[Next] [Up/Previous] [Home]

Two-Move and Three-Move Restrictions

A 40-game match between James Wyllie and Robert Martins in 1863 involved the same game of Checkers being played, from start to finish, for 21 of those 40 games. This led to the adoption of what was known as the two-move restriction or two-move ballot for serious Checkers.


The score of that game, which might at least be suspected of being the "perfect" game of Checkers, is as follows (moves are to be read vertically):

 11-15 | 20-11 |  9-14 | 27-18 | 19-23 | 10- 3 | 26-30
 23-19 |  3- 7 | 22-18 | 10-17 | 26-19 |  9-18 | 12-16
  8-11 | 28-24 | 14-23 | 25-21 | 17-22 | 21-17
 22-17 |  7-16 | 17-14 |  1- 6 | 19-15 | 18-22
 11-16 | 24-20 | 10-17 | 21-14 | 22-26 | 17-14
 24-20 | 16-19 | 21-14 |  6-10 | 18-14 | 22-26
 16-23 | 25-22 |  2- 7 | 30-25 | 26-31 | 20-16
 27-11 |  4- 8 | 31-27 | 10-17 | 15-10 | 12-19
  7-16 | 29-25 |  6-10 | 25-21 |  5- 9 |  3-12

Under the two-move restriction, the first two moves of a game of Checkers were chosen randomly. The choice was not from all 49 possibilities; the following six possibilities were excluded, either because they were certain losses for one side, or because they were, at least, regarded as excessively unbalanced.


The six excluded pairs of first moves were:

 9-14 21-17
 9-14 23-18
10-14 21-17
10-14 23-18
11-16 23-19
12-16 23-19

When this rule is used, an opening chosen as random is played once with one player moving first, and then again with the other player moving first, to prevent the luck of the draw from directly affecting the outcome of the game.

Later, it became the case that even the two-move restriction was inadequate to avoid the problem of excessive draws, and so a three-move restriction was adopted in the United States. Most other English-speaking countries remained with the two-move restriction until quite recently.

There are 176 possibilities for the first three moves in Checkers. Initially, 138 of those possibilities were used. One of them was removed, leaving 137, and more recently, 144 possibilities were used. In August, 2003, a further twelve openings were added to the choices, as noted on the website of the American Checker Federation. If I understand the statement of this correctly, it appears they were added not because they were found to be balanced, but simply that instead of being a certain loss for one player, that player could draw with careful play. Also, the original 137 openings are noted at another place on the site as ones that are sound for both players, although some give a degree of advantage to one or the other player. Of course, the number 137 happens to have some significance elsewhere than in the game of checkers.

The possible moves are:

9-13

 9-13 21-17   9-13 22-17   9-13 22-18   9-13 23-18   9-13 23-19   9-13 24-19   9-13 24-20

 9-13 21-17   9-13 22-17   9-13 22-18   9-13 23-18   9-13 23-19   9-13 24-19   9-13 24-20
 5- 9        13-22         6- 9         5- 9         5- 9         5- 9         5-9

 9-13 21-17                9-13 22-18   9-13 23-18   9-13 23-19   9-13 24-19   9-13 24-20
 6- 9                     10-14(C)      6- 9         6- 9         6- 9         6-9
 
 9-13 21-17                9-13 22-18   9-13 23-18   9-13 23-19   9-13 24-19   9-13 24-20
10-14(C)                  10-15        10-14(C)     10-14        10-14(D)     10-14

                           9-13 22-18   9-13 23-18   9-13 23-19   9-13 24-19   9-13 24-20
                          11-15        10-15        10-15(E)     10-15(C)     10-15

                           9-13 22-18   9-13 23-18   9-13 23-19   9-13 24-19   9-13 24-20
                          11-16(E)     11-15        11-16        11-15        11-15

                           9-13 22-18   9-13 23-18                9-13 24-19   9-13 24-20
                          12-16        11-16(E)                  11-16        11-16(E)

                                        9-13 23-18                             9-13 24-20
                                       12-16                                  12-16(C)

9-14

 9-14 21-17   9-14 22-17   9-14 22-18   9-14 23-18   9-14 23-19   9-14 24-19   9-14 24-20
(A)                                    (A)

