The Odds of the Common GamesSection I

Roulette Odds, Probability and the True Odds of the Table Games, Charted

Section I of the annual. The games whose arithmetic is settled — true odds against paid odds, drawn rather than described.

Take the cleanest example first. A European roulette wheel has thirty-seven pockets. Bet on one number and you win once in thirty-seven spins, which is a probability of 2.70%. The table pays you 35 to 1. If the game were fair it would pay 36 to 1, and the missing unit is the whole business model. European roulette odds are unusual in being this legible: one number explains everything, and it never changes with the bet you pick.

How roulette odds and true odds actually work

Every bet on the European table is a different slice of the same thirty-seven pockets, priced so that the shortfall stays constant. Cover two numbers and the payout halves. Cover eighteen and it drops to even money. The chance rises and the price falls in lockstep, which is why the last column below is the least interesting one on the page.

European roulette, single-zero wheel: chance and price for every standard bet

BetNumbersPaysChanceHouse edge
Straight up135:12.70%2.70%
Split217:15.41%2.70%
Street311:18.11%2.70%
Corner48:110.81%2.70%
Six line65:116.22%2.70%
Column or dozen122:132.43%2.70%
Red, black, odd, even, high, low181:148.65%2.70%

The even-money bets are the ones people misread. Red is not a coin flip. It wins eighteen times in thirty-seven, not eighteen in thirty-six, because the zero belongs to neither colour. That single green pocket is doing all the work, and it is why European roulette odds on red come out at 48.65% rather than a flat half.

Add a second green pocket and the game changes character entirely. American roulette odds pay exactly the same 35 to 1 on a number that now comes up once in thirty-eight rather than once in thirty-seven, and the edge jumps to 5.26%. The layout looks almost identical. The cost of playing it is nearly doubled.

The American wheel, and where it differs

Everything above assumes a single-zero wheel. Add a second green pocket and every number on the table pays the same as before while there is one more way to lose, which moves the house edge from 2.70% to 5.26% on every bet — with one exception that is worse still.

American roulette, double-zero wheel: the same bets, repriced, plus the one outlier

BetNumbersPaysChanceHouse edge
Straight up135:12.63%5.26%
Split217:15.26%5.26%
Street311:17.89%5.26%
Corner48:110.53%5.26%
Five-number (0, 00, 1, 2, 3)56:113.16%7.89%
Six line65:115.79%5.26%
Column or dozen122:131.58%5.26%
Red, black, odd, even, high, low181:147.37%5.26%

Two things fall out of that table. The first is uniformity again: eleven of the twelve standard bets carry exactly 5.26%, so on an American wheel as on a European one there is no clever bet to find. The second is the exception. The five-number bet covering zero, double zero, one, two and three pays 6:1 where the arithmetic asks for 6.2:1, and that rounding leaves it at 7.89% — half again worse than every other bet on the same layout, and the only bet on either wheel that is priced differently from its neighbours.

The practical reading is short. A European wheel returns 97.30% and an American wheel 94.74%, on identical play, so where both are offered the choice is worth more than any decision made afterwards.

The house edge, compared across six games

Games are easier to rank than to describe. The figures below are the standard long-run edges for correct play, which for blackjack means basic strategy and for craps means sticking to the pass line.

0%1.5%3%4.5%6%Blackjack, basic strategy0.5%Baccarat, banker bet1.06%Craps, pass line1.41%Roulette, European2.7%Slots, typical online4%Roulette, American5.26%
House edge by game, assuming correct play. Blackjack is the outlier: it is the only entry on this chart where the player's decisions move the number.
CategoryValue
Blackjack, basic strategy0.5%
Baccarat, banker bet1.06%
Craps, pass line1.41%
Roulette, European2.7%
Slots, typical online4%
Roulette, American5.26%
Plate II

House edge by game, assuming correct play. Blackjack is the outlier: it is the only entry on this chart where the player’s decisions move the number. Source: House-edge figures as published by the game manufacturers and standard probability texts; blackjack varies roughly 0.4–0.8% with deck count and dealer rules.

Two things fall out of that plate. The spread between the best and worst bets on a casino floor is roughly tenfold, and the two roulette variants sit at opposite ends of the respectable range despite looking like the same game.

Blackjack, and why the player’s decisions matter

Blackjack is the exception that makes the rest of the section worth drawing. Roulette gives you nothing to decide: pick a bet, and the house edge is fixed at 2.70% whatever you do next. In blackjack the cards impose a decision on every hand, and the quality of that decision changes the number.

Basic strategy is the complete set of correct decisions for every combination of player hand and dealer upcard. Played perfectly it holds the edge near 0.5%. Played by instinct it drifts to something closer to 2%, which is worse than roulette. The game rewards study in a way no other table game does, and that is the honest reason it keeps its reputation.

Probability is not the same as payout: the table games compared

The confusion that produces most bad betting is treating a payout as a statement about probability. It is not. A 35 to 1 payout describes what the house will give you, not how often it expects to. True odds describe the second thing, and the difference between the two is the only number that matters over any length of time.

Where those true odds are published and audited rather than derived from the geometry of a wheel, they go under a different name. That is the subject of the next section, which deals with return to player and the payout percentages operators are required to disclose.

In this section

  1. 01 Blackjack Odds: Basic Strategy, Dealer Bust Rates and What the Rules Cost Matrix and bar chart
  2. 02 House Edge: What It Costs Per Hour, Why Hold Differs and Why No Betting System Moves It Cost per hour, charted

Queries answered

What are the odds of hitting a single number in roulette?

On a European wheel, one in thirty-seven, or 2.70%. The bet pays 35 to 1. That gap between a 1-in-37 chance and a 35-to-1 return is the entire house edge, and it is the same 2.70% on every other bet the European table offers.

Which casino game has the lowest house edge?

Blackjack played to correct basic strategy, at roughly 0.5% depending on the table rules. Baccarat’s banker bet is next at 1.06%, then the craps pass line at 1.41%. No table game beats a well-played blackjack shoe.

Are American and European roulette odds different?

The payouts are identical. The wheel is not. American wheels add a double zero, so a single number is 1 in 38 rather than 1 in 37, while still paying 35 to 1. That one extra pocket takes the house edge from 2.70% to 5.26%, which is nearly double.

Does betting red every time improve my odds?

No. Each spin is independent, and the wheel keeps no record of what it did last. A red bet on a European wheel wins 18 times in 37 whether the previous spin was red, black or zero.

Can a betting system beat the house edge?

Not on a game with a fixed edge. Progression systems such as the Martingale change the shape of the win and loss distribution, making small wins frequent and large losses rare but severe. The expected value per unit staked does not move.