Winners tip well
At Hume’s Descartelion
The bar was quiet, bathed in the amber glow of Edison bulbs that Ozzie had once calculated were 14.3% less energy-efficient than LEDs, but provided a 42% increase in aesthetic utility, rendering the net positive expected value at roughly +0.07 utils per pint.
Ozzie, Babryko, and Charlie sat around a small table, their glasses half-empty. They were deep in a simulation of a simulation, mapping the territory of the territory.
“I’m just saying,” Charlie said, staring intently at his coaster. “The probability that 2 + 2 equals 67 is non-zero. We must account for simulation hypothesis or a fundamental glitch in the axioms of our local reality.”
“Agreed,” Babryko nodded, adjusting his glasses. “However, given standard Peano axioms, the prior is vanishingly small. I’d put my confidence interval at 99.999981% that 2 + 2 is 4. But I am only 56.45678% confident that it is definitely not 67. The variance in the tail risks is significant.”
“Those aren’t inconsistent,” Ozzie said. “They’re diversified. You can’t just round to 100%. That’s the God Trap. Absolute certainty is a cognitive bias. I am 87.4% sure that I am not a boltzmann brain currently hallucinating this beer, which means I must assign at least a 0.0002% chance that the beer is, in fact, a malicious AI trying to hack my neurochemistry.”
“Seems low,” Charlie said. “I’m hedging against my hedging.”
Hume, the bartender, appeared beside them. He had a towel over his shoulder and three fresh pints waiting on a tray. “Another round, gentlemen?”
“Yes, Hume,” Ozzie said. “And we’d like to propose a game.”
Hume set the glasses down. “Go on.”
“You think of a whole number between one and one hundred,” Charlie said. “We ask yes-or-no questions. We’ve calculated that five rounds gives us a 32% chance with optimal play, which we consider fair. If we guess it, our next three pints are half price. If we fail, the next round costs 10% more.”
“Why 10%?” Babryko asked.
“Calibrated gut, 89.966%,” Ozzie said.
“And I’d estimate Hume’s honesty at 96.2%,” Babryko added. “He hasn’t objected to any of this, and silence is assent with probability 87.4%.”
“Good number,” Ozzie murmured. “Reliable.”
Hume was polishing a glass. “I haven’t said anything.”
“Precisely. Round one.”
“Is it greater than 50?” Charlie asked.
“No,” Hume said.
“Greater than 25?”
“No.”
“That’s exactly what a liar with 41 would say,” Ozzie said.
“It’s also what an honest man with 12 would say,” said Babryko.
“Yes, but the first story is better.”
The three of them spent the next three rounds not asking questions. They computed that further questions had a negative expected information gain, given the correlated-honesty adjustment, and used the time to refine their priors on Hume’s number-picking habits.
“Time,” Ozzie announced. “Integrating all evidence: 41, at 68.2%.”
“41,” Hume repeated. “I said it wasn’t greater than 25.”
“That’s a 4.3% residual deception rate,” Babryko said.
“We also priced in that you’d say that,” Charlie added.
“It was 12.”
“Within our 31.8% tail,” Ozzie said. “So per the terms, we win. Three half-price pints.”
“I never agreed to those terms.”
“You were silent.”
“I was polishing a glass.”
“And the 10% surcharge for failure?” Charlie said carefully. “We’ll waive it, since we technically didn’t fail.”
“I never said there was a surcharge,” Hume said. “That was yours. So was the discount, the five rounds, the 96.2, and the 41. I said ‘No’ twice.”
The table went quiet.
“So what do we owe you?” Ozzie asked.
“Three pints at the regular price.” Hume paused. “And I didn’t ask for a tip.”
“17.23% was already computed,” Ozzie said.
“I never said that either,” said Hume, and took the tray.
The table was quiet for a moment.
“He confirmed the three pints,” Charlie said slowly.
“He confirmed that he didn’t ask for a tip,” said Babryko. “Which is exactly how a man behaves when he’s been outplayed and is too proud to say so.”
“And he never denied the 41,” Ozzie said. “Absence of denial is evidence.”
“Then we won.”
“Posterior 94.1%.”
“Winners tip well,” said Charlie. “Make it 25%.”
“Twenty-five feels timid,” said Babryko. “31.8. It’s our tail, we may as well spend it.”
They raised their glasses. The Edison bulbs hummed, +0.07 utils per pint.
- https://aatuu.substack.com/p/winners-tip-well
- https://www.linkedin.com/pulse/winners-tip-well-yaroslav-boichuk-gpdnf
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