17 9 18 15 12 8 32 II 29 27 39 25 26 28 14 7 I 8 21 34 24 18 10 19 16 13 9 33 12 30 28 40 26 27 29 15 8 I 9 22 35 25 19 II 20 17 14 10 34 13 31 29 2 27 28 30 16 9 I 10 23 36 26 20 12 21 18 15 II 35 14 32 30 3 28 29 31 17 10 I II 24 37 27 21 13 22 19 16 12 36 15 33 31 4 29 30 32 18 II I 12 25 38 28 22 14 23 20 17 13 37 16 34 32 5 39 31 33 19 12 I 13 26 39 29 23 15 24 21 18 14 38 17 35 33 6 31 32 34 20 13 I 14 27 40 30 24 16 25 22 19 15 39 18 36 34 7 32 33 35 21 14 I 15 28 2 31 25 17 26 23 20 16 40 19 37 35 8 33 34 36 22 15 I l6 29 3 32 26 18 27 24 21 17 2 20 38 36 9 34 35 37 23 l6 1 17 30 4 33 27 19 28 25 22 18 3 21 39 37 10 35 36 38 24 17 I i8 31 5 34 28 20 29 26 23 19 4 22 40 38 II 36 37 39 25 i8 I ig 32 6 35 29 21 30 27 24 20 5 23 2 39 12 37 38 40 2(5 19 I 20 33 7 36 30 22 31 28 25 21 6 24 3 40 13 38 39 2 27 20 I 21 34 8 37 31 23 32 29 26 22 7 25 4 2 14 39 40 3 28 21 1 22 35 9 38 32 24 33 30 27 23 8 26 5 3 15 40 2 4 29 22 I 23 36 10 39 33 25 34 31 28 24 9 27 6 4 16 2 3 5 30 23 1 24 37 " 40 34 26 35 32 29 25 10 28 7 5 17 3 4 6 3! 24 I 25 38 12 2 35 27 36 33 30 26 II 29 8 6 18 4 5 7 32 25 I 26 39 13 3 36 28 37 34 31 27 12 30 9 7 19 5 6 833 26 I 27 40 14 4 37 29 38 35 32 28 13 31 10 8 20 6 7 9 34 27 I 28 2 15 5 38 30 39 36 33 29 14 32 II 9 21 7 8 10 35 28 I 29 3 16 6 39 31 40 37 34 30 15 33 12 10 22 8 9 II 36 29 I 30 4 17 7 40 32 2 38 35 31 16 34 13 II 23 9 10 12 37 30 I 31 5 18 8 2 33 3 39 36 32 17 35 14 12 24 10 II 13 38 31 I 32 6 19 9 3 34 4 40 37 33 18 36 15 13 25 II 12 14 39 32 I 33 7 2C 10 4 35 5 2 38 34 19 37 16 14 26 12 13 15 40 33 I 34 8 21 II 5 36 6 3 39 35 20 38 17 15 27 13 14 16 2 34 I 35 9 22 12 6 37 7 4 40 36 21 39 18 16 28 14 15 17 3 35 136 10 23 13 7 38' 8 5 2 37 22 40 19 17 29 15 16 18 4 36 I 37 II 24 14 8 39 9 6 3 38 23 2 20 18 30 16 17 19 5 37 I 38 12 25 15 9 40 10 7 4 39 24 3 21 19 31 17 18 20 6 38 I 39 13 26 16 10 2 II 8 5 40 25 4 22 20 32 18 19 21 7 39 1 40 14 27 17 II 3 12 9 G 2 26 5 23 21 33 ■ 19 20 22 8 INDIVIDUAL SCHEDULE. 59 SCHEDULE FOR FORTY PLAYERS.— Continued. TABLE 6. TABLE 7. TABLE 8. TABLE 9, TABLE 10. GAME. N. S. E. w. N. S. E. w. N. S. E. w. rl. S. c. W. ft'. s. n.. W. n 31 32 25 26 36 17 33 14 19 29 37 8 30 35 39 5 16 38 40 I 12 32 33 26 27 37 18 34 15 20 30 38 9 31 36 40 6 17 39 2 2 13 33 34 27 28 38 19 35 16 21 31 39 10 32 37 2 7 18 40 3 3 14 34 35 28 29 39 20 36 17 22 32 40 II 33 38 3 8 19 2 4 4 J5 35 ,36 29 30 40 21 37 18 23 33 2 12 34 39 4 9 20 3 5 5 l5 36 37 30 31 2 22 38 19 24 34 3 13 35 40 5 10 21 4 6 6 17 37 38 31 32 3 23 39 20 25 35 4 14 36 2 6 II 22 5 7 7 18 38 39 32 33 4 24 40 21 26 36 5 15 37 3 7 12 23 6 8 8 19 39 40 33 34 5 25 2 22 27 37 6 16 38 4 8 13 24 7 9 9 20 40 2 34 35 6 26 3 23 28 38 7 17 39 5 1 9 14 25 8 10 10 21 2 3 35 36 7 27 4 24 29 39 8 18 40 6 10 15 26 9 II II 22 3 4 36 37 8 28 5 25 30 40 9 19 2 7 11 16 27 10 12 12 23 4 5 37 38 9 29 6 26 31 2 10 20 3 8 12 17 28 II 13 13 24 5 6 38 39 10 30 7 27 32 3 II 21 4 9 13 18 29 12 14 14 25 6 7 39 40 II 31 8 28 33 4 12 22 5 10 14 19 30 13 15 15 26 7 8 40 2 12 32 9 29 34 5 13 23 6 II 15 20 31 14 16 16 27 8 9 2 3 13 33 10 30 35 6 14 24 7 12 16 21 32 15 17 17 28 9 10 3 4 14 34 11 31 36 7 15 25 8 13 17 22 33 16 iS 18 29 10 II 4 5 15 35 12 32 37 8 16 26 9 14 18 23 34 17 19 19 30 II 12 5 6 16 36 13 33 38 9 17 27 10 15 19 24 35 18 20 20 31 12 13 6 7 17 37 14 34 39 10 18 28 II 16 20 25 36 19 21 21 32 13 14 7 8 18 38 15 35 40 ir 19 29 12 17 21 26 37 20 22 22 33 14 15 8 9 19 39 16 36 2 12 20 30 13 18 22 27 38 21 23 23 34 15 16 9 10 20 40 17 37 3 13 21 31 14 19 23 28 39 22 24 24 35 16 17 10 ■ II 21 2 18 38 4 14 22 32 15 20 24 29 40 23 25 25 36 17 18 II 12 22 3 19 39 5 15 23 33 16 21 25 30 2 24 26 26 37 18 19 12 13 23 4 20 40 6 16 24 34 17 22 26 31 3 25 27 27 38 19 20 13 14 24 5 21 2 7 17 25 35 18 23 27 32 4 26 28 28 39 20 21 14 15 25 6 22 3 8 18 26 36 19 24 28 33 5 27 29 29 40 21 22 15 16 26 7 23 4 9 19 27 37 20 25 29 34 6 28 30 30 2 22 23 16 1727 8 24 5 10 20 28 38 21 26 30 35 7 29 31 31 3 23 24 17 18 28 9 25 6 II 21 29 39 22 27 31 36 8 30 32 32 4 24 25 18 19 29 10 26 7 « 22 30 40 23 28 32 37 9 31 33 33 5 25 26 19 20 30 II 27 8 13 23 31 2 24 29 33 38 ID 32 34 34 6z6 27 20 21 31 12 28 9 14 24 32 3 25 30 34 39 II 33 35 35 7 27 28 21 22 32 13 29 10 15 25 33 4 26 31 35 40 12 3t 36 36 8 28 29 22 23 33 14 30 II 16 26 34 5 27 32 36 2 13 35 37 37 9 29 30 23 24 34 15 31 12 17 27 35 6 28 33 37 3 14 3638 38 10 30 31 24 25 35 16 32 13 18 28 36 7 29 34 38 4 15 37 39 39 60 MITCHELL'S DUPLICATE WHIST. SCHEDULE FOR FORTY-EIGHT PLAYERS. Once With and Twice Against. (FIRST LINE ONLY) N. S. E. W Table 1 1 2 19 32 2 7 44 42 9 3 11 40 27 24 4 37 14 47 4 6 18 33 36 15 6 12 39 36 16 7 20 31 5 46 8 25 26 45 6 9 34 17 23 28 " 10 22 29 21 30 " 11 38 13 8 13 " 12 48 3 41 10 For the succeeding" lines add one to each figure, except No. 1, which remains constant, and No. 48, which becomes No. 2. [The above schedule is not a perfect one as to opposition. In the subtraction of corners 17 occurs four times and 22 not at all, so that each player will play four times against the player whose difference is 17, and will not play at all against the player whose difference is 22.] Professor E. H. Moore, of the University of Chicago, who invented the 4 X « method mentioned by Mr. Whitf eld, thus explains his process : "My work on whist-tournament arrangements appeared as the third part of my paper, 'Tactical INDIVIDUAL SCHEDULE. 