With thanks to Yishin Cho and Karl Brandt for their help in collating and interpreting this information.
This Korean draw and discard game was reported by Stewart Culin in his book, Chinese Games With Dice And Dominoes (1895) under the name Tjak-Ma-Tchi-Ki ('making pairs'), which is simply a different way of writing the same name using the Roman alphabet. The same description appears in his book Korean Games (1895).
Korean dominoes, known as gol-pae (골배) come as a set of 32 tiles, equivalent to a Chinese domino set. The aim is to be the first player to a complete winning hand of three pairs.
Players and Equipment
One set of 32 tiles is used for the game. The 11 'civilian' tiles ([6:6], [1:1], [4:4], [3:1], [5:5], [3:3], [2:2], [6:5], [6:4], [6:1], [5:1]) are duplicated, and two identical tiles form a pair. The 10 'military' tiles appear only once each. Military tiles with the same total number of spots form pairs:
- [6:3] with [5:4],
- [6:2] with [5:3],
- [5:2] with [4:3],
- [4:1] with [3:2].
Finally the [4:2] and [2:1] form a pair called supreme.
There can be 2, 3 or 4 players. The direction of play is anticlockwise.
To choose the first player each draws a tile from the shuffled set. If any player draws the [2:5] (koan-a) that player plays first. If not the first player is whoever drew the tile with most spots. It is not specified who should play first in subsequent hands - possibly the winner of each hand should be the first player in the next.
The tiles are shuffled face down. The first player draws six tiles and the others draw five tiles each. The remaining tiles form a reserve, a face-down row from which tiles are drawn during the game. Culin says that a sheet of paper or bamboo should be laid on top of this row after the deal: this is presumably to make it harder for players to cheat by recognising imperfections on the backs of the tiles.
The first player begins by laying down one or more pairs if held. If able to lay down all six tiles as three pairs, the first player immediately wins the hand. If not, the first player discards one of the unpaired tiles face up, and the turn passes to the right.
Each player in turn may either claim the tile discarded by the previous player to complete a pair or draw one of the undealt tiles. Having laid down any pairs, the player discards a tile face up and the turn passes to the next player.
This continues until a player completes three pairs and wins the hand.
If there are two or three players, a player cannot use the 6-6 tiles to form their third and final pair, but with four players this is allowed.
If the winner's third pair is completed using a tile drawn from the reserve, the winner is paid the agreed stake by each opponent.
If the winner's third pair is completed by taking the previous player's discard, the discarder must pay the winner on behalf of all the other players - so the discarder pays two stakes to the winner if there are three players , or three stakes if there are four players.
The sources do not say what happens if no player succeeds in completing three pairs. Probably in this case there is no winner, the tiles are shuffled, and the first player in the drawn game plays first again.
Unfortunately, using the rules stated above, on which all the sources seem to agree, drawn games are quite frequent. With two players around 14% of games will end with no winner, with three players almost half of all games will end this way, and with four players around 85% of games will have no winner.
Dmytro Polovinkin has suggested that to avoid this problem, players should be allowed to take a discarded tile that forms a pair with a tile in their hand even if it is not their turn to play. If this does not immediately result in a win, the player who took the tile discarded tile discards an unwanted tile in the usual way and the play continues anticlockwise from that player. Relaxing the rules in this way increases the precentage of games with a winner to over 95% if there are three players and over 90% with four players.
Some play that a player's third pair, with which they win the game, can only be made by matching a tile in hand with a tile drawn from the reserve. In other words, it is impossible to win by taking a discarded tile.
Karl Brandt describes a version in which the shuffled tiles are placed in a row and tiles are drawn from one end of the row.
A different method of pairing the military tiles is found in some sources, including Stewart Culin's book:
A short account of the game appears in Lee E-Wha’s Korea’s Pastimes and Customs – A Social History (2001), but the description creates the impression that the author was unfamiliar with the game. It is stated that the set features 8 groups of 4 identical tiles even though the accompanying illustration is of a normal Chinese-style domino set. E-Wha implies that the payment to the winner is doubled for each identical pair of tiles in the winner's hand, which would make sense if applied to the game described above in which there are identical (civil) and non-identical (military) pairs, but not if the set were as described by E-Wha (8 sets of 4 identical tiles), since that would have no non-identical pairs.