The math of roulette

Roulette rules for beginners

Roulette is a casino game played with a numbered wheel and a table of possible bets. A ball settles in one pocket, and that outcome determines which wagers win.

A round in order

Check the wheel and table rules, choose a bet, and place it before betting closes. After the ball settles, winning wagers are paid and losing stakes are collected. Chip placement identifies the numbers covered.

The terms that matter

A pocket is a possible wheel outcome. Coverage is the set of outcomes that win a ticket. Stake is the amount wagered. Net profit excludes the returned stake, while total return includes it. House edge measures expected loss as a share of money wagered.

Zero is neither red nor black

Zero pockets are separate from the 1–36 groups. They do not win red/black, odd/even, low/high, dozen or column bets under ordinary rules. Check separately for La Partage or other zero-settlement rules.

Minimums and maximums

Limits belong to the actual table. They can differ between bet types, so this site does not give one universal minimum. Calculator amounts are hypothetical and do not show that a particular casino accepts a stake.

How to play roulette step by step

  1. Check the wheel type, the minimum and maximum bets and any zero rule on the table sign.
  2. Exchange money for chips and place them on the layout to choose your numbers or groups.
  3. The dealer spins the wheel and the ball, then announces that betting is closed.
  4. The ball settles in one pocket and the dealer marks the winning number.
  5. Losing bets are collected and winning bets are paid at the posted payouts.

The roulette bets and table layout guide shows where each chip goes.

Roulette terms

Inside bet
A bet on one to six numbers on the number grid: straight-up, split, street, corner or six-line.
Outside bet
A bet on a group of 12 or 18 numbers: dozens, columns, red, black, odd, even, low or high.
Even-money bet
A bet that pays 1:1.
Payout
The net profit paid on a winning bet, stated as a ratio such as 35:1.
House edge
The average share of wagers the game keeps in the long run.
La Partage
A single-zero rule that returns half of an even-money stake when zero lands.
En Prison
A rule that holds an even-money stake for the next spin after zero instead of settling it at once.