Lanternby

Lanternby's lantern is a way of thinking about the solver. When the solver plays a deal, it searches through the possible moves, trying one path, then another, looking for a way to win. But it can't search forever. It has a budget, a limit on how many positions it will look at before it stops. A small budget is a small lantern: it lights up only the paths close by. A big budget is a bright lantern: it lights up far down the tunnels.

One afternoon a young hedgehog came down the ladder, quills drooping. She had run a test with a small search and gotten a disappointing number of wins. "I think these deals are just hard," she said. "Most of them can't be won."

Lanternby held his lantern up so it lit her face. "Are you sure they can't be won," he asked kindly, "or did your lantern just not reach the ending?"

She didn't know.

So Lanternby did an experiment that he loves more than any other. He took the very same deals, not new ones, the exact same deals, and had the solver play them twice. Once with a small lantern, a search of a few thousand positions. Once with a big lantern, a search five times larger.

The small lantern proved some wins. The big lantern proved those same wins, and then more. Deals that had come back not sure yet under the small light came back won under the bright one.

The hedgehog stared. "But they're the same deals. Nothing about the deals changed."

"Exactly," said Lanternby, and his whiskers glowed gold in the lamplight. "The deals didn't change. Only the lantern did. Those wins were there all along, waiting down the tunnel. A bigger search didn't make the deals easier. It just let us see further."

"So my number wasn't really about the deals," she said slowly. "It was about the deals and my lantern."

"That's it," said Lanternby. "When you tell someone how many deals you won, you have to tell them how big your lantern was too. Otherwise they might think the deals are hard, when really the light was small. The tool you measure with is part of the answer."