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.
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
The complete rules of Bao are lengthy; you can find them at
and more information at
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 <email@example.com>
Last modified: Fri May 8 15:03:00 1998