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Comment by abstractbill | Hacker News Reader

... the players cannot affect the result by their play ... a game starting with an odd number of crosses will be a first player win, while a game starting with an even number will be a second player win regardless of the moves.

That makes the brussel variation a lot less interesting I think.

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By enumerating all possible moves, one can show that the first player can always win in normal-play games starting with n = 3, 4, or 5 spots. The second player wins when n = 0, 1, 2, or 6.

Am I missing something, or is the outcome of every sprouts games predetermined?

Thats exactly what i said!! What is the big deal? Actually I did play someone with 6 dots and won... so i think there might be ways of changing the outcome, for example if you use a line to encircle other lines to cut off their access. Either way, I thought this was a strategy game and it seems closer to the "dots and boxes" pencil game, ie...

clarification: i played someone as player 1, with 6 dots, and won.

Brussels Sprouts is completely determined: it doesn't matter how you play, the winner is a function only of the number of spots.

Sprouts is not; one can play it well or badly, and it makes a difference.

Dots-and-boxes is a game with real strategy to it, too. See "Winning Ways" or Berlekamp's book that's just about D+B.

Just because he can force a win, doesn't mean he will. So it's still fun for novices, or large numbers of initial spots.

This means the first player wins for n = {3, 4, 5} if both players play perfectly. Similarly, if both players play perfectly, tic tac toe and checkers games result in draws. Fortunately, humans can make mistakes, rendering the outcomes less certain. :-)

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