Bao as a research problem

Bao is an African board game for two players. This document studies the question "can a move in a game of Bao end up in an infinite loop?".

I have treated this as a research problem to illustrate some of the ways in which a theoretical physicist's work proceeds.

Rules of Bao.

Bao is played on a board with 64 beans in 32 holes arranged in four rows of eight. Two rows belong to one player, and two to the other. The holes are called mashimo (singular shimo) and the beans are called kete (singular kete). Here is a view of the board, with each "O" being one shimo.
                   player A
Back row of A	O O O O O O O O
Front row of A	O O O O O O O O
Front row of B	O O O O O O O O
Back row of B	O O O O O O O O
		   player B
The complete rules of Bao are lengthy; you can find them at and more information at Here I mention one rule which seems as if it might lead to infinite loops.


In a type of move called kutakata, a player selects any shimo containing at least two kete (but not more than 15), picks up all the kete from it, then moves either anti-clockwise or clockwise around their two rows. One kete is put in each of the mashimo, starting from the shimo adjacent to the one from which the kete were taken. If the last kete falls into an empty shimo, the turn is finished. If the kete falls into an occupied shimo, the player picks up all the kete therein (including the last one played) and moves in the same direction as before, continuing to put one kete into the adjacent shimo until the last kete falls into an empty shimo.

Was that clear? If not, look at the examples which come next.

I'll call each sub-move of kutakata, in which the kete in one shimo are distributed, a `sowing' (until I find the Kiswahili word for it). I'll call each drop of a kete into a shimo a `drop'.

| Read on for an example of kutakata |

David MacKay <>
Last modified: Fri May 8 15:03:00 1998