"This one's going to be a tie," Inez announces.
You open your mouth to object but think better of it.
"Watch this," Inez says. She takes her pen back and draws an X in Square h:
"I now have two in a row, so you have no choice but to block me by putting an O in Square b:
"…which forces me to put an X in Square c:
"What follows is a cascade of blocking moves, each one forcing the next. You take Square g:
"… which forces me to take Square d:
"… so you have to take Square f.
"At this point, every horizontal, vertical, and diagonal in the grid has at least one X and one O. It's impossible for either of us to win."
You've been watching her closely as she fills the grid, but she's right. All the moves after her second X were automatic. Inevitable.
"Tic-tac-toe is designed to make you feel like you have a choice, which makes it feel like a game," Inez says, "but you never really do, so it's not. It's the illusion of a game. Whoever goes first takes the center square and controls the board for the rest of the game."
You shake your head. "That can't be right. If it's impossible to win then no one would ever play it."
"Do you ever play tic-tac-toe anymore?"
"Point," you concede.
Inez pulls another napkin from the holder. "Let's go back to the very beginning:"
"Now, in both of the previous examples, the game wasn't decided until I placed that second X – in both cases, across and one column over from your O:
"And we know that the mirror image second moves – g for i and f for h – are also the same:
"… but that still leaves you with 10 alternatives:
"…which we know, thanks to mirror images, is really only 6 alternatives:
"So here's your next puzzle: of these 6 possible moves – a, d, h, k, l, and r – how many of them will ensure O the win?"
"Do we really have to do this?" you all but beg her.
Her lips purse into a wicked smile. "You don't have to keep playing the game if you don't want to."
And you have to admit that, for a few seconds, you consider just going back to the House and calling it a night. The only thing stopping you is that you'd have to live through this entire conversation a second time if you ever want to try again. "Fine," you sigh.
"Great! Now: we're going to assume perfect play here. I mean, O could win every single time if X makes it a point to try not to win:
"When I played this a kid, I lost only when I got sloppy, not noticing the other guy was about to get a tic-tac-toe. In perfect play, there's only one way to beat your opponent: you have to present her with two winning moves at once."
". . . and she can't block both," you finish for her. "A fork."
"Right. So in perfect play, any time you have a chance to build a fork you take it."
"Makes sense."
Inez shows you the napkin again:
"We saw that if X takes g or i on the first board, they're guaranteed a win. From that moment on, O can't do anything to prevent it." She looks up from the napkin and flashes you a mischievous smile. "In how many of the other second moves available to X – a, d, h, k, l, or r – can O, not X, be guaranteed a win?"
You frown, studying the napkin. "This is going to take some trial and error."
"Well," Inez says, tapping the house key hanging around her neck, "time isn't exactly an issue, is it?"
"I guess not."
She waggles her fingers at you and then disappears. You take another panicked look around the room, but no one seems to have noticed. "Got lucky," you grumble. You turn your attention back to the napkin again.
You can determine the answer to Inez's question and find that on the Solution Page.