# Roulette Odds

Roulette, like all gambling games, is all about odds. To get the most out of your roulette play it is critical to know how often you can expect to win and how much of an advantage you need to overcome.

At the most basic level, we talk about roulette odds in terms of the house edge – the advantage the casino holds over the player. In American roulette the house edge on virtually all bets is 5.26% (or 2/38), while in European roulette, the edge for the casino is 2.70% (1/37). Essentially, you can figure out the edge by dividing the number of zeroes on the wheel by the total number of pockets. That is true at least for standard roulette games that pay out at odds that would be fair if the wheel only contained the 36 numbers without zeroes.

However, these are only the most basic of roulette odds. Looking deeper into the odds is a good way to get a better understanding of what’s actually going on in this game.

### Roulette Payouts and Odds

Let’s look at how likely you are to win various bets in roulette and why the odds ultimately result in the same house edge for nearly every bet on the table. For the purposes of these examples we’ll be using American roulette, though the same calculations can easily be done for European roulette as well.

For an even money bet – let’s say red/black – players win if the ball stops on any of the 18 pockets that share that color. That makes your chances of winning 18/38, or approximately 47.37%. Calculating the house edge for a bet that pays out even money is simple – 47.37% of the time you gain a bet and 52.63% of the time you lose a bet.

This makes the calculation:

.4737 – .5263 = -.0526 (or 5.26%)

However, things get a little trickier when we talk about other bets. For instance, let’s say we make a bet on a single number. This bet pays 35-1. We can only win if our exact number hits, meaning that our odds of winning on any given spin are 1/38, or 2.63%. In addition, when we win we win 35 units, but when we lose we only lose one unit.

That makes the calculation:

(.0263 * 35) – .9737

.9211 – .9737 = -.0526 (5.26% house edge)

While the odds and payouts vary on different roulette bets, ultimately the house edge is the same. While in many other games proper strategy is required to get the best possible odds for the player, roulette merely requires that players place bets in order to win.

### Winning Roulette Odds

Many of the most famous incidents in roulette history have involved players taking advantage of biased wheels. These are roulette wheels that do not have the proper construction to ensure that every pocket will be hit with equal probability. If a particular wheel has a bias towards certain numbers then players might be able to take advantage of this, as it is possible that those numbers could be hit frequently enough to overcome the house edge.

But just how often does a number have to be hit in order for players to be able to bet on it profitably? It’s important to remember that roulette games pay out “fairly” for a 36-number wheel. That means we’d have to hit our number once every 36 spins in order to break even – or 2.78% of the time. That’s not much more than the 2.63% of the time you’d expect to hit a number on an American wheel, or the 2.70% of the time your number should hit on a European roulette wheel.

This should show why it’s so important for casinos to make sure their wheels are free of even small amounts of bias. Since the edges on individual numbers are based on just a small difference between the payouts and the odds of numbers being hit, any tiny change could put things in the player’s favor.

For instance, in European roulette, if a single number is expected to win 5% more often than at random – meaning it would be hit just 21 times on average for every 20 times each other number was hit – that would be enough to give the player a slight edge. Should a number manage to be hit on a full 3% of spins, the player edge would be an enormous 8% over the casino.

### Odds of Unusual Roulette Events

Players are sometimes curious about the possibility of odd occurrences happening in roulette. For instance, many players wonder how often they will lose their entire stake when attempting to use the Martingale system, in which players double their bets each time they lose. It might take seven consecutive losses on an even money bet in order to hit the table limit, at which point the player will no longer be able to double their bet. On a European roulette table, the odds of this occurring are approximately 1 in 106.

Sometimes, unlikely events can turn in your favor as well. It’s not impossible for the same number to hit two or even three times in a row, though it’s not something you should count on happening. Before any spin the odds that a number you’ve chosen repeating on the next three spins is 50,652-1 in European roulette and 54,871-1 in the American game.

It is worth remembering that while betting systems sound like a good idea, they have been proven beyond any shadow of a doubt to be losing plays.

### American Roulette Odds

The American Roulette wheel has a zero, a double-zero and 36 regular numbers. Hence, you have 38 possible spaces on which the ball may land. When you bet on a single number, you have a 1/38 chance of winning. Over time you will win 1 out of every 38 spins. Take a look at the probabilities for every possible outcome illustrated in the table below.

Bets | Payout | Probability |
---|---|---|

Odd | 1:1 | 46.37% |

Even | 1:1 | 46.37% |

Black | 1:1 | 46.37% |

Red | 1:1 | 46.37% |

1-18 | 1:1 | 46.37% |

19-36 | 1:1 | 46.37% |

1-12 | 2:1 | 31.58% |

13-24 | 2:1 | 31.58% |

25-36 | 2:1 | 31.58% |

Single Number | 35:1 | 2.63% |

Combination of two numbers | 17:1 | 5.26% |

Combination of three numbers | 11:1 | 7.89% |

Combination of four numbers | 8:1 | 10.53% |

Combination of six numbers | 5:1 | 15.79% |

Combination of 1-2-3-0-00 | 6:1 | 13.16% |

Remember that these are the American Roulette odds. The European table does not have the double zero and, due to this fact, is much more advantageous to the player.

### European Roulette Probabilities

In European roulette there is no “00” hole, giving players a much better chance of winning. For example, for every $1 you bet on European Roulette you could expect to get back 97.37 cents over the long run ($1 minus the house edge of 2.63%, or 2.63 cents). Playing American roulette, you can expect to get back only 94.74 cents.

Bets | Payout | Probability |
---|---|---|

Odd | 1:1 | 48.6% |

Even | 1:1 | 48.6% |

Black | 1:1 | 48.6% |

Red | 1:1 | 48.6% |

1-18 | 1:1 | 48.6% |

19-36 | 1:1 | 48.6% |

1-12 | 2:1 | 32.4% |

13-24 | 2:1 | 32.4% |

25-36 | 2:1 | 32.4% |

Single Number | 35:1 | 2.7% |

Combination of two numbers | 17:1 | 5.4% |

Combination of three numbers | 11:1 | 8.1% |

Combination of four numbers | 8:1 | 10.8% |

Combination of six numbers | 5:1 | 16.2% |