Wednesday, June 20, 2012

Pay-to-Play Tic-Tac-Toe

This is my favorite casual game for two with little equipment. It adds a lot of richness to the tic tac toe game, and eliminates the first-mover advantage.
The rules start with tic tac toe, but you have an account of play points. The first player gets one point; ever 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:
  1. 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

  2. Bob gets two points and plays on the left side. That costs two points, so his balance goes back to zero.
    OX
         Bob's points:0
         Alice's points:-3

  3. Alice gets two points, bringing her balance to negative one; that's not above zero, so she can't play.
    OX
         Bob's points:0
         Alice's points:-1

  4. Bob plays in the corner, which costs three points, bringing his balance to negative one.
    OX
    O
         Bob's points:-1
         Alice's points:-1

  5. Alice gets two points, bringing her balance to one, so she can play on the corner (cost three) to block Bob.
    X
    OX
    O
         Bob's points:-1
         Alice's points:-2

  6. Bob plays in the corner, which costs three points, bringing his balance to negative two.
    X
    OX
    OO
         Bob's points:-2
         Alice's points:-2

  7. Alice's balance goes to zero, which isn't positive, so she can't play to block Bob.
    X
    OX
    OO
         Bob's points:-2
         Alice's points:0

  8. Lucky for her, Bob also can't play: on his turn, his balance goes to zero.
    X
    OX
    OO
         Bob's points:0
         Alice's points:0

  9. Now Alice gets two and plays on the bottom to block Bob, returning her balance to zero.
    X
    OX
    OXO
         Bob's points:0
         Alice's points:0

  10. Bob plays on the top.
    XO
    OX
    OXO
         Bob's points:0
         Alice's points:0

  11. Alice sees she can't win, so she passes, keeping her two points.
    XO
    OX
    OXO
         Bob's points:0
         Alice's points:2

  12. Bob plays on the right.
    XO
    OXO
    OXO
         Bob's points:0
         Alice's points:2

  13. Alice is forced to play at the top.
    XOX
    OXO
    OXO
         Bob's points:0
         Alice's points:1

  14. 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:

Ethan Bradford said...

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.

Aashit Singh said...

The posts are really interesting. I m thinking about giving up PC games to go for these.