Kalah Page

last updated September, 2000

Kalah is a count-and-capture game that is a fairly recent addition to the large group of Mancalah games. (see awale links for an overview over these games). According to the Museum and archive of games at the University of Waterloo, The game is introduced in the 1950's commercially by the "Kalah Game Company".

Rules of the game

Kalah is played on a board with two rows of round pits and two additional oval collect pits, called 'kalah' or 'kalahah'.

To begin playing, the two players sit on opposite sides of the board and deposit three (four, or up to six) seeds in each of the twelve round pits. Each player in turn picks up all the seeds in any one of their own six pits and puts them one by one in each pit around to the right. If there are enough seeds to go beyond that player's kalah, these seeds are distributed in the opponent's pits (except in the opponent's kalah). All seeds placed in an opponent's pit now belong to the opponent.

If the player's last seed lands in that player's own kalah, that player gets another turn. If the last seed lands in an empty pit on that player's own side, that player captures all of the opponent's seeds in the opposite pit and puts them in that player's kalah together with the capturing piece.

The round is over when all six pits on one side are empty. The other player adds the remaining seeds in the pits to his kalah. The score is determined by who has the most seeds.

Play Kalah on the web

There is a growing number of places on the web at which you can play Kalah.

Play Kalah on your computer

At the following two sites you can download a Kalah game for MS Windows. There is also a Kalah version for the Palm top computer: And on your Nokia Cellular Phone (They call it Bantumi...) For related mancala-type programs see:

Solving Kalah

The game of Kalah-6(5) (six pits per side and five seeds per pit) has recently been solved by Geoffrey Irving at Caltech! It appears that the starting player wins. Geoffry Irving has used all the latest tricks that are known from Game Research in Artificial Intelligence: Alpha-beta search, MTD(f), transposition tables, end game database, and so on. At this moment he is working on a parellel version of the program in order to solve Kalah-6(6).

The game values of Kalah can be summarized in the following table:

(Ref: George Irving, Jeroen Donkers, and Jos Uiterwijk (2000). Solving Kalah. Submitted to the ICGA Journal.)

Full-game databases

For our research on probabilistic opponent modelling, we are interested in measuring the quality of heuristic evaluation functions. Therefore we created full-game databases for smaller instances of Kalah. These databases contain all board situation that can occur during a real play (about 1 percent of all possible compisitions), their game-theoretic value, and the optimal win/loss depth. The table below gives a summary of these databases. Per instance, the game-theoretic value and the win/loss depth of the start situation is given, the number of positions in the game (the size of the game-graph), and the number of compositions (size of the state space).

pits / seeds123456
1 Draw in 1
2 pos /
20 com		 Loss in 1
2 pos /
70 com		 Win in 1
2 pos /
168 com		 Loss in 2
3 pos /
330 com		 Win in 3
4 pos /
572 com		 Draw in 5
2 pos /
910 com
2 Win in 2
8 /
252		 Loss in 5
24 /
2,574		 Loss in 6
138 /
12,376		 Loss in 4
168 /
40,698		 Win in 5
58 /
106,260		 Win in 11
2482 /
237,510
3 Draw in 5
73 /
3432		 Win in 8
2,941 /
100,776		 Win in 11
24,936 /
961,400		 Win in 20
190,579 /
5,259,150		 Win in 13
755,748 /
20,590,944		 Loss in 15
1,522,350 /
64,448,228
4 Win in 7
880 /
48,620		 Win in 10
226,774 /
4,085,940		 Win in 13
4,604,996 /
38,567,100
5 Draw in 10
11,465 /
705,432
6 Win in 13
178,708 /
10,400,600

Kalah Facts

Did you know... Jeroen Donkers,