Addison

"How is that possible?" asked the oldest rabbit. "Maybelle says the missing wins are probably in the maybe pile. But how can we be sure our rule isn't really worse?"

Addison set down his block and thought for a long moment. Then he asked a question.

"Under your rule, can you still make every move the normal rule allows?"

The rabbits thought. "Yes," said one. "A King can still go into an empty column. We just let other cards go there too."

"So your rule only adds moves," said Addison. "It never takes any away."

He picked up a block and set it on his tower. "Think of every way to win a deal under the normal rule as a path. Now, under your rule, is that same path still allowed?"

The rabbits' eyes widened. "It is," said the oldest slowly. "Every move on that path is still allowed in our rule. So if the normal rule can win a deal, our rule can win it too, by doing exactly the same moves."

"Exactly," said Addison. "Adding moves is like adding a block. It can't take away a win that was already possible. So your rule can never truly win fewer deals than the normal one. It can only win the same, or more."

He placed another block, perfectly level. "We worked that out without running a single deal. Just by thinking."

"But then why did the lab show fewer wins?" asked a young rabbit.

"Because the lab isn't showing the truth directly," said Addison. "It's showing what the solver managed to prove in the time it had. Your rule has more moves, so there are more paths to search, so the solver runs out of time more often. Those extra not sure yets made your rule look worse. But our thinking tells us they can't really be losses that the normal rule would have won."

The rabbits looked at each other, amazed. They had come in worried that their rule was bad. Now they understood that the strange result was about the solver's time, not about their rule, and they had worked out why using nothing but careful thought.