4 ms·
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
by benjamincanfly 18y ago
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?
- timm5 18y agoThats 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...
- timm5 18y agoclarification: i played someone as player 1, with 6 dots, and won.
- gjm11 18y agoBrussels 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.
- gjm11 18y agoDots-and-boxes is a game with real strategy to it, too. See "Winning Ways" or Berlekamp's book that's just about D+B.
- ars 18y agoJust because he can force a win, doesn't mean he will. So it's still fun for novices, or large numbers of initial spots.
- jacobolus 18y agoThis 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. :-)