Pong Hau K'i
Pong Hau K'i (Chinese: 裤裆棋, pinyin : kùdāng qí, Cantonese : Pong Hau K'i) is a Chinese traditional board game for two players. In Korea, it is known as Ou-moul-ko-no or Umul Gonu (우물고누)[1][2] or as Gang Gonu (강고누). "Umul" translates as "a spring", and the appearance of the board is like that of a spring in the center, with water running out in all directions. "Gang" translates as "river", and has a similar interpretation. Equivalent games are also played in Thailand (Sua tok tong) and in northern India (Punjab: Do-guti).
The board consists of 5 vertices and 7 edges. Each player has two pieces. Players take turns to move. At each turn, the player moves one of his two pieces into the adjacent vacant vertex. If a player can't move, he loses.
Only one type of position can make a player lose. If both players play perfectly, the game continues endlessly with no winner.
It is a children's game in both China and Korea, and is often used for childhood education.
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One kind of board.
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One kind of board, esp. for Pong Hau K'i.
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One kind of board.
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One kind of board, esp. for Umul Gonu.
Starting position
The starting position for Pong Hau K'i is shown on the left. The two players are labeled as "A" and "B"; the central spot is left unoccupied at the beginning. The first move must be "A" moving either of their pieces to the center. By symmetry, those two possible moves are equivalent.
Analysis
This game has been analyzed by P. Straffin,[3] who showed that it is a draw so long as both players can see 2-ply ahead, i.e. see the results of their move and of what their opponent would do in response. In particular, any win in Pong Hau K'i must go through the position shown on the left (or a symmetrically equivalent position). In this position, with "A" to move, that player has two choices: (1) They can move their top piece West along the top edge; or (2) They can move their bottom piece North along the left edge. In case (1), the game continues. But in case (2), the game will almost surely end quickly. If "B" then moves their bottom piece to the left, they win. If they are foolish enough to move their center piece instead, then "A" can win by moving their top-right piece to the center. Thus with "2-ply lookahead", player "A" can see the result of their (bad) move of the bottom piece (the first ply), realize that "B" then has a winning move (the second ply), and hence "A" will choose to not make that move.
Notes
References
- Bell, R. C. (1979). Board and table games from many civilizations.. (Revised Edition). New York: Dover Publications Inc. ISBN 0-486-23855-5
- Bell, R. C. (1980). Discovering old board games. (2nd Edition). Princes Risborough, Bucks.: Shire Publications. ISBN 0-85263-533-8
- Straffin, Philip D. (1995). "Position Graphs for Pong Hau K'i and Mu Torere". Mathematics Magazine, 68(5), Dec. 1995, pp. 382–386.
See also
In China, there are some traditional board games like Pong Hau K'i.