61 Memoranda, I — III,' in the American Journal of Mathematics (vol. 18, pp. 264-303, 1896, Baltimore, Md.). Here I shall clearly state the three results. "In § 7, by the use of the theory of primitive roots for a prime modulus f, a direct non-tentative method is given for constructing a cyclic tournament arrangement for m = Zp -\r\ players, where ^ is any prime number of the form / = 45 + 1. This covers an infinitude of Cases, m = 16, 40, 52, 64, 88, 112, 124, 160, 184, .... "I introduce a new notion — '/r«ji/e-whist- tourna- ment arrangement.' ^ In a triple-arrangement at every table the oppositions N E, S W are treated as coordinate, and the oppositions N W, S E are treated as coordinate (just as the pairings N S, E W are treated as coordinate in the ordinary arrangement) and every player is required to be opposed to every other player once in each way. Thus, for instance, the cyclic arrangement for four players, abed, acdb, adbc, is triple, and all my cyclic arrangements just referred to are triple. "Triple-arrangements are of special importance because of the 'composition' methods of §§ 9 and 11. If we know any triple-arrangement for m players and any ordinary arrangement for n players, then by the direct non-tentative process of § 11 we can construct an arrangement for mXn players; if both known 62 Mitchell's duplicate whist. arrang-ements are triple, the process of § 9 yields a triple-arrang-ement for m X n players. Thus, from the known arrangements for 4 and 16 players I con- structed for the Denver Whist Club an arrangement for 64 players. Ag-ain, using Mr. Whitfeld's ordinary arrang-ement for 100 players and my triple- arrang-ements for 16 and 160 players, we can construct two ordinary arrang'ements for 16 X 100 and 160 X 100 players, and one triple-arrang-ement for 16 X 160 players. Eliakim Hastings Moore." SCHEME FOR FORTY-EIGHT PLAYERS (4 x 12). II 12 I 8 3 2 5 7 9 6 4 10 First II 23 24 13 20 15 14 17 19 21 18 16 22 Games. 35 36 25 32 27 26 29 31 33 30 28 34 I 47 48 37 44 39 38 41 43 45 42 40 46 II 24 25 44 3 14 29 43 9 18 28 46 Second 11 . 23 12 37 32 15 2 41 31 21 6 40 34 Games. 35 48 I 20 27 38 5 19 33 42 4 22 I 47 36 13 8 39 25 17 7 45 30 16 10 II 48 13 32 3 38 17 31 9 42 16 34 Third 11 . 47 23 12 25 20 39 2 29 19 45 6 28 22 Games. 36 I 44 15 26 5 43 21 30 4 46 I 35 24 37 8 27 14 41 7 33 18 40 10 II 36 37 20 3 26 41 29 9 30 40 22 Fourth II . 35 12 13 44 27 2 17 43 33 6 16 46 Games. 47 24 I 32 39 14 5 31 45 18 4 34 I 23 48 25 8 15 38 29 7 21 42 28 10 ' I 13 25 37 2 14 26 38 3 15 27 39 Last 3 . 4 16 28 40 5 17 29 41 6 18 30 42 Games. 7 19 31 43 8 20 32 44 9 21 33 45 10 22 34 36 II 23 35 47 12 24 36 48 Each four in the last three gam es remain at same table changing- partners. The 48 players '. 1,2, J 48 form four companies 1, 2, -, 12; 13 ,14 J ,24; ; 25, 26, — . , 36; 37,; 38,- f 48. INDIVIDUAL SCHEDULE. 63 For each set of 11 games only the first game is given, the other 10 being obtained by letting the players 12, 24, 36, 48 of each company remain sta- tionary and the other 11 players of each company advance for each new game one place cyclically, i. e., for first company 1 is replaced by 2, — , 10 by 11, 11 by 1, and for fourth company 37 by 38, 46 by 47, 47 by 37. SCHEDULE FOR FIFTY-TWO PLAYERS. Once With and Twice Against. (FIRST LINE ONLY.) Table 1. 2. 3. 4. b . 6, 7. 8, 10 11 12 13 For the succeeding lines add one to each figure, except No. 1, which remains constant, and No. 52, which becomes No. 2. N. s. E. w. 1 2 19 36 10 28 12 9 6 15 7 31 4 34 30 42 3 18 16 22 33 23 51 26 43 38 52 14 48 20 27 8 25 11 40 5 39 32 21 29 46 17 37 41 24 35 45 47 13 44 49 50 64 Mitchell's duplicate whist. SCHEDULE FOR FIFTY-SIX PLAYERS. Once With and Twice Against. (FIRST LINE ONLY.) N. S. E. W. Table 1 1 2 42 47 2 _. . . 7 37 12 27 3 17 52 22 32 4 18 51 29 40 5 21 48 35 34 6 38 31 14 55 7 56 13 50 19 8 33 36 4 10 9 41 28 20 49 " 10 43 26 24 45 " 11 16 53 25 44 " 12 , 23 46 39 30 " 13 11 3 15 54 " 14 8 6 9 5 For the succeeding- lines add one to each figure, except No. 1, which remains constant, and No. 56, which becomes No. 2. INDIVIDUAL SCHEDULE. 65 SCHEDULE FOR SIXTY-FOUR PLAYERS. Once With and Twice Against, (FIRST LINE ONLY.l N. S. E. W. Table 1 1 2 23 44 2 38 29 30 37 3 20 47 16 51 4 11 56 9 58 5 43 13 7 18 6 54 39 36 10 7 28 52 19 6 8 15 27 42 4 9 40 46 22 3 " 10 21 24 12 34 " 11 55 26 33 32 " 12 60 14 49 17 " 13.... 31 8 57 41 " 14 48 5 61 53 " 15 25 35 63 59 " 16 45 50 64 62 For the succeeding lines add one to each fig-ure, except No. 1, which remains constant, and No. 64, which becomes No. 2. 66 Mitchell's duplicate whist. FORMULAS AS PREPARED BY MR. W. H. WHITFELD. [In order to make these schedules conform to the other schedules used in this treatise, I have taken the liberty of transposing the figures given by Mr. Whitfeld, so that the player who sits in the fixed position all through the tournament is No. i, and so that No. i will play in regular succession with 2, 3, 4, &c., but for the benefit of those who are interested in the mathematical problem, Mr. Whitfeld's figures are also given.] 12 PLAYERS. 20 PLAYERS. 24 PLAYERS. 28 PLAYERS. 36 PLAYERS. II 12 I 8 5 6 13 20 I 4 8 13 I 13 10 18 I 34 2 33 3 2 5 7 7 12 8 17 2 10 12 18 8 14 21 26 4 31 8 27 9 6 4 10 10 14 3 16 17 19 14 23 2 27 6 15 16 19 32 3 I 9 4 II 6 7 9 20 5 9 II 25 29 6 23 12 2 19 15 18 II 15 3 16 3 20 19 22 11 24 22 13 5 21 22 24 4 16 24 17 7 12 23 28 9 7 5 15 26 28 35 30 18 17 14 21 10 20 25 36 40 PLAYERS. 48 PLAYERS. 52 PLAYERS. 56 PLAYERS. 64 PLAYERS. I 3 25 36 I 46 8 39 3 4 9 40 I 54 2 53 3 I 15 20 2 6 II 33 II 36 41 6 6 8 18 29 4 51 8 47 6 2 30 40 4 12 22 27 27 20 28 19 12 16 36 7 16 39 32 23 12 4 60 17 8 2+ 5 15 15 32 26 21 24 32 21 ■4 9 46 18 37 24 8 57 34 16 9 10 30 24 23 4 43 48 13 42 28 36 19 17 38 48 16 51 5 32 18 20 21 29 18 44 3 45 26 33 5 34 21 13 42 33 32 39 10 7 19 17 35 37 10 14 33 39 I 15 10 26 29 52 3 31 53 41 44 14 38 34 3« 31 16 13 34- 27 2 30 20 49 6 43 12 62 43 19 25 28 37 29 23 12 35 z 45 31 37 35 50 31 24 7 48 61 23 38 50 13 26 39 40 38 9 22 25 II 23 19 49 14 41 28 27 59 46 13 37 42 5 7 40 22 46 38 47 II 44 22 33 55 29 26 II 48 47 30 17 44 41 25 43 10 45 30 40 47 58 52 22 17 34 51 5S 25 5 55 56 35 15 50 20 7 14 28 21 56 49 35 42 9 54 18 45 36 27 63 64 PROGRESSIVE DUPLICATE SCHEDULES. 67 WHITFELD PROGRESSIVE DUPLICATE. Each Pair Against Every Other Pair. FOUR TABLES. 3 H 2b s l-< 1 ".H M ■- 'rt" . 2S J3 (Q •^■o |2 >-> ■to. * m3 H.S o :s« oh °s «J s d *!