What would be the strategy for the game Boxes? (Boxes is the game in which players connect dots on a grid and whoever encloses a box gets a point, along with an extra turn, until all lines are made)
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asked Oct 29, 2014 at 0:25
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2$\begingroup$ Elwyn Berlekamp has written a whole book on the subject. It is a surprisingly deep game, given how simple it seems. $\endgroup$– Ross MillikanCommented Oct 29, 2014 at 2:00
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4$\begingroup$ How is this a puzzle? $\endgroup$– MinimanCommented Oct 29, 2014 at 2:29
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2$\begingroup$ @Miniman - I see it as a question of game theory, too, instead of a puzzle. $\endgroup$– wbogaczCommented Oct 29, 2014 at 3:46
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1$\begingroup$ @wbogacz: Some games of that general flavor (e.g Bridg-It) may be regarded as puzzles, in that a relatively simple 100%-winning strategy exists for a particular player and the puzzle is to find it. Boxes doesn't happen to fall into that category, though I don't think that's intuitively obvious. In a sense, the question is "Can this game be viewed as a puzzle"; the answer is "Not in general; some situations might reasonably be viewed as puzzles [e.g. "In this situation, the next player has one guaranteed-winning move; find it."], though most are probably not very interesting. $\endgroup$– supercatCommented Oct 30, 2014 at 17:09
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1 Answer
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The game Boxes is another form of the game "Dots and Lines" or "Dots and Boxes", where the strategy is understood as a game of early control. The idea is to force the opponent into a condition to draw the third line into a long chain of near-complete boxes, where the ability to complete boxes with the fourth side yourself in a repetitive, connective manner is possible.
Strategy can better be explained on wikipedia, but in general terms details the use of a strategic sacrifice to the opponent to get to collect a few box wins, but be placed into a position to yield much greater returns for yourself because the last required move closes a third side into a long open chain.
