Lopsy and Twinnie

"How do we find out for sure?" Burr asked.

Twinnie stepped forward first, because the first step is hers. "We make it fair," she said. "If you play your rule on some deals and the normal rule on different deals, then luck gets mixed in with the rule. Easy deals, hard deals, we'd never know which was which."

She took a fresh deck and dealt sixty hands, slowly and carefully. Then she dealt the same sixty hands again, card for card, into a second row. Two rows of twins. The first row went to the usual four-cell game. The second went to Burr's three-cell game. The solver played every single game.

When the results came back, the table was covered. One hundred and twenty games, sixty pairs, won and lost and not sure yet scattered everywhere. Burr's eyes went wide. "There's so much," she said. "How do we read it?"

That's when Lopsy hopped up onto the table, flopped ear swinging. "Now it's my turn," she said. "Because Twinnie made the deals fair, I get to do something really simple."

She picked up the first pair. Both rules had won it. "Both won. That deal was easy for everyone. It can't tell us which rule is better." She set it on the big pile. The next pair: both lost. Big pile. Then both won again. Big pile.

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

"Not throwing away," said Lopsy. "Setting aside. A pair that agrees can't show a difference. And here's the key." She looked over at Twinnie. "This only works because the deals are twins. If the deals weren't the same, a pair that agreed might just be luck. Twinnie's fairness is what makes my sorting honest."

Twinnie gave a small, pleased nod.

Lopsy kept going, fast now. Big pile, big pile, big pile. Every so often she found a pair where the two rules disagreed, and she set it apart on the small pile. When she finished, fifty-two pairs sat in the big pile. Only eight sat in the small one. In every one of those eight, the four-cell game had won and the three-cell game had lost.

"There's the whole story," said Lopsy, ears quivering. "On fifty-two deals, the missing cell made no difference. On eight, it did, and every time, it was the four-cell game that won."

Burr let out a long breath. "So one fewer cell does matter. Just not on most deals."

"A small difference, on a few deals, measured fairly," said Twinnie. "That's a real answer."