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Incomplete information Tic-Tac-Toe

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iirc both players can force draws, so it seems whoever rolls more 3s or 4s would win?

We have the following situations

Win win -> no one wins due to draw

Win draw -> player 2 forces draw

Win lose -> both players get points

Draw lose -> i think player 1 can play suboptimally to draw

Draw draw -> both players get what they want
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So if I roll 3 or 4, my game becomes Tic-Tac-Toe-Tie
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i think an interesting rule would be that neither of you reports your score at all to the other person, only that they have won. it would be a lot spicier. otherwise, there are some situations where your only play is to go for something mental, but it's hard to do that if they have the information of you tallying a point or not
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I highly recommend the game Gobblet Gobblers for anyone interested in this tic tac toe variation. It adds a lot of complexity and strategy to your old tic tac toe.

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