Roulette Odds – Understanding The Odds of Roulette

If you want to truly understand roulette, the best place to start is by learning the odds involved in the game. Since it’s a game of chance that the player can’t (legally) influence, the odds of roulette don’t change during play, and the numbers in this article will be accurate whether you play roulette online or in a casino.

How Roulette Odds Are Calculated

In many casino games, calculating the exact odds takes some pretty complex math. Finding the house edge for a game like video poker and blackjack usually requires a computer program – it’s not something you can quickly do with a piece of paper.

But roulette is different. It’s a fundamentally simple game, and calculating the odds for any given bet can be done with just a little bit of math.

Take, for instance, a bet on a single number on an American roulette wheel. This bet pays 35-1, meaning you’ll win 35 units when you hit your number, and lose one unit each time you don’t.

There are 38 numbers on the roulette wheel, which makes the odds of winning on any given spin 1/38 – or 2.63%. Conversely, you’ll lose the other 97.37% of the time, or 37/38.

This makes calculating the roulette house edge rather simple:

(1/38 * 35) – (37/38 * 1)
35/38 – 37/38
= – 2/38 or – 5.26%

Since the final result is negative, the house has the advantage, which works out to 5.26% or 2/38. In other words, the house edge is exactly equal to the number of zeroes on the wheel divided by the total amount of numbers on the wheel.

This is not at all coincidental. Virtually all roulette bets pay out at perfectly fair odds for a wheel that only contained the numbers 1-36, without including the zeroes. By adding the zeroes to the wheel without changing the payouts, the house guarantees itself a mathematical advantage over the player.

One way to reduce this house edge is to decrease the number of zeroes on the wheel. European roulette wheels have only a single zero, which cuts the house edge almost in half (it doesn’t cut it exactly in half because there’s also one less number of the wheel in total). Instead of 2/38, the house edge is now 1/37 – or 2.70%.

What does that difference mean for you? Imagine you made 1,000 bets on roulette, with each bet being for $10. That makes $10,000 in bets in total. If you played American roulette, you’d be expected to lose $526. Meanwhile, if you played European roulette, you’d only be expected to lose $270 – a savings of $256.

Interesting, what bets you were making in each game would have very little effect on your end results, as the house edge in roulette is usually the same for every bet you make.

What will change is your variance. If you bet only on red or black, you’d expect relatively little variation in your results – you aren’t likely to win or lose an amount that’s more than a few hundred dollars away from your expected loss. On the other hand, if you bet on individual numbers, you could easily win or lose thousands more based on how lucky (or unlucky) you were over your 1,000 bets.

Exceptions in Roulette

Some bets don’t have the normal roulette odds associated with them. For instance, in American roulette, the “top line” bet – the combination that covers 0-00-1-2-3 – pays out at 6-1, which results in a house edge of 7.89% (or 3/38). It’s very rare that you’ll ever see another player make this bet, and you should avoid it as well.

One great place to cut down on the house edge is in European roulette tables that utilize the en prison rule. Under this rule, if you make an even money bet – say betting on red or black – and the result of the spin is a zero, you don’t immediately lose your bet.

Depending on the exact rules your casino uses, you might get half of your money back when this occurs, or you may have your bet “imprisoned.” An imprisoned bet is released if you win on the next spin, or else it is lost. While the exact numbers will depend on the specific rules being used, an en prison rule usually cuts the house edge to about 1.38% or less on even money bets.