An "Underdog" Game
by Stephen Sniderman


Players:   Two — "ODD" and "EVEN". ODD takes the odd turns (1, 3, 5, etc.); EVEN takes the even (2, 4, 6, etc.)

Equipment:   Pencil and paper

To start:   Make a 4 x 6 grid. One player (decided randomly) writes an X on any square of the grid. The other decides whether to be ODD or EVEN.

Goal:   EVEN wins if, at the end of the game, there are six or more Tic-Tac-Toes on the board. Otherwise, ODD wins. A Tic-Tac-Toe consists of exactly three consecutive Xs or three consecutive Os in a row, column, or diagonal. If a row, column, or diagonal contains four or more consecutive squares with the same symbol, it does not contain a Tic-Tac-Toe. A symbol may be part of two or more Tic-Tac-Toes going in different directions, so it is possible to complete two, three, or even four Tic-Tac-Toes in a single move.

To play:   On your turn, you may write an X or an O on any empty square.

Ending the game   The game is over when all the squares have been filled in.

SIX-TAC-TOE is an “underdog” game because the two players’ chances of winning are almost certainly not equal; one player, the so-called underdog, has a disadvantage, even though it may be very slight. But which player (EVEN or ODD) has the advantage? How big is it? We don’t know, so we’re asking for your help.

    Demonstrate which player has an advantage (or that neither does).

    Demonstrate how much of an advantage EVEN or ODD has.

    Figure out a way to “level the playing field,” that is, to guarantee that both EVEN and ODD have the same chance of winning a single game.

Kadon will award a prize to the best answers received by January 1, 2008. Send your answers to:

Stephen Sniderman
2214 Coronado Avenue
Youngstown, OH 44504

Results will be added here with next issue..

The Life of Games
No. 4 (April 2007)
©2007 Kadon Enterprises, Inc.