| This means, if a region of 6 to 9 vacant squares is fenced off, it becomes a "dead zone" where no one may play. If you have no legal move on your turn, you lose.The winner is the last player to make a move. This can be an absorbing and fun game, and is usually finished in 20 minutes or less. The pieces are fun to play with! There are several puzzles involving pentominoes, and this game gives you four complete sets, made of durable plastic! The board is framed in plastic, with a raised border around the perimeter. This helps protect the board, and helps to align pieces that touch the edge. Unfortunately, the board I got was not quite true. The pieces are made accurately, but if you try to fill all 200 squares, some pieces will always pop out somewhere. Perhaps this is why the rules prohibit fencing off regions of 1-4 squares. Besides speeding up the game, it tends to result in more empty space, so play is still possible even if the board is a bit warped. I suppose I could shave down the sides a little... Ironically, although the opening is the most difficult phase of the game to understand, it is possible to throw away the game on the first move of a two-player game! If the first move occupies either one or two of the four central squares, then in almost every case, the opponent can respond by making the rotationally symmetric move. I call this the "symmetric strategy." Once the central region is closed off, White cannot break symmetry, and Black will make the last move. But there are a couple of exceptions to this. How can White occupy one or two of the four central cells on the first move, and yet not lose to the symmetric strategy? Note that these moves might very well be losers, but Black will have to try another approach. Answer Suppose the board were 10x9 instead of 10x10. Now there are just two central cells, instead of four. White makes a first move which occupies precisely one of the two central cells. Black responds with the symmetric strategy for as long as possible. If this strategy becomes impossible, Black makes the best possible sequence of moves. Even so, White is able to win the game. How could this happen? Answer The move tree in the opening is quite dense, but each move drastically reduces the number of legal moves remaining for each player. For example, if White makes the initial move 12-D3-C5 as shown in the previous diagram, Black's legal responses are reduced from 3960 to 2988, and White's choices go down from 3960 to 2632. As far as the first move is concerned, if you don't count symmetrically identical moves or moves that immediately lose, you need consider only 427. Even so, an exhaustive "brute force" search is not likely to get past 3 ply in the opening. There are natural criteria for evaluating early moves. For example, the asymmetric pieces 3, 4, 7, 12, and especially 6, can be placed on the board in lots of different ways, and are therefore more likely to be playable in the endgame. 12-D3-C5 is probably a bad first move; piece 12 should be saved for later. Piece 1 is a much better piece to "get rid of" early on; there are only 60 ways to play that piece (as opposed to 568 ways for piece 6), and it is probably the most difficult piece for your opponent to try and fence off a region of that shape. The most important goal to aim for is to fence off a move only you can make, and which your opponent cannot block. Such a region is usually 5 squares in size, but could also be a portion of a larger region (10 squares or more). Once you get this reserve move, if you can prevent your opponent from doing the same to you, a win is assured. Naturally, you'd want to keep that move in reserve until the end. A reasonable secondary objective in the opening would be to reduce the opponent's responses as much as possible, while reducing your own future choices as little as possible. Here is a puzzle, to introduce you to tactics. The regions are labeled to help clarify the solution. |
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