What is bantumi?

Bantumi is an African board game, which resembles chess in that the game is entirely decided by skill - there is no random element. I came to know it as bantumi but it is also known as mancala. The rules themselves are remarkably simple, but the strategies available are many and varied, and can be extremely complex.

I'm slightly ashamed to admit that I only encountered this game recently, and then as a digital incarnation on a recent Nokia 'phone. However, since then I've been teaching it to anyone who'll listen. I suggest you do the same.

The board

I suspect bantumi may mean bean in some central African language (not Afrikaans - thanks StrawberryFrog), since the game is played typically with beans. Of course, any counters will do, and I've been using stones because they're conveniently sized. You'll need forty-eight of these, with twelve small cups and two big ones. Then lay them out as suggested in this gorgeous diagram:

  _   <> <> <> <> <> <>   _
 / \                     / \
 \_/                     \_/
      <> <> <> <> <> <>

Put four stones into each of the small pots. Now onto the rules. Sitting comfortably? Then I'll begin.

The rules

Bantumi is a game for two players, who sit facing each other; one above the board depicted and one below. The aim is to get more beans into your big pot -- the one on your right -- than your opponent does into his. The game continues until one player has no more beans in his small pots - the six on his side.

Players take it in turns to pick one of the six small pots on their side. The beans are taken from the chosen pot and dropped one by one into the other pots, proceeding in an anti-clockwise way round the board. That includes dropping into their own big pot - the one on the right - and the opponent's small pots. However, you never drop a bean into the opponent's big pot.

This continues until all the beans picked up have been dropped off again. One of three things then happens:

  • You drop the last bean into your own big pot. You now earn another turn. You can have as many turns as you like in this way, while you continue to finish in the big pot.
  • You drop the last bean into a small pot that was previously empty. This is the real meat of the game. Not only does this final bean go straight into your big pot, but also all beans from the opposite small pot of your opponent. This is stealing and it's usually the stolen beans that decide the outcome of the game. The strategical implications of this rule are enormous.
  • You finish anywhere else. Play switches to your opponent.

Play continues until one player has only empty pots. Then the other player empties any beans left in his own small pots into his big pot, and player's totals are counted up.

Openings

Another similarity to chess is in the variety of different openings available. However, due to the highly chaotic way in which the game develops in comparison to chess, a bantumi opening usually only consists of one or two moves. And whereas a chess player could (theoretically) play twenty different opening moves, a bantumi player has at most eleven possibilities before his opponent has a turn. For these reasons, the opening is not quite so important nor so varied as in chess. Nevertheless, here are a few options:

The most obvious opening is clearly the third pot from the left - what I would call Pot 4, numbering from the right. This then immediately gets one bean in the big pot and earns you another turn. You still have to think of another move, of course. But what?

Another opening that I have seen the Nokia play, on higher difficulty levels, is Pot 1. This also puts away one bean, and makes life a little more difficult for the opponent. You do forfeit the extra turn however.

It doesn't take a genius, then, to see that a very powerful opening is to combine the above two: Pot 4, to get an extra turn, and then Pot 1 to obstruct your opponent. I've used this opening many times and it seems to set you up nicely. YMMV.

The strategies

There are a number of different strategies available to the discerning bantumi player, but here I present a "priorities list" which, except in the most unusual situations, is at least worth bearing in mind.

  • Priority 1: Get as many turns as possible: If you can finish in the big pot, do. It's likely that you will sometimes have several pots than can earn you an extra turn. In this case, start from the right - this avoids disturbing your other "extra turn" pot, so you can get as many extra turns as possible.
  • Priority 2: Wherever your opponent has empty pots, make sure you have empty pots opposite: This makes it much more difficult for your opponent to steal from you. It's still not impossible, as they could create new empty pots during the course their turns; the ability to spot these in advance comes simply from experience.
  • Priority 3: Create your own points of attack: Once you are in a safe position, it's time to start putting pressure on your opponent. Create empty pots opposite full pots of your opponent to force them to offload. Leave, say, four counters in Pot 5, restricting your opponent's options as he does not wish to over-run his own pots and effectively gift you an extra turn. Create combinations of multiple empty pots, such that they must inevitably allow you to steal. The opportunities for attacking play are infinite and a highly individual choice.

A game theory perspective

As explained in safe position, a non-random game inevitably gives advantage to one player from the outset. In a symmetrical game such as Bantumi, it is usually safe to assume that this is the player who goes first, although it is possible to devise pathological games where this is not the case. A consequence of this is that there is a perfect strategy for the first player, against which no victory is possible. In fact, this strategy has recently been compiled, via some enormous computation power. You can read more on that little adventure under game theory.

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