Spoke Sami

Sami had learned that real secret the hard way — by first believing the wrong reason, out loud, in front of everyone.

When she was young she'd loved the crossroads too, but for a reason she'd never checked. "They're strong because they're on more mills!" she'd declared confidently, planting herself on a junction. And an older piece had simply asked her to count. Sami had counted the mill-lines through her crossroad: two. She'd counted the mill-lines through a lowly corner: also two. Exactly the same. Her whole proud reason had been wrong. The crossroads weren't on more mills at all — every point on the board was on precisely two.

She'd been embarrassed, and then, slowly, fascinated. Because the crossroads were stronger — she could feel it, she won from them — so if it wasn't the mills, what was it? She counted again, differently this time. Roads. Neighbours. Ways out. And there it was: the corner had two, the crossroad had four. "It was never the mills," she said, wonderingly. "It was the mobility. I was right that these squares are strong — I just had the wrong reason. And a right feeling with a wrong reason is a dangerous thing to teach anyone." She made herself a promise then: to understand why a thing was true, not just that it was — because the wrong reason, however confidently held, would eventually lead her astray.

At the House of the Board, Sami claimed a crossroad in the middle of the floor almost without thinking, and the Elder watched her do it.

"The prime points," the Elder said. "You find the strong squares better than anyone. But I've heard young players parrot that they're strong 'because they're on more mills' — which isn't so. Will you teach them the true reason?"

"I'll teach them to count," said Sami. "That's the whole cure. Every point on this board is on two mills — corner, crossroad, all of them, exactly two. So the strong points can't be strong for that. They're strong for neighbours — for how many roads run out of them. Four at a crossroad, two at a corner. I'll teach my students to take the busy junctions not because someone told them to, but because they counted the roads themselves and saw the mobility for what it is. A player who knows the real reason will find the strong squares on a board they've never seen. A player who just memorized 'crossroads good' will be lost the moment the board changes."

"Teach the counting," said the Elder. "A reason understood outlasts a hundred rules memorized."

Sami's student was a boy named Deko who'd been told "take the crossroads, they're on more mills" and believed it without ever checking — and got confused and stuck whenever the board didn't match his half-understood rule.

"You keep saying the crossroads are on more mills," Sami said. "Let's count. How many mill-lines run through this crossroad?" Deko counted. "...Two." "And through this corner over here?" He counted, and blinked. "...Also two. They're — they're the same?" "Every point on the board is on two mills," said Sami. "So why is the crossroad worth more? Count something else. Count the roads out of each." Deko counted: four out of the crossroad, two out of the corner. "Oh," he said. "It's not the mills. It's how many ways I can move." "Now you don't need me to tell you which squares are strong," said Sami. "You can find them — on any board, ever — by counting the roads. That's worth more than any rule I could hand you."

Deko stopped parroting the rule he'd been given and started counting — roads, neighbours, ways out. And suddenly the board made sense from the inside: he could feel why the busy junctions were worth fighting for, because he'd measured it himself.

"Knowing why is different from knowing that," Deko said slowly.

"It's everything," said Sami.