Playing tic-tac-toe against a three-year-old for the fate of the world would actually be a really harrowing experience. The space of possible moves is small enough that he’s reasonably likely to force a draw just by acting randomly.
If he goes on a flat side, you’re golden (move in a nearly-opposite corner, you can compel victory).
If he goes in a corner, you go 90° away. Now, if he’s really acting randomly, he has a 1⁄6 chance to block your next-turn win.
Then you block his win threat, making a new threat of your own, that he has a 1⁄4 chance to block. If he does, he’ll make the last block half the time. So, a 1⁄96 chance to tie by moving randomly.
That would be enough to make me nervous if the fate of the world were at stake. Would you like to play Global Thermonuclear War?
1⁄96 (I was thinking of a different algorithm, but the probability is the same) would be enough to make me nervous, but I wouldn’t call it ‘reasonably likely’
Playing tic-tac-toe against a three-year-old for the fate of the world would actually be a really harrowing experience. The space of possible moves is small enough that he’s reasonably likely to force a draw just by acting randomly.
Not if you can go first.
So, you go center.
If he goes on a flat side, you’re golden (move in a nearly-opposite corner, you can compel victory).
If he goes in a corner, you go 90° away. Now, if he’s really acting randomly, he has a 1⁄6 chance to block your next-turn win.
Then you block his win threat, making a new threat of your own, that he has a 1⁄4 chance to block. If he does, he’ll make the last block half the time. So, a 1⁄96 chance to tie by moving randomly.
That would be enough to make me nervous if the fate of the world were at stake. Would you like to play Global Thermonuclear War?
1⁄96 (I was thinking of a different algorithm, but the probability is the same) would be enough to make me nervous, but I wouldn’t call it ‘reasonably likely’