subtraction

The passage around this formula

Batch size interacts with the value of parallel experiments in a way worth costing out explicitly. If a single proposed experiment succeeds with probability p , and a batch of k proposals were independent, the probability that at least one succeeds is $P(\text{at least one success in } k) = 1 - (1-p)^{k}$. which is why both systems ran in batches — parallel throughput converts a low per-attempt success probability into a high per-batch one. Two caveats matter in practice: proposals drawn from the same model on the same pool are correlated, so realised batch success rates fall short of this bound, and a larger batch is only worth its cost if throughput, not sample count, is the bottleneck actually being relieved.

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