Odds & Probability
Casino odds come down to one idea: payouts are set slightly below the true probability of an outcome, and that gap is the house's profit. Understanding true odds versus payout odds — and that each result is independent — explains every casino game.
| True Odds | The real probability of an outcome |
|---|---|
| Payout Odds | What the casino pays (set below true odds) |
| Independence | Each spin/roll/deal is independent |
| The Gap | True odds minus payout odds = house edge |
True odds vs payout odds
Every bet has a true probability. On a single-zero roulette wheel a specific number has a 1-in-37 chance, so the ‘fair’ payout would be 36-to-1. The casino pays 35-to-1 instead. That one-unit shortfall, applied across all 37 outcomes, is the house edge. Once you see the gap between true odds and payout odds, you can read the value of any bet on the table.
Independent events and the long run
Most casino outcomes are independent: a roulette wheel or a slot has no memory of previous results, so a colour being ‘due’ after a streak is an illusion (see the gambler’s fallacy). Probability only asserts itself over large numbers of trials, which is exactly the scale at which the house edge guarantees the casino’s profit — and at which any betting system’s promises fall apart.
Frequently asked questions
What is the difference between true odds and payout odds?
True odds reflect the real probability of an outcome; payout odds are what the casino actually pays, set slightly lower. The difference is the house edge.
Are casino outcomes really independent?
On fair games, yes — each spin, roll or deal is independent of the last. Believing otherwise is the gambler's fallacy.
Sources
- Probability theory
- Published game rules