Roulette odds

We’ve decided to go kind of deep into the matter, apply maths, look through the main aspects of gambling behaviour again, and even quote Einstein. Hopefully, all of that will help you understand roulette odds better.

Continents matter

When it comes to better odds, the question of choosing between European and American roulettes should never even appear on the table. Remember this once and for all: both roulettes promise the same payout – 35/1, but the winning odds are different. The wheels of American roulettes have 1 pocket more than European – 00, double zero, the second green slot. So, there are 38 slots on an American roulette and 37 – on a European. Meaning that placing a bet on one of 38 options, your chance to win is 1 out of 38, while when there are 37 slots, the odds look better: 1 to 37.

Let’s talk math

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Albert Einstein isn’t only the world’s most famous physicist: gamblers also have a soft spot for him. They just love chewing over his quote about winning odds at Roulette. According to him, “No one can win at roulette unless they steal money from the table while the croupier isn’t looking”. The gambling experts rose and started writing articles, debating vehemently and proving here and there how wrong the Nobel Prize winner was.

We don’t know Albert from Adam but will go out on a limb and say that we mostly see what he is getting at.

Roulette is a game with a negative expected gain, no matter which position you bet on. Einstein wasn’t just a witty man who also had a way with words, he knew his math, to put it mildly.

And the math clearly states:

Expected value of a $1 bet = 1/n(36 – n) = 36/n – 1.

Where n – the number of pockets on the wheel.

Why 36? All the casinos offer a payout of 35/1. It means that if the number you’ve bet on wins, you will get your bet back plus the amount of 35x – your bet multiplied by 35. For example, if you bet $1, you’ll get $36 when you win.

What casinos don’t mention though, is that the winning odds are 37:1 (in European roulette) and 38:1 (American), not 36:1, as there are additional pockets on the wheel – 0 and 00.

If 00 and 0 weren’t there, then:

Expected value of a $1 bet = 36/36 – 1 = 0.

In this case, the game would be fair: 36 numbers on the wheel – 36 chances to win, the odds 36:1 with the payout of 35/1. Then none of the sides would have an advantage – neither gamblers nor the House.

But everyone knows that the House always wins, don’t they?

That’s why an expected value of a $1 bet for European roulette would be 36/n – 1 = 36/37 – 1 = -0.027.

For the American wheel: 36/38 – 1 = -0.0526 (-0.053).

The numbers led by the negative expected value want to tell us that when you bet on one number on the wheel, you will lose at least $2.7 for every $100 you spend ($5.3 for American roulette).

Odds, payouts, bets

However, you don’t always have to place 1 bet and play with odds 37:1 (38:1). There are different ways to do it. Let’s see how the odds will look for different kinds of Roulette bets.

To calculate the odds and the payout, we’ll use the same formula. When calculating the odds, we’ll use the numerators 37 (European roulette), 38 (American roulette). When calculating the payout rate the numerator has to be 36 (35/1).

36/n – 1, where n is the number of roulette pockets that your bet covers.

For instance, if you bet on 4 numbers, then 36/4 – 1 = 8. The payout rate will be 8/1 meaning that if you bet $1 and win, the casino will pay you 8+1=$9.

Winning odds for different kinds of Roulette bets

winning odds

Let’s look how the odds will change depending on the number of chosen numbers and the kind of bet you might go for.

Straight up

A bet on one number (including 0 or 00). Winning odds for European roulette: 36:1. For American roulette: – 37:1. The payout = 35/1.


A bet on 2 adjoining numbers both vertical or horizontal. European roulette: 17.5:1, American roulette: 18:1. The payout = 17/1.


A bet on 3 adjoining numbers located horizontally (1, 2, 3). European roulette: 11⅓:1, American roulette: 11⅔:1. The payout = 11/1.


A bet on 4 adjoining numbers creating a square (1, 2, 4, 5). European roulette: 8.25:1, American roulette: 8.5:1. The payout = 8/1.

Top Line or Basket

A bet on 0,1,2,3 at European roulette and on 00,0,1,2,3 at American. European roulette: 8.25:1 with the payout 8/1, American roulette: 6.3:1 with the payout = 6/1.

Double Street

A bet on 6 numbers making up 2 horizontal rows (16, 17, 18, 19, 20, 21). European roulette: 5⅙:1, American roulette: 5⅓:1. The payout = 5/1.

First, Second, and Third columns

Bets on all the numbers of the 1st, 2nd and 3rd columns of the layout. European roulette: 21⁄12 :1, American roulette: 21⁄6:1. The payout = 2/1.

First, Second and Third dozens

Bets on the numbers from 1 to 12, 13 to 24, 25 to 36. European roulette: 21⁄12 :1, American roulette: 21⁄6:1. The payout = 2/1.


A bet on all the odd numbers (1, 3, 5, 7…35). European roulette: 11⁄18:1, American roulette: 11⁄9:1. The payout = 1/1.


A bet on all the even numbers (2, 4, 6, 8…36). European roulette: 11⁄18:1, American roulette: 11⁄9:1. The payout = 1/1.


A bet on all the red numbers. European roulette: 11⁄18:1, American roulette: 11⁄9:1. The payout = 1/1.


A bet on all the black numbers. European roulette: 11⁄18:1, American roulette: 11⁄9:1. The payout = 1/1.

1 to 18

A bet on all the numbers from 1 to 18. European roulette: 11⁄18:1, American roulette: 11⁄9:1. The payout = 1/1.

19 to 36

A bet on all the numbers from 19 to 36. European roulette: 11⁄18:1, American roulette: 11⁄9:1. The payout = 1/1.

Better odds with no math required

Now let’s talk about some steps that you should take before even placing a real money bet. Funny enough, they will increase your odds of winning at Roulette, minimize your losses, and won’t require any math formulas.

Number 1. Consider the outside bets, especially if you are a newbie at the table with the Devil’s wheel. Although they won’t shower you with millions, these bets have the best winning odds with the payout = 1:1. There’s no mystery, intuition, or luck here: it’s pure math. Outside bets are the safest.

Number 2. If you are gambling online, make sure the casino is licensed by a legitimate gambling authority and has a reputation of a fair game provider. Do the Internet research, if you are not sure: go to themed forums, read reviews, players’ feedback, and check the industry watchdogs’ blacklists.

Number 3. Don’t be overconfident and play Roulette in demo mode first. There are more than enough options on the Internet to do that.

Number 4. Evaluate table bet limits – minimum and maximum bets allowed at the game. Don’t play roulette with the minimum bet that will cost you half of your gambling budget. Start small: minimum bets of $1 are considered standard.

Number 5. Money management is crucial. Don’t drink alcohol while playing, set budget limits and follow them. Cash out all the winnings, however small. Don’t bet the money you win – use only the amount of your gambling budget.

Number 6. Don’t play Roulette to make money. Treat the game as a game: have fun, test your luck and quit before you decide to compensate for your losses.

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