Definition
Plain language
The math of counting how many wins you'd expect from a fixed number of independent yes-or-no tries.
As stated in the literature
The probability distribution over the number of successes in N independent trials each with fixed success probability p; underlies the calculation that a group of independent rollouts collapses to all-same outcomes with probability that improves only linearly in budget.
Also called: binomial
Why it matters: It lets you predict the spread of outcomes from repeated independent attempts, so you can judge whether a result is normal luck or something unusual.
For example, if you flip a fair coin ten times, the binomial distribution tells you how likely you are to get exactly six heads.
Heard on the show
“It's a binomial calculation and a union bound — the kind of thing you can check on a napkin.”Episode 162 — The Empty-Lake Proof: Why More Rollouts Stop Helping Reasoning Models