Definition
Plain language
A simple rule that the chance of any one of several bad things happening is at most the sum of their individual chances.
As stated in the literature
A basic probability inequality stating P(∪Aᵢ) ≤ ΣP(Aᵢ); used to give a quick, machinery-free proof bounding the probability that a group of rollouts collapses to a uniform, uninformative outcome.
Why it matters: It gives a quick, safe upper limit on the odds of any bad event in a group, letting you reason about overall risk without complicated math.
For example, if each of three machines has a one-in-a-hundred chance of failing today, the chance that at least one fails is at most three in a hundred.
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