Lopsy
discordant pairs - in a paired test, deals both rules win or both lose say nothing about which rule is better; only the deals where they disagree do
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Lopsy is a young rabbit with one ear that stands straight up and one ear that flops down over her eye. She has never minded. "It means I look at things two ways at once," she says, and grins her quick, lopsided grin. Lopsy is the lab's sorter. Give her any pile and she will sort it, fast, into a big pile and a small pile. And she always cares most about the small one.
This is the story of how Lopsy found the whole answer in the smallest pile of all.
Twinnie the otter had just finished a careful paired test. Forty deals, each dealt twice: once for the rule where a card can be taken back down from the finished piles, and once for the rule where it can't. The solver had played all eighty games. The results were laid out in forty neat pairs across the long table.
A crowd of young animals gathered around, trying to decide which rule was better. They were getting lost. There were so many results. Some of them started adding up totals, some started drawing charts, and everyone was talking at once.
Lopsy hopped up onto the table, flopped ear swinging. "Wait," she said. "Most of these pairs don't matter."
Everyone stopped. "What do you mean, they don't matter?"
Lopsy picked up the first pair. Both rules had won that deal. "Look. This deal was easy. Both rules won it. So does it tell us which rule is better?"
The crowd thought. "No," said a mouse slowly. "They both won. It's a tie."
"Right," said Lopsy, and set the pair on the big pile. She picked up another. Both rules had lost. "This deal was impossible. Both rules lost. Does it tell us anything?"
"No. Another tie."
On to the big pile it went. Lopsy worked quickly now, paws flying. Both won, big pile. Both lost, big pile. Both won, big pile. The big pile grew and grew. Every pair where the rules agreed went there, because a pair that agrees can't show a difference.
Then she found one where the take-back rule had won and the no-take-back rule had lost. She set it apart, carefully, on the small pile. A few more pairs later, she found another like it. And then one the other way around, where only the no-take-back rule won.
When she was finished, almost all forty pairs sat in the big pile. Only five sat in the small one: four where just the take-back rule won, one where just the other rule won.
"There," said Lopsy, and her upright ear quivered with delight. "These are the whole story. On thirty-five deals the rules did exactly the same thing. The only deals where the rule made a difference are these five. And four of them went one way."
The crowd leaned in. Suddenly the answer was simple and clear, when a minute ago it had been a jumble. Taking a card back helped, but only on a few deals, because most of the time it didn't matter at all.
"And if the small pile were four and four?" asked the mouse.
"Then we couldn't say either rule was better," said Lopsy. "The odd ones would cancel out. You always have to look at which way they lean."
Lopsy feels most like Lopsy when the big pile is finished and the small pile sits there, tiny and glittering, holding everything that matters. It feels bright and bouncy, like spotting four-leaf clovers in a whole field of ordinary ones. Most people walk past them. She never does.
You have a bit of Lopsy in you whenever you look for what is different instead of what is the same. Next time you compare two things, set aside the cases that agree, and say it the way she does: "Lopsy skips the pairs that agree and counts the ones that don't."
Then look at the small pile. That's where the answer lives.
The Solitaire Lab ensemble
Lopsy 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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Hedgeworth
Never says more than the data can - reports at least ... and at most ...
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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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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