Lopsy and Twinnie

"I'm sure one fewer cell hardly changes anything," Burr said. "It's just a little less parking. But how do we find out for certain?"

Twinnie stepped forward first, because the first step always belongs to her. "We make it fair," she said. "If you play your three-cell rule on some deals and the normal four-cell rule on different deals, then luck gets tangled up with the rule. Some deals are easy, some are brutal, and we'd never know whether a difference came from the cell or from which deals each rule happened to get."

She took a fresh deck, shuffled it, and dealt sixty hands, slowly and with great care. Then she dealt those exact same sixty hands again, card for card, into a second row beneath the first. Two rows of perfect twins. The top row went to the solver under the usual four-cell game. The bottom row went under Burr's three-cell game. And the solver played all hundred and twenty.

When the results came back, they covered the long table from end to end: sixty pairs, won and lost and not sure yet scattered everywhere in a confusing patchwork. Burr's eyes went very wide. "There's so much," she whispered. "How do we even begin to read it?"

That was when Lopsy sprang up onto the table, flopped ear swinging. "Now it's my turn," she said, grinning. "And because Twinnie made the deals fair, my part is wonderfully simple."

She lifted the first pair. Both rules had won it. "Both won. That deal was easy for everyone, three cells or four. So it can't tell us which rule is better." Onto the big pile. The next pair: both lost. "Hopeless either way." Big pile. Then both won again. Big pile.

Burr frowned. "Wait. You're throwing most of them away?"

"Not throwing them away," said Lopsy. "Setting them aside, because they can't answer this particular question. A pair that agrees can't show a difference between the rules. But here's the part that matters most." She glanced across the table at Twinnie. "This only works because the deals are twins. If the two rules had played different deals, then a pair that agreed might just be luck, and a pair that disagreed might just be luck too. It's Twinnie's fairness that makes my sorting honest. Without identical deals, my small pile would be full of noise."

Twinnie gave a small, pleased nod and said nothing, which for Twinnie was high praise.

Lopsy went on, fast now, paws blurring. Big pile, big pile, big pile. Every so often she came across a pair where the two rules had disagreed, and she lifted it out and set it apart on the small pile. When the table was finally clear, fifty-two pairs stood in the big heap. Only eight sat in the small pile. And in every one of those eight, the four-cell game had won and the three-cell game had lost. Not one pair leaned the other way.

"There's the whole story," said Lopsy, both ears quivering now, even the flopped one. "On fifty-two deals the missing cell made no difference at all. On eight deals it did, and every single time it went the same direction. Eight to nothing."

Burr let out a long, slow breath. "So one fewer cell really does matter," she said. "Just not on most deals."

"A small difference," said Twinnie quietly, "showing up on only a few deals, but pointing the same way every time, and measured fairly. That's a real answer. You can stand behind it."