 9-14 21-17   9-14 22-17   9-14 22-18   9-14 23-18   9-14 23-19   9-14 24-19   9-14 24-20
14-21(C)      5- 9         5-9         14-13         5- 9         5- 9         5- 9

              9-14 22-17   9-14 22-18                9-14 23-19   9-14 24-19   9-14 24-20
              6- 9        10-15                     10-15(C)     10-15(C)     10-15

              9-14 22-17   9-14 22-18                9-14 23-19   9-14 24-19   9-14 24-20
             11-15        11-15                     11-16        11-15        11-15

              9-14 22-17   9-14 22-18                9-14 23-19   9-14 24-19   9-14 24-20
             11-16        11-16                     14-18        11-16        11-16

                           9-14 22-18
                          12-16(C)

                           9-14 22-18
                          14-17(C)

10-14

10-14 21-17  10-14 22-17  10-14 22-18  10-14 23-18  10-14 23-19  10-14 24-19  10-14 24-20
(A)                                    (A)

10-14 21-17  10-14 22-17  10-14 22-18  10-14 23-18  10-14 23-19  10-14 24-19  10-14 24-20
14-21(C)      7-10         6-10        14-23         6-10(D)      6-10         6-10

             10-14 22-17  10-14 22-18               10-14 23-19  10-14 24-19  10-14 24-20
              9-13(E)      7-10(D)                   7-10(D)      7-10         7-10

             10-14 22-17  10-14 22-18               10-14 23-19  10-14 24-19  10-14 24-20
             11-15(E)     11-15                     11-15(D)     11-15(C)     11-15

             10-14 22-17  10-14 22-18               10-14 23-19  10-14 24-19  10-14 24-20
             11-16(E)     11-16                     11-16        11-16        11-16

             10-14 22-17  10-14 22-18               10-14 23-19  10-14 24-19  10-14 24-20
             14-18        12-16(D)                  14-18        14-18        14-18

10-15

10-15 21-17  10-15 22-17  10-15 22-18  10-15 23-18  10-15 23-19  10-15 24-19  10-15 24-20

10-15 21-17  10-15 22-17  10-15 22-18  10-15 23-18  10-15 23-19  10-15 24-19  10-15 24-20
 6-10         6-10        15-22         6-10         6-10        15-24         6-10

10-15 21-17  10-15 22-17               10-15 23-18  10-15 23-19               10-15 24-20
 7-10         7-10                      7-10         7-10                      7-10

10-15 21-17  10-15 22-17               10-15 23-18  10-15 23-19               10-15 24-20
 9-13         9-13                      9-14        11-16(E)                  11-16(C)

10-15 21-17  10-15 22-17               10-15 23-18                            10-15 24-20
 9-14(C)      9-14(B)                  11-16                                  15-19

10-15 21-17  10-15 22-17               10-15 23-18
11-16        11-16                     12-16

10-15 21-17  10-15 22-17
15-18        15-19

11-15

11-15 21-17  11-15 22-17  11-15 22-18  11-15 23-18  11-15 23-19  11-15 24-19  11-15 24-20

11-15 21-17  11-15 22-17  11-15 22-18  11-15 23-18  11-15 23-19  11-15 24-19  11-15 24-20
 8-11         8-11        15-22         8-11         8-11        15-24         8-11

11-15 21-17  11-15 22-17               11-15 23-18  11-15 23-19               11-15 24-20
 9-13         9-13                      9-14         9-13                     12-16

11-15 21-17  11-15 22-17               11-15 23-18  11-15 23-19               11-15 24-20
 9-14        15-18                     10-14         9-14                     15-18

11-15 21-17  11-15 22-17               11-15 23-18
10-14(C)     15-19                     12-16

11-15 21-17                            11-15 23-18
15-19                                  15-19

11-16

11-16 21-17  11-16 22-17  11-16 22-18  11-16 23-18  11-16 23-19  11-16 24-19  11-16 24-20
                                                    (A)

11-16 21-17  11-16 22-17  11-16 22-18  11-16 23-18  11-16 23-19  11-16 24-19  11-16 24-20
 7-11         7-11         7-11         7-11        16-23(E)      7-11         7-11(D)

11-16 21-17  11-16 22-17  11-16 22-18  11-16 23-18               11-16 24-19  11-16 24-20
 8-11         8-11         8-11         8-11                      8-11        16-19

