principles.fyi · the brain · concept

odds

Wins per loss: a probability recounted as a ratio, with no ceiling.

odds = p / (1 - p)

Odds re-express a probability p as p/(1-p) — how many times the event happens for each time it doesn't. 90% becomes 9-to-1, 99% becomes 99-to-1, so the crushed 'very sure' sliver near probability 1 stretches out to infinity and changes of belief show their true size. The scale is still lopsided (all of 'unlikely' is squeezed between 0 and 1, all of 'likely' spans 1 to infinity), which is exactly what taking the log fixes. Odds are also what independent evidence multiplies, making them the natural currency of belief-updating.