Lanternby

His lantern is also the way he explains the solver, the patient machine in the lab that plays each deal of solitaire to find out whether it can be won. When the solver plays a deal, it explores possible moves the way a mole explores tunnels: try one path, follow it as far as it goes, back up, try another. But no solver can explore forever. Each one is given a budget, a limit on how many positions it may examine before it has to stop and report. A small budget is a small lantern, lighting only the tunnels nearby. A large budget is a blazing lantern, throwing light far down every passage.

One afternoon a young hedgehog climbed down the ladder with her quills drooping. She had run a test using a small search, and the number of wins had come back disappointingly low. "I think these deals are just hard," she told Lanternby. "Most of them can't be won at all."

Lanternby lifted his lantern until its glow warmed her face. "Are you sure they can't be won?" he asked, very kindly. "Or did your lantern simply not reach the end of the tunnel?"

She opened her mouth to answer and found that she didn't know.

So Lanternby ran his favorite experiment, the one he considers the most important test in the whole lab. He took the very same deals she had used. Not new deals, not similar deals, but exactly the same ones, card for card. He had the solver play them twice. The first time, with a small lantern: a search of a few thousand positions per deal. The second time, with a lantern five times brighter.

The small lantern proved a certain number of wins. The bright lantern proved every one of those same wins, and then more besides. Deals that had come back not sure yet under the dim light came back, under the bright one, clearly won.

The hedgehog stared at the two result sheets side by side. "But they're the same deals," she said. "Nothing about the deals changed."

"Nothing at all," said Lanternby, and in the lamplight his whiskers shone like fine gold wire. "The deals didn't change. Only the lantern did. Those extra wins were down there the whole time, waiting at the ends of tunnels your small light couldn't reach. A bigger search didn't make the deals any easier. It just let us see further into them."

She was quiet, putting it together. "So my number wasn't really about the deals," she said slowly. "It was about the deals and my lantern, tangled up together."

"That's it exactly," said Lanternby. "And that's why, whenever you tell someone how many deals you won, you must also tell them how big your lantern was. If you don't, they might decide the deals are hard, when really your light was small. Or they might compare your number to someone else's without realizing the other lab searched twenty times harder. The tool you measure with is part of the answer. Leave it out, and the answer stops meaning anything."

Then he added the part that made her smile, because it was hopeful. "And notice one more thing. The bright lantern never turned a win into a loss. Not once. A win the solver proves is a real, finished win, a complete path from start to end, and it stays true forever. Looking harder can only ever add wins. It can never take one away. So a bigger search is always safe. It can only show you more of what was already there."