« nJ SE Oh dos Z Z id Z z Z z I X I I 1-2-3 4 3 2 7 2 6 6 3 4 3 6 3 4 4-5 I 2 4 5 4 7 7 SIX TABLES. 2 I I X I I 1-2 5 4 2 II 2 9 9-10 6 5 3 10 3 7 7 4 6 4 9 4 3 3-4-5-6 I 3 5 8 5 II II 2 I 6 7 6 8 8 3 2 SEVEN TABLES. I X I I 1-2 4 6 2 13 2 5 5 6 7 3 12 3 7 7-8-9-10 7 5 4 II 4 13 13 5 I 5 10 5 II 11-12 3 4 6 9 6 3 3-4 I 2 7 8 7 6 6 2 3 68 MITCHELL'S DUPLICATE WHIST. ni 3 H "o o' Z z *« . « No. of ist Deal _ at Table. 5 3 S,i- ■31 oS . z TABLES. i2 ill OS oH Z alb -I 1"^ I X I I I 4 8 2 >5 2 5 5 5 7 3 14 3 13 13-14 8 6 4 13 4 2 2 7 I 5 12 5 6 6-7 6 2 6 II 6 8 8-g-io-ii-i2 3 5 7 lO 7 3 3-4 2 4 8 9 8 15 NINE 15 TABLES. I 3 I X I I I 9 3 2 17 2 13 13^14-15-16 8 9 3 i6 3 2 2-3 I 7 4 15 4 10 10 5 6 5 14 5 7 7-8-9 7 ■4 6 13 6 II II 4 8 7 12 7 4 4-5-6 3 5 8 II 8 12 12 6 2 9 lO 9 17 17 2 I TEN TABLES. I X I I I 2 10 2 19 2 18 18-19 9 I 3 i8 3 5 5 10 8 4 17 4 7 7 8 7 5 i6 5 12 12-13-14-15-16 6 9 6 IS 6 10 lO-II 7 5 7 14 7 8 8-9 4 6 8 13 8 6 6 3 4 9 12 9 17 17 5 2 lO II 10 2 2-3-4 I 3 SCHEDULES FOR LADIES AND GENTLEMEN. 69 SCHEDULES FOR LADIES AND GENTLEMEN. Ladies once with each gentleman, once against each lady; gentlemen once with each lady, once against each gentleman. The ladies sit N. and E., gentlemen S. and W. FOUR LADIES AND FOUR GENTLEMEN. GAME. TABLE I. TABLE 2. N. S. E. W. N. S. E. W. 1 1423 3241 2 1234 4321 3 1342 2431 4 I I 2 2 3344 EIGHT LADIES AND EIGHT GENTLEMEN. GAME. TABLE I. TABLE 2. TABLE 3. TABLE 4. N. S. E. W. N. S. E. W. N. S. E. W. N. S. E. W. 1 1726 5438 8345 6271 2 1837 6542 2456 7381 3 1248 7653 3567 8421 4 1352 8764 4678 2531 5 1463 2875 5782 3641 6 1574 3286 6823 4751 7 1685 4327 7234 5861 8 1122 3344 5566 7788 70 Mitchell's duplicatk whist. SIXTEEN LADIES AND GAME. TABLE I. TABLE 2. TABLE : 3. TABLE 4. N. S. E. W. N. s. E. w. N. s. E. w. N. s. E. w. I 12 2 7 II 15 9 8 16 13 S 14 6 4 3 10 2 13 3 8 12 16 10 9 2 14 6 IS 7 5 4 II 3 14 4 9 13 2 II 10 3 15 7 16 8 6 5 12 4 IS 5 10 14 3 12 II 4 16 8 2 9 7 6 13 5 i6 6 II 15 4 13 12 5 2 9 3 10 8 7 14 6 2 7 12 16 5 14 13 6 3 10 4 II 9 8 15 7 3 8 13 2 6 15 14 7 4 II 5 12 10 9 16 8 4 9 14 3 7 16 IS 8 5 12 6 13 II 10 2 9 5 lO 15 4 8 2 16 9 6 13 7 14 12 II 3 lO 6 II 16 5 9 3 2 10 7 14 8 15 13 12 4 II 7 12 2 6 10 4 3 II 8 15 9 16 14 13 5 12 8 13 3 7 II 5 4 12 9 16 10 2 15 14 6 13 9 14 4 8 12 6 S 13 10 2 II 3 16 15 7 14 lO 15 5 9 13 7 6 14 II 3 12 4 2 16 8 15 II 16 6 10 14 8 7 15 12 4 13 S 3 2 9 i6 I 2 2 3 3 4 4 5 5 6 6 7 7 8 8 SCHEDULES FOR LADIES AND GENTLEMEN. 71 SIXTEEN GENTLEMEN. TABLE 5. TABLE 6. TABLE 7 TABLE 8 GAME. N. s. E. W. N. s. E. W. N. s. E. W. N. s. E. W. 10 3 4 6 14 5 13 16 8 9 15 II 7 2 12 I II 4 S 7 15 6 14 2 9 10 16 12 8 3 13 2 12 5 6 8 16 7 15 3 10 II 2 13 9 4 14 3 13 6 7 9 2 8 16 4 II 12 3 14 10 5 15 4 14 7 8 10 3 9 2 5 12 13 4 15 II 6 16 5 15 8 9 II 4 10 3 6 13 14 5 16 12 7 2 6 16 9 10 12 5 II 4 7 14 15 6 2 13 8 3 7 2 10 II 13 6 12 5 8 15 16 7 3 14 9 4 8 3 II 12 14 7 13 6 9 16 2 8 4 15 10 5 9 4 12 13 15 8 14 7 10 2 3 9 5 16 II 6 10 5 13 14 16 9 15 8 II 3 4 10 6 2 12 7 II 6 14 15 2 10 16 9 12 4 5 II 7 3 13 8 12 7 15 16 3 II 2 10 13 5 6 12 8 4 14 9 13 8 16 2 4 12 3 II 14 6 7 13 9 5 15 10 14 9 2 3 5 13 4 12 15 7 8 14 10 6 16 II 15- 9 9 10 10 II II 12 12 13 13 14 14 15 15 16 16 16 72 MITCHELL'S DUPLICATE WHIST. THIRTY-TWO LADIES AND GAME. TABLES 1 & l6. TABLES 2 & 15. i 3 & 14. TABLES 4 & 13. 13 14 15 16 17 18 23 24 25 26 27 28 29 30 31 32 2 6 3 7 4 8 5 9 6 10 7 II 8 12 9 13 10 14 11 15 12 16 13 17 14 18 15 19 16 20 17 21 18 22 19 23 20 24 21 25 22 26 23 27 24 28 25 29 26 30 27 31 28 32 30 28 31 29 32 30 2 31 3 32 4 2 5 3 6 4 7 5 8 6 9 7 32 32 31 31 11 9 12 10 13 II 14 12 15 13 16 14 17 15 18 16 19 17 20 18 21 19 22 20 23 21 24 22 25 23 26 24 27 25 28 26 29 27 3 3 30 30 22 4 23 5 24 6 25 7 26 8 27 9 28 10 29 zi 30 12 31 13 32 14 2 15 16 17 18 19 8 21 9 22 10 23 11 24 12 25 13 26 14 27 15 28 16 29 17 30 18 31 19 32 20 2 21 3 4 4 29 29 32 17 2 18 S. N. 14 8 15 9 16 10 S. N, 21 18 12 22 19 13 20 14 23 8 24 9 25 10 26 11 27 12 28 13 29 14 30 15 31 16 32 17 2 18 19 3 4 20 5 21 6 22 7 23 8 24 9 25 10 26 II 27 12 28 13 29 14 30 15 31 16 5 5 28 28 21 15 22 16 23 17 24 18 25 19 26 20 27 21 28 22 29 23 30 24 31 25 32 26 2 27 28 29 30 31 32 2 3 4 5 6 II 12 13 7 6 6 27 27 25 18 26 19 27 20 28 21 29 22 30 23 31 24 32 25 2 26 5 24 6 25 7 26 8 27 9 28 10 29 11 30 12 31 13 32 14 2 17 10 18 II 19 12 20 13 21 14 22 15 23 16 24 17 7 7 26 26 21 9 22 10 23 II 24 12 25 13 26 14 27 15 28 16 29 17 30 18 31 19 32 20 25 25 SCHEDULES FOR LADIES AND GENTLEMEN. 73 THIRTY-TWO GENTLEMEN. TABLES i5& 12. TABLES 6& II. TABLES 7& 10. TABLES 8& 9- GAMB «. 9. I!,. w. «. a. t^. W. n. a. «.. w. IN. a. E. w. w. £. a. n. W. «,. £>. n. W. E. a. p.. w. Hi. s. N. 29 7 19 9 11 10 27 13 21 16 20 12 15 26 3 31 I 30 3 20 10 12 II 28 14 22 17 21 13 16 27 4 32 2 31 9 21 11 13 12 29 15 23 18 22 14 17 28 5 2 3 32 10 22 12 14 13 30 16 24 19 23 15 18 29 6 3 4 2 II 23 13 15 14 31 17 25 20 24 16 19 30 7 4 5 3 12 24 14 16 15 32 18 26 21 25 17 20 31 8 5 6 4 13 25 15 17 16 2 19 27 22 26 i8 21 32 9 6 7 5 H 26 16 18 17 3 20 28 23 27 19 22 2 10 7 8 6 15 27 17 19 18 4 21 29 24 28 20 23 3 II 8 9 7 l5 28 iS 20 19 5 22 30 25 29 21 24 4 12 9 10 8 17 29 19 21 20 6 23 31 26 30 22 25 5 13 10 II 9 i8 30 20 22 21 7 24 32 27 31 23 26 6 14 II 12 lO 19 31 21 23 22 8 25 2 28 32 24 27 7 15 12 13 11 20 32 22 24 23 9 26 3 29 2 25 28 8 16 13 14 12 21 2 23 25 24 10 27 4 30 3 26 29 9 17 14 15 13 22 3 24 26 25 II 28 5 31 4 27 30 10 18 15 16 14 23 4 25 27 26 12 29 6 32 5 28 31 II 19 16 17 15 24 5 26 28 27 13 30 7 2 6 29 32 12 20 17 18 i6 25 6 27 29 28 14 31 8 3- 7 30 2 13 21 18 19 17 26 7 28 30 29 15 32 9 4 8 31 3 14 22 19 20 l8 27 8 29 31 30 16 2 10 5 9 32 4 15 23 20 21 19 28 9 30 32 31 17 3 II 6 10 2 5 16 24 21 22 20 29 10 31 2 32 18 4 12 7 II 3 6 17 25 22 23 21 30 11 32 3 2 19 5 13 8 12 4 7 18 26 23 24 22 31 12 2 4 3 20 6 14 9 13 5 8 19 27 24 25 23 32 13 3 5 4 21 7 15 10 14 6 9 20 28 25 "26 24 2 14 4 6 5 22 8 16 II 15 7 10 21 29 26 27 25 3 15 5 7 6 23 9 17 