Lanternby and Maybelle

"We tested a rule where any card can go into an empty column," the tallest squirrel explained. "And we got loads of not sure yets. Our poster is due soon, so our teacher said we should just count them all as losses and be done."

Maybelle tilted her head, one ear rising. "Hmmm," she said, gently but firmly. "That's the one thing we mustn't do."

She set the heavy tray down inside the round pool of Lanternby's light. "A not sure yet isn't a loss," she told the squirrels. "It's a maybe. It means the solver was still in the middle of searching when its time ran out. It hadn't found a win. But it hadn't proven there wasn't one, either. If we count it as a loss, we'd be saying we know something we don't. And with this many in the tray, that could flip your whole conclusion upside down."

"But then how do we ever finish?" asked the smallest squirrel, twisting her paws. "We can't leave everything as a maybe forever. Nobody hangs a poster that just says 'we don't know.'"

Lanternby lifted his lantern high, and its light swung warm and golden across the curved tunnel walls. "That's exactly where I come in," he said. "Maybelle keeps the maybes safe, so nobody throws them away by mistake. I'm the one who goes looking for their answers."

The squirrels crowded close as he explained. The solver, he told them, works like a mole in a maze of tunnels, exploring possible moves one path at a time. But it has a limit, a search budget, which is like a lantern that can only light so far down each tunnel before the dark swallows it. "Your rule allows more moves at every step," Lanternby said, "so each deal has many more tunnels branching off in every direction. A small lantern runs out of light before it reaches the end of a lot of them. That's why your tray is so full. It isn't that your rule is losing. It's that your rule gives the search much more ground to cover."

"So a bigger lantern would..." began the tallest squirrel.

"...reach further," said Lanternby, and he turned the little brass knob so the flame rose tall and bright. "The same deals. Not one card different. Just a brighter light shining further down the same tunnels."

So they asked the solver to search again, this time five times as far, on only the deals sitting in Maybelle's tray. The squirrels held their breath as the answers began to come back.

Won. Won. Lost. Won. Won. Won. Some of the maybes turned out to be wins, hiding just beyond the point where the small lantern had given up. A few turned out to be genuine losses, and now they were proven losses, fully searched, no longer guesses. And a small handful stayed not sure yet, even under the much brighter light.

Maybelle sorted the new results into their places with quick, happy paws. "Look at this," she said. "Most of the maybes were wins all along. If we had counted them as losses the way you were told to, you'd have announced to the whole valley that your rule was worse than the normal one. It's actually better."

"And those last few that are still unsure?" asked the smallest squirrel.

"They stay in my tray," said Maybelle, "and we say so, plainly, on the poster. Some deals are so tangled they need an even brighter light, or more time than we have. That's allowed. Saying 'three deals remain unsettled' is honest, and honest is the whole point. A poster that pretends to know everything is a poster nobody should trust."