Navigation Fritz Dooley Home Mancala Home Mancala Game Rules Mancala Resources Mancala Game Theory Thesis Introduction Terminology Structural Analysis of Mancala Human versus Computer Mancala Mancala Strategies Best Opening Move in Mancala Conclusion Exhibit 1: Rules of the Game Exhibit 2: Number of Game States email me: email@example.com
As computer-based approaches to solving the mancala game tree became less promising, I turned my thoughts to articulating the strategies by which I found myself actually playing the game. A set of definable strategies emerged; some of them having been foreshadowed in the example in Figure 10 through Figure 17.
Hoarding occurs when a player allows pebbles to accumulate in a certain bin, refusing to play that bin. This allows that bin to serve as a sort of “virtual mancala.” If the player succeeds in avoiding playing from that bin until the end of the game, its contents are swept to the mancala. A risk of this strategy is that it makes tempting bait for the opponent, as Yo’s eight pebbles in Figure 10 did for Mi. On the other hand, if one is a more foresightful player than ones opponent, baiting in this way can itself be a useful strategy. Who is to say that Yo didn’t foresee the unfolding of the game when she left the board in the state in which Mi found it in Figure 10?
Raiding is the name I give to the rule by which one captures a bin of the opponent’s pebbles by placing the last pebble of a move in an empty bin on ones own side of the board, directly across from the opponent’s bin being raided.
Starving ones opponent is refusing to repopulate the opponent’s side with pebbles carried around beyond ones own mancala. Yo starved Mi by failing to repopulate Mi’s side of the board, when Yo saw that Mi would go out in two moves. Starving is a useful strategy when one has enough pebbles on ones own side of the board to win the game, and can force the opponent to go out quickly. Risks of this strategy include failure to count correctly to make sure that one can outlast the opponent, and failure to take into account pebbles on ones own side of the board that the opponent might capture in the process of going out.
Rushing is seeking to go out of pebbles quickly on ones own side of the board. Sometimes a single board setup can lend itself to a player going out in one turn (by a carefully planned long sequence of moves), or to extending play for many more turns if that is to ones advantage. Again, Mi found herself with this choice in Figure 10, and unintentionally rushed the game when she might have been better served to stall.
Stalling is, of course, the opposite of rushing. Yo stalled following Figure 17, waiting for Mi to run out of pebbles. Stalling is a companion strategy to starving, but stalling does not necessarily avoid putting pebbles on the other players side. The two strategies can be used in conjunction with one another for the best outcome. But with all strategies, there’s no guarantee of their effectiveness unless you’re able to adjust and react.
Stuffing is the opposite of starving. It is a defense against being rushed out of the game. It is also a defense against being raided. In Figure 18 (Mi’s turn), bin D is at risk of being raided by a play from H. Mi “stuffs” Yo’s side with pebbles from F, making it impossible for Yo to raid D in any combination of moves from G, H, and I. Mi sacrifices three pebbles over to Yo’s side of the board, but the tradeoff is justified because she retains eight pebbles on her own side.
Mi engaged in a successful looping maneuver in Figure 16. Looping is going all the way around the board to raid pebbles from an opponent’s bin which is too far to the left to be accessed without the loop. There is usually an overhead cost of five pebbles involved in a loop, as one populates the opponent’s side on the way around. As has been shown, pebbles on the opponent’s side of the board often ultimately wind up in the opponent’s mancala. Looping is therefore usually reserved for occasions when considerable booty is involved.
Since game rules state that pebbles cannot be touched or handled except when being played, looping is often an effective ambush strategy in a game where the opponent is not keeping careful count. Bins fill easily to the point that pebbles cannot be counted by mere inspection. Once an opponent has lost count of the pebbles in a bin on your side, you have the advantage of a surprise attack when you know that the number of pebbles has reached the target for making a successful raid.
Mi’s looping maneuver was also a successful ambush because she was able to build up the pebbles in bin F during the same turn in which she made the loop. The three pebbles sitting in F at the beginning of her turn did not appear to Yo as a serious threat for a looping play.
A beginning player will often avoid being raided at all costs. A careful player will count the cost of being raided (or of giving up pebbles by playing around to the other side of the board) and weigh the cost against alternatives or simultaneous benefits. Sometimes the future cost of avoiding a present raid is higher than the present cost of being raided. Sacrificing is deliberately giving up pebbles for a greater net gain or lower net loss. Sacrificing, as seen above, can also be a good baiting strategy.
Though not an explicit strategy in itself in the way that the other mentioned strategies are, setting up is a tactic that advanced players employ. As in chess, it involves building a competitive board position that may lend itself to a variety of strategies, depending on choices made by the opponent.
Many strategies interact with each other, or can be shifted from one to another as the unfolding game demands. For example, hoarding is a very powerful strategy when it can be pulled off effectively, but is very difficult to maintain through the end of the game. Hoarding buys an option on looping, however, which can prove invaluable. It also can be switched to a stuffing strategy if necessary.
Other General Principles of Play
Playing from Bin F as Often as Possible
Games are often won or lost on the margin. One or two extra pebbles stashed away in the mancala can make the difference. A technique I often use is to empty my bin F as early as possible in the game. Then whenever I get a pebble in it, I play that pebble into the mancala on my immediate next move, whether as part of the current turn or the next. This not only accelerates the accumulation in the mancala; it also avoids having to pass pebbles over to the opponent if more than one pebble accumulates in bin F.
Avoiding Excessive Buildup
Similarly, unless engaging in deliberate hoarding, I often try to keep the number of pebbles in each bin less than or equal to the number needed to hit my own mancala. This preserves the option of starving the opponent; it allows more often for compound turns, which build up the mancala quickly; and it gives great flexibility in building a setup within a single turn, as Mi accomplished in the example.
Timing Ones Plays to the Other Side
It is inevitable that Mi must occasionally overshoot her own mancala and play pebbles to Yo’s side. There are ways for Mi to time this event, though, in order to minimize the cost. Particularly, when Yo has at least enough pebbles in I, H, and/or G to reach her own mancala, then pebbles played into those bins will often eventually be played on around the board back to Mi’s side. A good player can watch for such opportune times to unload too-full bins, or can weigh that factor when deciding whether to unwind a hoarding strategy. This also reduces the overhead cost of a looping maneuver. The strategy can be employed preemptively to keep Yo from making a compound turn (hitting her mancala several times in succession in a single turn).
(c) 2008 by Fritz Dooley