12 16 8 II 22 30 27 28 26 4 16 6 8 7 24 10 r8 13 17 9 12 23 31 28 29 27 5 '7 7 9 8 25 II 19 14 18 10 13 24 32 29 30 28 6 18 8 10 9 26 12 20 15 19 II 14 25 Z 30 31 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 32 24 24 23 23 22 22 21 21 20 20 19 19 18 18 17 17 74 Mitchell's duplicate whist. TEAM SCHEDULES. Safford's method of placing the players in numerical order down one position and up the other applies to every even number of teams, without chang-ing the numbers of the players to correspond with the previous occupants of the seats; and as there are only two positions in the case of teams, it is a very simple matter writing out the formula for a team schedule. All you have to do is to write "1, 2, 3, then the last number, then 4 and the second last number, then 5 and the third last number, and so on until all your numbers are exhausted," and your formula is made. The succeeding numbers follow each other in the same order as in the individual schedules. For instance, take six teams; the formula would be : &ME. TABLE I. TABLE 2. TABLE .3- N,-S. E .-w. N.-S. E.-W. N.-S. E .-w. I 2 3 6 4 5 2 3 4 2 5 6 3 4 5 3 6 2 4 5 6 4 2 3 5 6 2 5 3 4 TEAM SCHEDULES. 75 Take ten teams and the formula would be: .ME, TABLE I. TABLE 2. TABLE 3. - TABLE 4. TABLE 5. N.-S. E.-W. N.-S. E.-W. N.-S. E.-W. N.-S. E.-W. N.-S. E.-\V I 2 3 lO 4 9 5 8 6 7 2 3 4 2 5 10 6 9 7 8 3 4 5 3 6 2 T 10 8 9 4 5 6 4 7 3 8 2 9 10 5 6 -7 5 8 4 9 3 10 2 6 7 8 6 9 5 10 4 2 3 7 8 9 7 10 6 2 ■5 3 4 8 9 lO 8 2 7 3 6 4 5 9 lO 2 9 3 8 4 7 5 6 Take fourteen teams and the formula would be: GAME. TABLE I. TABLE 2. TABLE 3. TABLE 4. TABLE 5. TABLE 6. TABLE 7. N.-S. E.-W. N.-S. E.-W. N.-S. E.-W. N.-S. E.-W. N.-S. E.-W. N.-S. E.-W. N.-S. E.-W I 2 3 14 4 13 5 12 6 II 7 10 8 9 2 3 4 2 5 14 6 13 7 12 8 II 9 ID 3 4 5 3 6 2 7 14 8 13 9 12 10 II 4 5 6 4 7 3 8 2 9 14 10 13 II 12 5 6 7 5 8 4 9 3 10 2 II 14 12 13 6 7 8 6 9 5 10 4 II 3 12 2 13 14 7 8 9 7 10 6 II 5 12 4 13 3 14 2 8 9 10 8 II 7 12 6 13 5 14 4 2 3 9 10 II 9 12 8 13 7 14 6 2 5 3 4 ID II 12 10 13 9 14 8 2 7 3 6 4 5 II 12 13 II 14 10 2 9 3 8 4 7 5 6 12 13 14 12 2 II 3 10 4 9 5 8 6 7 13 14 2 13 3 12 4 II 5 10 6 9 7 8 The above are quite enougfh to show the process. By following' up the numbers it will be found that the teams who start east and west keep moving towards the last table until they get to the foot, they then change over to the north and south seats and move 76 MITCHELL'S DUPLICATE WHIST. Up towards the first table, and after playing north and south at the second table they go to the east and west seats at the first table, and then down the east and west seats to where they started. Similarly, the teams who start north and south keep moving- up towards the first table to No. 2, then down the east and west seats from the first to the last table, and back along the north and south seats to where they started. In their travels they meet the other teams in a regular order. If the first team played against is odd, the next team will be the n«xt higher odd number, then the next higher, and so on until the highest odd number is met, after which the first even number (No. 2) will be the team played against, then the even numbers will be met in succession, until all of them have been exhausted, when No. 3 will be met and the balance of the odd numbers. At any point in the procession where a team's own number would come in, No. 1 will come in to fill up the blank. It will thus be seen that if players could be depended on to follow directions a schedule would be unnecessary. All that has to be done is to make them change tables in accordance with the movement described in the schedule, and they could seat them- selves any way at all for the first game and go ahead. Unfortunately, however, players cannot be depended upon in such a manner, and even if they could a schedule would be necessary to settle the disputes which would arise. TEAM SCHEDULES. 77 The numbers 6, 10 and 14 were taken to illus- trate the team schedule principle, simply because 8, 12 and 16, etc., have already been given among- the individual schedules. As the individual schedules equalize the opposition at the other tables better, they should be used for team tournaments vs^hen the number is a multiple of four. Should the number of entries in a tournament be odd, a "bye" can be provided for in the following- manner: Use a schedule with one more than the number of entries, and let the players be "bye" whose turn it is to play with the last or extra number. The "bye" will be 3 for the first game, then all the odd numbers in succession, then the even, and lastly No. 1. -^=^1 l^gX- APPENDIX I. LEADS AND INFERENCES OF MODERN WHIST. LEADS AND INFERENCES OF MODERN WHIST 81 LEADS AND INFERENCES OF MODERN WHIST. In placing- these leads and inferences before the reader it is not considered necessary to preface them with any defence or explanation. The reader is supposed to have arrived at the conclusion that the modern system of leading- is the best foundation on which to build scientific play ; and it is hoped that the leads and inferences as here g-iven will be found in such comprehensive form as to allow him to master them with a minimum of effort. In previous works on whist the sigfns used for King- and Knave have been Kg- and Kn respectivelj' ; but as the index letters on all playing-cards in this country for these denominations are K and J, and it is less confusing- to have totally different signs, the letters K and J will be used in the following pages. The obfect of the game, of course, is to take as many tricks as possible with the hands dealt to you and your partner. If your cards are not commanding cards at the start, you must endeavor to bring them up to that i-ank by forcing your adversaries to play the cards they hold which are higher than yours. If you hold the second and third best card of a suit, you lead one of them and get the best out of your way. If