The rules start with tic-tac-toe, but you have an account of play points. The first player gets one point; every subsequent turn a player gets two points. It costs two points to play on an edge square, three to play on a corner, and four to play in the center (i.e. it costs one point per tic-tac-toe that could be made through that square). You can make a play that makes your account go negative, but you need a positive account to play. Even if you have the points to play, you may pass on your turn and keep the points.
Here's an example game:
- Alice goes first, gets one point, and plays in the center. That costs four points, so her balance is negative three.
X Bob's points: 0 Alice's points: -3
- Bob gets two points and plays on the left side. That costs two points, so his balance goes back to zero.
O X Bob's points: 0 Alice's points: -3
- Alice gets two points, bringing her balance to negative one; that's not above zero, so she can't play.
O X Bob's points: 0 Alice's points: -1
- Bob plays in the corner, which costs three points, bringing his balance to negative one.
O X O Bob's points: -1 Alice's points: -1
- Alice gets two points, bringing her balance to one, so she can play on the corner (cost three) to block Bob.
X O X O Bob's points: -1 Alice's points: -2
- Bob plays in the corner, which costs three points, bringing his balance to negative two.
X O X O O Bob's points: -2 Alice's points: -2
- Alice's balance goes to zero, which isn't positive, so she can't play to block Bob.
X O X O O Bob's points: -2 Alice's points: 0
- Lucky for her, Bob also can't play: on his turn, his balance goes to zero.
X O X O O Bob's points: 0 Alice's points: 0
- Now Alice gets two and plays on the bottom to block Bob, returning her balance to zero.
X O X O X O Bob's points: 0 Alice's points: 0
- Bob plays on the top.
X O O X O X O Bob's points: 0 Alice's points: 0
- Alice sees she can't win, so she passes, keeping her two points.
X O O X O X O Bob's points: 0 Alice's points: 2
- Bob plays on the right.
X O O X O O X O Bob's points: 0 Alice's points: 2
- Alice is forced to play at the top.
X O X O X O O X O Bob's points: 0 Alice's points: 1
- That's a cat's game, but with a small differentiator: Alice has a remaining balance of one and Bob has a balance of zero, so Alice wins.
2 comments:
We haven't come up against the situation where both players pass forever. I suggest the rule that a player can't pass with a positive account for two turns in a row (so that, e.g., if your account is at -2, you can pass three times; twice to get to 2, and once at 2).
We've discussed, but not played, assigning a number of points granted for a tic tac toe, so that you can have a multi-game tournament with accumulated points. How many points should it be? I'm thinking 8 points, the cost of playing an edge-to-edge win. This makes a corner-to-corner win give a profit, but just barely, against a player who hoards play points; a side-to-side or an on-edge win against a hoarding player gives a profit of 3.
The posts are really interesting. I m thinking about giving up PC games to go for these.
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