Clump Strategies

The general idea is to stay alive for as long as possible. But how long is enough?

Sixteen hexes can be played (eight by each player), without having a clump. There are several different such patterns; you'll find one after playing a a few games. Seventeen played hexes, on the other hand, always result in a clump for one or the other player (prove this!).

So a winning strategy for the second player is to try to make eight moves; the first player is then forced to make a clump on their ninth move. (Incidentally, it is possible to color nine hexes without a clump (how?), though you can't get to this position in a real game since the other player will have already clumped out by then).

Trying for eight hexes turns out to be about the best strategy for the first player too, though it's not guaranteed to win. It turns out that the first player has a significant disadvantage. Since there's no draws in Clump, either the first or the second player must have a guaranteed winning strategy, and it sure doesn't seem to be the first player!

So, as you are playing, try to foresee a configuration having 8 of your hexes without a clump. If you can see more than one such configuration, even better! At the same time, look for configurations of 8 hexes that your opponent can achieve. The best moves are those which preserve your possibility of getting an 8-hex while at the same time denying a needed hex to the opponent.

As you play, you will note that some open hexes will be forbidden to the opponent, since they would produce a clump. You can delay playing into these hexes, since they will always be available to you. It is often better to play on a hex that is open to both players, particularly if that hex is also a critical one for the opponent.

Sometimes, however, it's better to let your opponent make a commitment by playing first in a common area. Remember: "Look before you leap", but "He who hesitates is lost!"

By the way, here's how the computer plays at the different levels:

Bozo At this level, the computer chooses moves at random from those which do not cause an immediate clump. It's amazing how easy it is to lose against a random player!
Novice The novice computer still plays randomly, but favours the corners initially. The central squares are dangerous - they commit the pattern too soon!
Amateur The computer tries to play in a hex which (a) does not immediately cause a clump, and (b) does not cause a clump if the opponent plays there either. The idea is to reduce the number of open moves for the opponent.
Professional The professional approach is ridiculously complicated. The computer enumerates the lists of the largest subsets of open hexes which can be played by itself and by the opponent, and then picks the hex which appears most often in the combined list. The idea is to preserve the maximum number of open moves for oneself, while reducing the number of open moves for the oponent.
Master The computer goes for the corners for the first three moves, and from the fourth move on computes the entire game tree. That's why it takes so long for the fourth move when it's playing first. You have to play rather accurately to beat it.

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