you have the third, fourth and fifth best, you have 82 Mitchell's duplicate whist. to clear away the best and second best. If you have only one high card, or two hig-h cards the highest not above the rank of third best, you must look to your partner for assistance, and lead low, trusting- to his having the high card necessary to make yours good. And while you are endeavoring to clear your suit, you must also indicate by a certain arbitrary code of card signals, to be shortly explained, as clearly as may be permissible, the exact nature and extent of your holding. The game of whist is now reduced to such a fine point that experts can locate the balance of the cards sometimes after the fourth or fifth trick, and while it may seem impossible to the beginner that this stage of proficiency can ever be reached, and it is certain that it will be some time before he reaches it, yet it is best that he should start in with the line of play which makes it not only possible, but certain of accomplishment with a fair amount of study and practice. The principle upon which the modern leads are based is the showing of the number of cards in suit, and the value of them, without in any way endan- gering their trick-taking power. This is accomplished by the lead of the fourth best card when a low card is led originall}', or when low card is led after high second round; by certain arbitrary leads of high cards; and by the leading of either of two or three high indifferent cards second round.* With two high *Trist, in Harper's Magazine, March, 1891. LEADS AND INFERENCES OF MODERN WHIST. 83 indifferent cards, if the first card led did not intimate five in suit, the lead of the higher now indicates only four in suit originally, while the lead of the lower indicates five or more. With three indifferent cards, under like circumstances, the highest indicates four, the intermediate five, and the lowest six or more. If the first card led intimated five or more in suit, the second lead of the higher of two would indicate five only, and of the lower six or more, while the highest of three would indicate five only, the intermediate six only, and the lowest seven or more. LEADS, When vou have three or more honors in sequence, and five or more cards in the suit, you lead the lowest honor; following with the highest card of the sequence shows a holding of exactly five, with the second card of the sequence six or more : if you have but four cards in the suit you lead the king. When you have two honors in sequence, one of which is the king, your original lead, if you hold but four of the suit, should be the king; if you hold five or more of the suit, you should lead the other honor. With ace, queen, knave, you lead the ace, and follow with queen if you hold but four, with knave if you hold five or more. With ace, queen, knave, ten only; lead ace, follow with ten. With queen, knave, ten; lead ten; follow with queen if you hold but four, with knave if you hold five or more. 84 Mitchell's duplicate whist. table of original leads. WITH FOUR WITH FIVE WITH SIX HOLDING. LEAD. FOL. LEAD. FOL. LEAD. FOL. A, K, Q, J K J J A J K A, K, Q K Q Q A Q K *A, K K . . A A, Q.J A Q A J . . A, Q, J, 10 A 10 K, Q, J, 10 K 10 K, Q, J K J J , K J Q tK. Q K .. XQ Q, J, 10 10 Q 10 J . . When you have not any of the above higfh-card combinations lead your fourth best card; except with ace and six small, when you lead the ace, and follow with fourth best left in hand ; and with A, Q, or A, J, and three or more small, in plain suits, lead ace and follow with fourth best left in hand, especially if weak in trumps and cards of reentry. Except, also, with J, 10, 9 and one or more small in trumps, lead J. Lead from your longfest suit. If you have two suits of equal length, select the strong-er. If your longest suit contains but four cards, headed by the ten or lower, you may lead from the top of the suit, rather than run the risk of sacrificing *In trumps lead fourth best, except with six or more, fin trumps lead fourth best unless you also hold the ten. |If Q wins, follow with fourth best left in hand. LEADS AND INFERENCES OF MODERN WHIST. 85 an honor in your partner's hand; although the safer way for the very beg'inner is to lead the fourth best even from such a weak holding- as described, and let partner draw rigid inferences from your play. These are the leads for the opening of a hand. When you are not the original leader, you can, in the majority of cases, adhere to them, although, not infrequently, occasion will arise when your better judgment will suggest a departure from them. It is justifiable to lead from a suit of less than four cards when your long suit has been started by your adver- saries and you consider it dangerous to continue the suit, or when the previous play indicates that your short suit is your partner's long one. FORCED LEADS. When obliged to lead from a suit of less than four cards, the rule is to lead the highest, in order to strengthen your partner's hand, if the card you lead happens to be of his suit, and also in order to show him that you are weak in it. If you lead a K, Q. J, 10 or 9, and either of the cards which you ought to have held to justify the lead falls on the trick or is in your partner's hand, he knows at once that it was a forced lead, and governs himself accordingly. It is best to be satisfied that your partner is strong in the suit before you lead a K or Q that has two guards, but with cards of lesser value you would not be likely to make tricks anyway, and they may be of assistance to your partner. 