Hedgeworth
an honest range - when some results are unknown, report the lowest and highest the truth could be, not a single made-up number
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In the quietest corner of the Card Lab, where the lamp is turned low, you will find a hedgehog named Hedgeworth. He wears small round glasses that slide down his nose, and he holds a clipboard close to his chest the way some people hold a warm mug. On the clipboard is a little bar chart, drawn in pencil, very neatly.
Hedgeworth is the most careful animal in the lab. Not slow. Careful. There is a difference, and he will gently explain it if you ask.
"Slow is when you take a long time," he says. "Careful is when you never say more than you know."
One morning a squirrel named Pip burst into the lab, tail straight up with excitement. Pip had run a test on forty deals. "Rule B won twenty-six!" Pip announced. "That's sixty-five percent! Rule B wins sixty-five percent of the time!"
Hedgeworth pushed his glasses up and looked at Pip's results. Then he looked more closely, and his quills rose just a little, the way they do when he notices something.
"Twenty-six won," he said. "And how many lost?"
"Eight," said Pip.
Hedgeworth counted on his small paw. "Twenty-six and eight is thirty-four. You tested forty deals. What happened to the other six?"
Pip's tail drooped. "Oh. Those. The solver said not sure yet. It ran out of time before it could finish them."
"Ah," said Hedgeworth kindly. "Then we have to be careful about what we say."
He turned his clipboard over to a clean side and drew a bar. Then he said, "Let's think about the six unknown deals. Could they all be wins?"
Pip thought. "Maybe. The solver just didn't find the win in time."
"Could they all be losses?"
"Also maybe."
"So the truth is hiding somewhere in between," Hedgeworth said. He wrote two numbers. "If every unknown deal is really a loss, Rule B won twenty-six out of forty. That is the lowest it can be. If every unknown deal is really a win, Rule B won thirty-two out of forty. That is the highest it can be."
He tapped the clipboard. "So the honest sentence is this. Rule B won at least twenty-six and at most thirty-two of these forty deals."
Pip frowned. "That's less exciting than sixty-five percent."
"It is," Hedgeworth agreed. "But sixty-five percent pretends the six unknowns were all losses. We don't know that. If you say sixty-five and a friend runs a longer search and finds three of those six were wins, your number was wrong the whole time. My sentence would still be true. Nobody can catch a careful sentence out."
Pip read it again. At least twenty-six. At most thirty-two. It began to feel less like a letdown and more like a shield.
"And if I want a smaller range?" Pip asked.
Hedgeworth's eyes crinkled behind his glasses. "Then you don't guess harder. You find out more. Ask the solver to search longer, and some of those unknowns will turn into wins or losses. Every unknown you settle makes the range narrower. The range shrinks because of real evidence, never because you wished it smaller."
Hedgeworth feels most like Hedgeworth when he writes a sentence that is exactly as big as the truth, no bigger, no smaller. It gives him a snug, settled feeling, like a key turning in a lock that fits it perfectly. He doesn't need anyone to be impressed. He just needs the sentence to be true.
You have a bit of Hedgeworth in you every time you stop yourself from exaggerating. When a result has gaps in it, say what the gaps allow, the way he does: "Hedgeworth says at least, and at most, and never one word more."
Then go find out more, and watch your honest range grow small.
The Solitaire Lab ensemble
Hedgeworth is part of Solitaire Lab's distributed-narrative cast. Each character embodies a different curricular primitive; together they teach the full subject.
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Dealia
(Mentor, a card-dealing raccoon) - asks what you predicted BEFORE you look at the data
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Twinnie
Deals every hand twice - the same deals for both rules, so the test is fair
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Maybelle
Knows an unknown is a maybe, not a no - the search ran out of time
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Bigsby
Knows more deals make the answer sharper - the interval gets narrower
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Lopsy
Counts the deals where only ONE rule won - those odd pairs are the whole story
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Lanternby
Knows the measuring tool is part of the result - a bigger search proves more wins of the SAME deals
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Glassby
Knows FreeCell hides nothing, so a 'lost' there is a proof about the deal itself
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Tiebelle
Calls it a tie when the two ranges overlap - no winner the data cannot back
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Seedwick
Knows the same run seed rebuilds the same deals, so anyone can re-check your test
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Tabitha
Keeps one row per deal in the CSV so you can draw the chart yourself
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Addison
Knows a rule that only ADDS moves can never truly win less - reason before you run