Bid-Tac-Toe

Bid-Tac-Toe is a game much like Tic-Tac-Toe, except that instead of alternating moves, you “bid” for the right to make the next move. So, in some situations, the same player may move twice or even three times in a row. Here are the rules:

Each player begins with $100 in the bank. The first player (let us say “X”) bids some whole number of dollars for the right to make the first move. The second player (let us say “O”) may then either accept the bid, thereby letting X make the first move, or may outbid X by bidding one dollar more, in which case O gets to make the first move. The player who wins the bidding then deducts the amount of his bid from his bank.

The player who did not win the bidding then gets to bid first for the right to make the next move. Play continues in this fashion until one player gets three in a row for a win. If there is no outright winner (a cat’s game), then the player with the most money left in the bank is the winner.

All bids must be made in whole numbers of dollars (no pennies!), and you may not bid more than you have in the bank (no borrowing!). You are allowed to bid $0, and there are rare situations where that is the best move.

If this game is played perfectly by both players, then the player to make the first bid at the beginning of the game can win every time. Finding the perfect strategy in all game situations is not easy, but it can be done.