Toby Ord: expected consecutive successes before failure exactly equals the odds of success

tobyordoxford · x · 2026-11-14

In a technical exchange about extrapolating AI task-horizon length, Toby Ord works out the math under a constant-hazard-rate model: the expected number of consecutive successes before a failure is exactly equal to the odds of success, and once success odds are high, the median (50% horizon) approaches a linear relation to the odds.

He also concedes the constant-hazard assumption he previously advanced doesn't quite hold, meaning the proportional odds–horizon relation is only an approximation — a technical rejoinder relevant to METR-style horizon extrapolation debates.

Related event: Oxford's Toby Ord: RL Compute Needs 10,000x Boost to Lift Benchmark Scores(17 posts)→

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