Bevvy

The afternoon Bevvy finally explained it to the whole League Field began, as so many good lessons do, with two young hares having an argument. They had each just finished a board, and they were comparing how many clicks they'd used.

"I cleared mine in forty clicks," said the first hare, rather smugly.

"I needed sixty," said the second, his long ears drooping all the way down. "So you're way better than me. That's a third more clicks."

Bevvy zoomed over and hovered in the air right between them, wings a soft buzz. "Wait, wait, wait! Before anybody decides who's better, did you play the same board?"

They hadn't, of course. Each had played a different one. So Bevvy landed lightly on the first hare's finished board and began to count, one leg tapping tile after tile.

"Here's how you find a board's hidden number," she said. "Some squares have no mines touching them at all. They're zeros. When you open a zero, the game opens every square around it for free, and if any of those are zeros too, they open their neighbors, and so on, spreading out like a ripple. Each of those spreading patches is called an opening, and the whole thing, right out to the numbers along its edge, opens with a single click. So an opening only ever costs one click, no matter how big it is." She tapped the board. "This board has four openings. That's four clicks."

"Then there are the numbers," she went on, buzzing from tile to tile. "Every number sitting along the edge of an opening gets uncovered for free when the opening spreads. But some numbers aren't touching any opening at all. Nothing will ever uncover them for you. Each of those has to be clicked by itself, one click apiece." She counted them carefully, tile by tile, antennae twitching. "This board has thirty-six of those lonely numbers. So the fewest clicks this board could ever need is four for the openings plus thirty-six for the lonely numbers. Forty. This board's number is forty."

The first hare's ears shot up. "Forty? That's exactly how many I used!"

"Then you played it perfectly," said Bevvy, delighted. "Not one wasted click. Every click did real work."

Then she flew over to the second hare's board and counted all over again. Openings, lonely numbers, tap and tap and tap. This board was larger and much busier, with its mines scattered so evenly that very few zeros appeared, which meant very few openings to do work for free. "This board's number," Bevvy announced at last, "is fifty-five. It needs at least fifty-five clicks, no matter who plays it. Even the best player in the whole valley couldn't clear it in fewer."

The second hare blinked slowly. "So I used sixty on a board that needed at least fifty-five..."

"...and your friend used forty on a board that needed at least forty," said Bevvy. "You both did really well. But you can't compare forty to sixty and decide anything, because the boards weren't the same. Yours was simply a harder board. It had fewer openings to help you. The number tells you how hard a board is before anyone ever lays a single click on it. That's what makes it so useful. It's a measurement of the board, not of the player."

The second hare's ears slowly lifted off the ground. There is a particular kind of relief in discovering that you weren't bad at something, only that you'd been handed something harder than your friend.