Artificial Intelligence / AI 0356 · Procedure · 60–90 seconds
The Umbrella Table
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One small table settles the umbrella: expected utility weighs both worlds and overturns the best-guess answer.
The utilities, honestly sketched: dry day unburdened, 100; dry day hauling the umbrella, 90; rain sheltered, 80; rain soaked, 10. Rain sits at 0.3. Carry: 0.3 × 80 plus 0.7 × 90 — 24 plus 63 — 87. Leave: 0.3 × 10 plus 0.7 × 100 — 3 plus 70 — 73. Carry wins by 14, while the best-guess policy, reading only the likelier column, picked Leave for its shiny 100. The table shows exactly what that policy ignored: the 10 — a soaked afternoon weighted by three mornings in ten. Two rows, two multiplications each, and the reflex that shrugs "probably fine" has been replaced by arithmetic that can defend itself.
The utilities were sketches — and even sketched utilities beat no utilities, because lopsided stakes forgive coarse numbers.