In the all-digital future, X and O are banished from the game of tic-tac-toe.
They are replaced by 1 and 0, the the result of such a game might look like this:
1 | 0 | 1
- + - + -
0 | 1 | 1
- + - + -
0 | 1 | 0
Under the usual rules that require getting 3-in-a-row, it would be a draw.
But this is the digital age, and there are different rules for winning.
If we sum the eight rows of three numbers we get 2, 2, 1 (horizontally) 1, 2, 2 (vertically) and 2, 2 (diagonally).
Six of the sums are even, and two are odd.
The final parity of the board is thus even, and the game is said to have an even outcome.
If there were more odd sums than even, the game would have an odd outcome.
If there were four even (and therefore four odd) sums, the game would have a neutral outcome.
The game is played as follows:
The winner of a fair-coin toss (call him player A) chooses whether to play first or second.
The other player (call her player B) decides whether she wants an odd, even, or neutral game outcome.
On each turn, a player places his choice of either a 1 or a 0 on any unoccupied place on the grid.
As in normal tic-tac-toe, players alternate turns; but here on each turn a player may play either a 0 or a 1.
When the places are filled, the board is examined to determine whether it is odd, even or neutral.
If the final board parity matches player B's choice, player B wins; otherwise player A wins.
The questions to answer are:
- Is there an advantage to winning the coin toss?
- Is there a winning strategy for either player?