Twinnie

A while ago, two badger cousins came to the lab arguing. One cousin, Pim, said you should never take a card back down once it has gone up to the finished piles. The other cousin, Mossy, said taking cards back was a clever trick and won more games. They decided to settle it with a contest.

Pim played ten games his way. Mossy played ten games her way. Mossy won six. Pim won three.

"See?" Mossy said. "My rule wins twice as often."

Twinnie had been watching from her shelf, whiskers twitching. She slid down, landed with a soft thump, and asked a question that made both cousins go quiet.

"Were your twenty deals the same?"

They weren't, of course. Pim had shuffled his own cards. Mossy had shuffled hers. Some deals come out easy, with the aces near the top and the long runs falling right into place. Some come out tangled, with every useful card buried under a King. Nobody can win a tangled deal, whatever rule they use.

"So maybe Mossy's rule is better," Twinnie said, "or maybe Mossy just got the easy deals. From your contest, there is no way to tell which. The luck and the rule are all mixed up together."

Pim looked relieved. Mossy looked annoyed. Twinnie looked like she had a plan.

She took one fresh deck and dealt twenty hands. Then she did something careful and slow. She dealt the same twenty hands again, card for card, into a second row. Two identical rows of twenty deals. She pushed the first row toward Pim's rule and the second row toward Mossy's rule, and the lab's solver played every single one.

Now each deal had a twin. Deal number seven for Pim was exactly deal number seven for Mossy. If a deal was easy, it was easy for both of them. If it was tangled, it was tangled for both of them. The luck was the same on both sides, so it could not tip the scale.

When the results came in, the gap between the cousins had almost disappeared. On most deals, both rules won, or both rules lost. Only a handful of deals came out differently.

"Those few," Twinnie said, tapping them, "are the only place the rule made a difference. Everything else was the deck."