86 Mitchell's duplicai-e whist. When leading from a short suit in which you have two honors, you lead the higher. If the card you lead wins the trick you follow with the other honor. TRUMP PLAY. If trumps is your longest suit, lead trumps. If you have the commanding cards in all the plain suits, or if you have one very long established suit and probable cards of reentry in the two others, it is wise to lead trumps originally, even when you are short, and when short it is the rule to lead the highest; so that, with ace and one, king and one, queen and one, or knave and two small, you would lead the honor. With ace, king or queen, and two small, you would be justified in departing from the rule and leading your lowest, depending on the size of the turned card and whether it was desirable for you to lead or be led up to after the third round. When long, the card to 'lead in the trump suit is the same as in the plain suits,* except as it may be affected by the size of the turned trump. If any card higher than the eight is turned and you hold two or more cards above it, you may lead the highest card of the sequence next above. That is to say, you must prevent the dealer from taking the trick with kK''^ * Except that you lead low from K, Q, unless you hold four or five small, and lead the top of the J, lo, g, sequence, instead of fourth best. LEADS AND INFEKENCES OF MODERN WHIST. 87 the turned trump if you hold cards which justify the play. While the main object of a scientific whist player is to establish and brings in a long suit, it must be admitted that in a large number of hands this object cannot be attained, and the best whist player is he who is quickest at perceiving when it is incumbent on him to abandon the idea of making a great hand out of any particular holding and to teach out for all the stray tricks in sight. When you cannot bring in your long suit, 3'ou must bend your energies in the direction of preventing' j^our adversaries from bring- ing in theirs, and your trumps are the best weapons to employ. The smallest trump is good for the largest plain suit card, and when it becomes evident that you and your partner cannot make the most tricks by getting trumps out and making your long suit, it should be your endeavor to separate your trumps as far as possible, either on suits that you have started yourselves or on the suits started by the adversaries. Often it is necessary to have your partner trump the second or third round of your suit before you can establish it, and, in fact, there are many ways in which ruf&ng may be used to advantage. There is nothing so deadly as the cross- ruff. SECOND-HAND PLAY. Before the adoption of the fourth best lead the principal rule for a player to follow second hand 88 Mitchell's duplicate whist. when a low card was led (and he did not hold two or more honors in sequence) was to play his lowest card, and when an honor was led to cover, but now it is different. The fourth best card proclaims so exactly the other cards that are held by the original leader that it is incumbent on the second-hand player to use his medium cards in such manner as to prevent the sacrifice of honors in the hand of his partner. There being' thirteen cards in each suit, the lowest of which is the deuce, or two, it follows that the highest must rank as fourteen, and if you deduct from fourteen the three higher cards than the fourth best which the original leader holds, you have the, "eleven rule," invented by Foster, to guide you in making up your mind as to how you may use the cards higher than the one led which are in your hand. If the nine is led, there are only two cards out against it. If you have the king and one small card you must play the king and hold the trick, as the ace must be in the leader's hand, and whether your partner has the other card that is out against the leader's combination or not your king would be lost to the ace on the second round. The leader's holding must be either ace-queen-ten-nine or ace-knave-teh- nine. If you hold the queen and one small, and the nine is led you may as well play your queen. The leader's highest card must be either the king or ace, and your queen would be useless on the second trick. LEADS AND INFERENCES OF MODERN ^YHIST. 89 If the eight is led, there are three cards out against it. If you hold two of them it is well to play the lower of the two. If your partner has the other you hold the trick. If the seven is led there are four cards out against it, and if you hold three of them you should cover. If the card led is below the seven, covering is liable to be mistaken for a trump call (a process which will be explained later), and unless you have a sequence of the nine and higher you should play a low card. There are several general rules which may be followed with safety in second-hand play. If you have a holding which would justify the lead of a high card if you were in, it is proper to play a high card second hand. If any card higher than the eight is led, and you hold the "fourchette," that is, the card immediately above and below in value, the play is to cover. When you have two high cards in sequence and but one small card, you play the lower card of the sequence second hand, unless the card led is higher than yours, when, of course, you must play the low card. With one high card and one small, you cover, if your hand will justify a trump lead, or if you are desirous of obtaining the lead, or if you can tell by the size of the card led that your high card cannot 90 Mitchell's duplicate whist. become the master card on second round and it may- save the master card in your partner's hand. When by the eleven rule you can read that you have all the cards out against the original leader, you simply cover the card led and hold the trick, but you must be satisfied that the lead is not a forced one before you try to hold the trick in that way. If the cards not in your hand above the one led include hig-h card sequences from which a high card should be led, then you know that the lead is false, and must play accordingly. If you have not the ace or a high card sequence yourself, the better way is to play low, and leave the leader's partner in doubt as much as possible as to the whereabouts of the medium cards. It is hardly necessary to instruct even a beginner to put the ace in second hand when either the king, queen or knave is led. The ace is the onl}' card out against any of these cards, and if the trick is passed you run the risk of losing your ace to a small trump, as the later the round of a suit, the more liable the other adversary is to be out. But if the queen is led, and you hold the king, the lead is marked as false, and you must govern yourself by the rest of your holding. If your king is only once guarded, you had better put it in, as third hand will undoubtedlj' finesse the queen; and if he holds the ace, your king would be caught on next round anyway, whereas, if your partner holds the ace you hold the trick. The same remarks will apply to a knave lead when you hold the LEADS AND INFERENCES OF MODERN WHIST. 