Probability versus odds
Two ways of saying the same thing, and when each one helps.
4 minute read
Probability is a share of the whole: 25% means one time in four. Odds compare the bad outcomes with the good ones: 3 to 1 against means three failures for every success — which is the same one time in four.
Odds against
(1 − P) ÷ P
P = 25% → 0.75 ÷ 0.25 = 3, written 3 : 1.
Probability from odds
P = 1 ÷ (odds + 1)
3 : 1 → 1 ÷ 4 = 25%.
Poker players use both. Draw probabilities are usually spoken as percentages ("about 35% to hit the flush"). Pot odds are spoken as ratios ("I'm getting 3 to 1") because a ratio is what the pot literally offers: three dollars to win for every one you risk.
Why the pot odds lesson needs this
The break-even decision is a comparison: is the probability my hand wins at least as large as the share of the pot I'm putting in? Being fluent in both forms is what lets you compare them in your head.
Quick check
A hand has 20% equity. What are the odds against it winning?
Show answer
4 to 1 against — 0.8 ÷ 0.2.