11-16 21-17  11-16 22-17  11-16 22-18  11-16 23-18               11-16 24-19
 9-13         9-13(E)     10-15(C)      9-14                     10-15(C)

11-16 21-17  11-16 22-17  11-16 22-18  11-16 23-18               11-16 24-19
 9-14        16-20        16-19        10-14                     16-20

11-16 21-17               11-16 22-18  11-16 23-18
10-14(C)                  16-20        16-20

11-16 21-17
16-20

12-16

12-16 21-17  12-16 22-17  12-16 22-18  12-16 23-18  12-16 23-19  12-16 24-19  12-16 24-20
                                                    (A)

12-16 21-17  12-16 22-17  12-16 22-18  12-16 23-18  12-16 23-19  12-16 24-19  12-16 24-20
 9-13        16-19        16-19         9-14(C)     16-23(C)     16-20         8-12

12-16 21-17  12-16 22-17  12-16 22-18  12-16 23-18                            12-16 24-20
 9-14        16-20        16-20        16-19                                  10-15(E)

12-16 21-17                            12-16 23-18
16-19                                  16-20

12-16 21-17
16-20

with the following notes applying:

Of the 49 sequences of two moves, six are noted with note (A), leaving 43 without a note. Of the 176 sequences of three moves, one is noted with note (B), nineteen are noted with note (C), seven are noted with note (D), and twelve are noted with note (E), leaving one-hundred and thirty-seven without a note.

Eleven-Man Ballot

An alternative method of starting a game of Checkers in a randomly-selected fashion is called eleven-man ballot. In this form of the game, both players start with only eleven checkers: one checker, chosen at random, is removed from each side.

The checker to be removed from each side is chosen independently, and only the checkers in the front two rows are subject to removal, so there are 64 possible initial arrays. However, in this form of the game, a two-move restriction is also included.

Since which checkers are removed will change which opening sequences are playable, all 49 sequences of two moves are selected from. When the opening sequence involves moving a piece that has been removed, in the usual case, one of the two checkers behind the one that was removed is moved to the space it was removed from; the one that is so moved is the one that would move in the same direction as the removed piece is directed to move. When the removed piece is on the edge of the board, there is only one checker behind it, and so it would be the one to move, even though it has to move in the other forwards direction.

Because the number of possible combinations is quite large in this game, unplayable combinations are usually rejected through mutual agreement. Since each player now starts with 11 pieces, this rule can be viewed as resulting in a different game, and thus it is not as popular as the three-move restriction in tournaments, but it does have supporters who regard it as the most challenging form of the game.

As noted, of the dark pieces, one of 5, 6, 7, 8, 9, 10, 11, and 12 is selected for removal.

Of the light pieces, one of 21, 22, 23, 24, 25, 26, 27, and 28 is selected for removal.


The possible first moves, and the substitute moves if the piece to be moved was removed, are:

 9-13 ( 6- 9)
 9-14 ( 5- 9)
10-14 ( 7-10)
10-15 ( 6-15)
11-15 ( 8-11)
11-16 ( 7-11)
12-16 ( 8-12)

The possible second moves, and the substitute moves if the piece to be moved was removed, are:

21-17 (25-21)
22-17 (26-22)
22-18 (25-22)
23-18 (27-23)
23-19 (26-23)
24-19 (28-24)
24-20 (27-24)

As it will be noted below, the game of Polish, Continental, or International Checkers has not needed a two-move restriction or other similar measure to permit tournament play to continue. However, the rule for capturing in International Checkers is quite a bit different from that in the conventional game of Checkers in the English-speaking world, making for quite a different game. If the eleven-man ballot is sufficient to make Checkers truly competitive at the highest level, then that is most likely the direction in which Checkers will develop in the future. For those who would like a game which has the capturing rules of Checkers as they know it, and yet which is of sufficient complexity as not to experience the problems noted with Checkers, thus not requiring even a two-move restriction, there is perhaps another alternative: the Parker Brothers game of Inside Moves, formerly known as Camelot, or its ancestor Chivalry.

However, the fact that Checkers players have put up with such things as the two-move and three-move restrictions, rather than having abandoned Checkers, at least for purposes of tournament play, for something more elaborate, speaks strongly of their intense devotion to their game in its current form.


[Next] [Up/Previous] [Home]