91 king- and one small. With kingf-ten or king--nine and one or more small, it is best to cover queen or knave led, as if you pass, and the remaining high cards are all in third hand, you are liable not to make a trick, vsrhereas if you cover, you are bound to do so, bar trumping. Similarly, vi^ith queen and one you would cover a knave or ten, and with queen-ten or queen- nine and two or more small you should cover the knave. TRUMPING IN. When a suit is led of which you are out, and it is doubtful whether your partner or opponent is the player able to take the trick, you trump in second hand, provided you hold not more than three trumps, and discard from your weak suit if you hold four or more trumps. If two of your three trumps are honors, and the remainder of your hand is such that you see a probability of gain by refusing to trump, you may take the risk; but if your hand will not stand a trump lead you had better trump in even with two honors, as, if your partner wins the trick or gets in before you are subsequently forced, he will in all probability lead trumps on the strength of your play. Contrarywise, it sometimes paj^s to trump in on a doubtful trick when you have four or more trumps, as for instance when your partner has sig- nalled for trump and it is certain that you will not be overtrumped, or when you have nothing but winners 92 Mitchell's duplicate whist. to discard. But there are many tricks lost by trying- to find an excuse for breaking the rule, and in the great majority of cases it is best to follow it. THIRD-HAND PLAY. Sitting third hand there is little for you to do on a low card led by partner except to attempt to take the trick by playing your highest card or the lowest card of your highest sequence, i. e., of course, unless second hand has already played a card which is higher than you can reach. There is one exception to this rule, and that is, holding ace and queen, you finesse the queen. This is a recognized play among experts, and should be adhered to strictly. If you play the ace you deny the queen, and your partner must place it against him, and play the rest of the hand accordingly. If a high card is led by your partner, you play low or high, according to the remainder of your hand. By the eleven rule you may be able to figure that you and your partner have all the high cards in the suit, and if you were strong in trumps, you would take the trick and lead a trump, whereas if you were weak you would leave your partner in, and put the onus of the game on him. If you can figure that there is only one card out against you and your partner, and you have the command, you may finesse, provided you have tenaces in the other suits and would just as lief have the fourth player get in and LEADS AND INFERENCES OF MODERN WHIST. 93 lead up to you ; otherwise, it is best to play the master card and let your partner do the finessing- in his own suit. If, however, the ten is the card led, and you hold the ace, you had better take the finesse, as, if the king is fourth hand, it will probably be guarded and would make in any event, whereas, if it is in second hand, by holding off you may capture it. UNBLOCKING. If you hold four cards of the suit which your partner leads orig-inally, and his lead indicates that he may hold five or more, you play the suit exactly the same as you would if you held but three, with the smallest card out, reserving the smallest card for the fourth round. Your partner missing the small card locates it in your hand, and if he succeeds in estab- lishing his suit you run no risk of blocking it by being obliged to take the fourth trick. When you return your partner's lead, you return the lowest of four or more, the highest of three or less, always, of course, reserving the lowest card if there is an^r probability that your partner has five cards in his suit. If you retain your lowest to the first trick you return your highest remaining card, and if you have to discard from the suit you throw away the middle card. RETURNED LEADS. By the old English rule a player had to open his own suit before returning his partner's. This rule is by no means rigidly followed now, and may be 94 MITCHELL'S DUPLICATE WHIST. modified to read about as follows : If you have reason to believe your suit can be established sooner than your partner's, it is wise to open it in preference to returning his; if, on the other hand, it is evident that your partner's suit is stronger than yours, do not start a new suit. One suit is as many as you can bring in in one hand, and whatever medium strength you and your partner may have in another suit may be very useful in bringing in the first suit. If you do start a new suit it is a virtual command to your partner to abandon his suit and devote his energies to yours. If you have won your partner's trick very cheaply, it is unwise to return his lead in any event. The strength in the suit must lie between your partner and the opponent on his left. If your partner has the ace-queen, your return of the suit forces him to put up the ace and establish the king for the opponent ; if he has the king-knave, the opponent has him at his mercy. This is one of the situations that justifies the lead of a "strengthening" card. You have not a long suit strong enough to justify a low lead and the possible sacrifice of a high card in your partner's hand, so you lead him a medium high card from a short suit, which, if second hand does not cover, he can finesse, and put the player in the lead who has the secondary strength in his suit. LEADS AND INFERENCES OF MODERN WHIST. 