Tiebelle

"Thirty beats twenty-eight! We win! Our rule is better!"

The teal team's faces crumpled. A few of them started to argue back, and then more joined in, and the voices climbed higher and higher. A young raccoon on the teal team stamped her foot so hard the cards on the nearest table jumped.

Tiebelle stepped quietly into the middle of the room. She didn't say a word. She simply raised her two ribbons high, crossed in the middle, and waited.

One by one, everyone fell silent and looked.

"Your two numbers aren't the whole story," she said, very softly, so that people had to lean in to hear. "Each rule really has a range, not a single number. Remember what Hedgeworth teaches. Some of these deals were marked not sure yet, so the truth for each rule sits somewhere between an at-least and an at-most. And fifty deals isn't very many, so there's luck mixed in too, which widens things further. Let me show you what that looks like."

She held up the teal ribbon alone. "This is the teal rule's honest range. Its true win rate is somewhere along here." Then she held up the gold ribbon beside it, a little higher. "And this is the gold rule's range. Its truth is somewhere along here."

She drew them slowly toward each other, closer and closer, until they overlapped, a long stretch of teal lying across a long stretch of gold.

"Look where they cross," she said. "Along this whole shared part, either rule could turn out to be the better one. The gold team's number is higher, yes. But the teal rule's truth might be all the way up here, near the top of its ribbon." She touched the high end of the teal. "And the gold rule's truth might be down here, near the bottom of its ribbon." She touched the low end of the gold. "If both of those were true, teal would be better. With ranges this wide and this overlapped, we simply can't tell which way it goes."

A gold-team rabbit frowned, her ears lowering. "So we didn't win?"

"Nobody won," said Tiebelle gently. "And nobody lost. It's a tie. Not because the two rules are the same. They might be quite different. But the evidence isn't strong enough yet to say which way the difference goes. If we crowned a winner right now, we'd be claiming more than we actually know. And if the next test flipped it, we'd have been shouting about nothing."

"Then how do we ever find out?" asked the young raccoon, who had stopped stamping and was now listening hard.

Tiebelle smiled, and her white spots seemed to glow a little brighter in the lamplight. "We make the ribbons shorter," she said. "Test far more deals, the way Bigsby would, so the luck averages out. And let the solver search longer, the way Lanternby would, so fewer deals are left as not sure yet. Each ribbon will shrink toward its true value. If they shrink until they pull apart and don't overlap at all, then one rule really is better, and you'll have earned the right to say so. And if they keep overlapping even when they're tiny, then maybe the two rules really are about the same."