The Solved Board (Gridley · Arbor · Rowan)

Then Gridley told the last part — the part that reached past both of them, to the machines. "Now imagine Arbor's tree-climbing," he said, "but instead of five branches deep, imagine going all the way — every branch, every reply, down to every finished game, win or lose, at the very tips. That's what it means to solve a game." He gestured at the Connect-4 board. "Someone did exactly that for this game. A computer climbed the entire Connect-4 tree — assuming best play at every single fork, backing the value up from every leaf — and proved that the first player, playing perfectly, always wins. Not usually. Always. The whole tree is known." Arbor's eyes were shining; this was her favorite thing in the world. "It's what I do," she breathed, "but complete." "It's exactly what you do," Gridley said, "just without stopping at five branches. You climb part of the tree. The machine climbed all of it. Rowan climbs one branch by instinct. All three of you are doing the same act — explore forward, assume good play, choose accordingly — at one branch, at five, and at all of them." He smiled at the three of them, standing in a row from instinct to depth to completeness. "Thinking ahead and solving a game aren't two different things. They're the same thing at three depths."

Then Gridley answered the kid's question. "So — why play a game a computer has solved?" He tapped the board. "Because knowing a fact and being able to see are different prizes. The machine solved Connect-4 so it could tell us who wins. But it can't hand you the ability to look five moves ahead — that you have to grow, one branch at a time, the way Arbor grew it and the way Rowan is starting to." He looked at Rowan. "Every game you play, you climb a little higher up the tree than last time. The machine's prize was a fact. Your prize is becoming someone who sees further — and that prize works on games no computer will ever finish solving, like chess, like Go, like every real decision you'll make where nobody's climbed the whole tree and you have to see as far as you can yourself." Rowan looked at Arbor's five-deep sketch, then at his own one-move instinct, and felt the small, steadying relief of a worry lifting — the kid's question had felt like it might make the whole game pointless, and instead it had made it feel bigger — and said, "So the point isn't to be the computer. The point is to climb higher than I did yesterday." "That," said Gridley warmly, "is the whole point — of this game, and of most things worth getting good at." And Arbor was already sketching a bigger tree, happy in the way she only ever was with one more branch left to climb.