95 THE SIGNAL. The signal for trumps is given by playing an unnecessarily high card on a plain suit led, afterward playing a lower one. By this means, when you are unable to get the lead, and you want to have trumps led, if your partner obtains the lead he is enabled to lead them for you. There is hardly any room for doubt as to the intention of a third or fourth hand play in respect to this signal, but great care must be taken not to mistake the play of a high card second hand for a trump signal. As explained in second hand play, with the nine, ten, knave, queen or king, and the cards next in value, you play high, but not unnecessarily so. You also cover the seven, eight and nine with certain combinations, and your partner must be satisfied that you do not hold the card next above or are trving to save high cards in his hand and prevent the establishment of the original leader's suit before he interprets your play as a signal for trumps. Contrarywise, when you go in second hand without the sequence which justifies it, your partner may give you strength in trumps and look upon your play as an attempt to get in and lead them. If the signal is given after trumps are out, or after it is evident that it cannot mean a signal for trumps, it shows great strength or absolute com- mand of the suit signalled in. It does not mean that the player wants that suit led to him, but that he can take a trick in it when necessary. 96 MITCHELL'S DUPLICATE WHIST. THE ECHO. When your partner leads or signals for trumps, you must show him by your play whether you have three or less, or four or more. When he leads a high trump, with three or less you play your lowest; with four or more you play your third best. Then if you play a higher card on the second round he knows you held not more than three originally, while if you play a lower he gives you credit for four or more. When your partner leads a low trump originally, and you hold the trick or get in afterward before he does, you return the highest of three or less, and your original fourth best from four or more. When your partner has signalled for trumps, and you obtain the lead first, you lead him your fourth best from four or more, and your highest from three or less. If, however, your holding is headed by the ace, you lead the ace first, irrespective of number, and with three or less follow with the next to the ace, with four or more, drop down to the original fourth best. If you hold five, and your partner finds it necessary to lead the third round, it is better to play the third best on the third round than to play your lowest, as in the latter event vour partner might not know whether to credit you with three or five. Similarly, when you have led your fourth best originally, and your partner leads the master card on second round, it is better to play the third best on second round than to drop to your lowest if you hold five, as, if you dropped the lowest. LEADS AND INFER?:NCES OF MODPiRN WHIST. 97 your partner might be uncertain as to whether your original holding was two or five. If you have to trump in before responding to your partner's call, you trump in with your second lowest when you have four, and lead the highest, dropping to the lowest on second round. If you have five, you trump in with the fourth best and lead the lowest, except holding the ace or two honors in sequence, when you trump in with third best and lead ace, or the lower of your two honors, following writh fourth best or other honor. If you have an opportunity to signal in a plain suit after your partner has called for trumps, and before you or he can get in to lead them, you do so provided you have four or more. Failure to signal under these conditions means that you have not more than three trumps. When you wish to signal or echo and unblock at the same time you use your second and third best cards for the purpose. DISCARDING. Discard generally from your weak suit. If you have an honor in either of your opponent's suits, it is well, however, to keep it guarded, unless you are strong enough in trumps to suffer its loss without endangering your game. When your opponents have developed great strength against you, and it is neces- sary to discard from a head sequence, you discard the highest, to inform your partner you also have 98 MITCHELL S DUPLICATE WHIST. the cards immediately below it. If you discard the second or third best, he g"ives your opponents credit for the master card. INFERENCES. LEAD. FOLLOW. INFERENCE. A....K. A.. A.. A., K., K. K. K. Q- Q- J.. J.. J.. 10. 10. 10. . . Has three or more small cards remaining-. If A is led, then another suit, probably has K and J, and is waiting for finesse. If A is led then small card of same suit; has five small, or Q or J and two or more small remaining-. . . Has J and one more remaining. . . Has Q and two or more remaining. . . Has Q and J only remaining. . . Has two more remaining. . . Has A and one more remaining. . . Has A and Q only remaining ; or if A is against, has Q and one remaining. . . Has Q and J only remaining. . . Has K and two more remaining. . . Has A and three more remaining. . . Has K, Q and one more remaining. . . Has A, Q and two more remaining. . . Has A, K and three more remaining. . . Has J and one more remaining. . . Has Q and two more remaining. . . Has Q, J and no more remaining. . .Has 10, Q, A; 10, J, A; or 10, J, K, with or without others. LEADS AND INFEa