subtraction

The passage around this formula

Consider what the o1 numbers alone expose about how these gains are produced. If a single attempt at a problem succeeds with probability p , and k attempts were independent, the probability that at least one succeeds is $p_k = 1 - (1-p)^k$. a curve that climbs fast and then saturates. It is tempting to read o1’s jump from 74% (one sample) to 83% (64-sample consensus) to 93% (1,000-sample rerank) as roughly this shape. It is not, for two reasons that matter for how the number should be read. First, repeated attempts by one model on one problem are correlated — the same misconception that causes one failure tends to recur — so the realised gain from added samples falls well below what…

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