Roulette is strictly a game of chance, but understanding your likelihood of success in any given circumstance is vital if you wish to hang in the game long enough to build your bankroll. From bet to bet, table to table, in roulette there is a host of mathematical and strategic factors to consider and we are here to simplify it all and eradicate any confusion. Below we will explain roulette odds and how they will impact the house edge.
House edge in roulette
The term house edge refers to the probability of a bet winning compared to the payout odds offered, and in effect, the amount the player loses relative for any bet made, on average.
All common casino games favour the house to some degree, and roulette is no different. For every kind of payout in roulette, they are always a fraction shorter than the actual probability of each bet-type winning, allowing for the house edge. The greater the discrepancy, the greater the advantage the casino holds over the player is.
European vs American roulette house edge
Although the payouts for European and American roulette games always remain the same (hitting a straight-up number pays out 35 to 1), the mathematical odds of any single number coming up are different across the two versions: the chance we have of the ball landing on our chosen single number is 1 in 37 in the European version, while when playing the American version, the chances of the same occurring are 1 in 38. This is due to the most telling factor in any game of roulette: how many zeros there are on the wheel. In European roulette, there is just one zero (0) and thus 37 numbers in total on the wheel, but in American roulette there are two zeros (0 and 00), and thus 38 numbers in total. That extra zero significantly increases the house edge.
The house edge can be explained as follows: a player who bets on a single number (in the American game), has a probability of 1 in 38 that he receives a payout 35 times his/her wager, and a 37 out of 38 chance of losing his/her wager. The formula to thus work out the edge is:
- American roulette: -1 x 37/38 + 35 x 1/38 = −0.0526 (5.26% house edge).
- European roulette: -1 x 36⁄37 + 35 x 1/37 = -0.0270 (2.70% house edge).
This formula will work to find the house edge of any casino games and casino bet, so long as you know the actual chances of winning, and the payout of the wager. For instance, the chance we have of drawing perfect pairs in blackjack of our first two cards (same rank and suit) is 1456 in 86320, and the payout for this side bet is 25 to 1.
So the formula to work out the house edge is: -1 x the number of possible losing outcomes (84864) divided by the total possible outcomes (86320), plus 25 x the number of possible winning outcomes (1456) divided by the total possible outcomes (86320), which is equal to -0.5614, or a whopping house edge of 56.14%.
Note: It is important not to get confused about the different ways the odds in roulette are expressed: continuing on from the above example, we’ve chosen to write the probability of a straight-up bet winning on a Euro table as a 1 in 37 chance, but often the odds will be expressed as 36 to 1. This ultimately means the same thing; when the odds are written as 36 to 1 (or sometimes 36:1) that actually represents the odds against winning, which are 36 non-winning numbers to 1 winning number. In percentage format, it will (or at least should) always be written as a 2.7% (1/37 x 100) chance of occurring.
Now, the zero pocket/s are green in colour and thus do not cover the red and black bets, nor do they cover even and odd wagers, nor wagers placed on the 1-18 or 19-36 bets. So if we bet on black at a European table, our chances of winning would be 18 in 37 (a probability of 48.65%, and the odds against winning of 19 to 18, or in simple form, 1.06 to 1).
In American roulette, the chances of winning the same wager are 18 in 38 (a probability of 47.37%, and the odds against winning of 20 to 18, or 1.111 to 1). The payout for such a bet across all roulette forms is 1:1, evidently less than the odds in both.
Top line bets
Another American feature that pushes the odds in favour of the casino is the existence of the top-line bet. Also called a first five bet, this is when a player wagers on 0, 00, 1, 2 and 3 (not available in European games). The payout for winning on the top line is 6:1, but the odds against winning are in fact 33 to 5 (or in simpler form, 6.6 to 1), with the probability of success just over 13% (five winning numbers divided by a total of 38 numbers).
This kind of bet boosts the house edge up to 7.89% (by following the formula as shown above), and that is 2.63% higher than any other U.S. wager, and some 5.19% more than all the possible bets in European roulette (if you haven’t realised yet, we are suggesting you stay well clear of such a bet).
La Partage & En Prison
French roulette is similar to the modern Euro game, with the aesthetics of the layout being the only outwardly obvious difference. However, there are some subtle contrasts in the betting set-up that make the traditional version an attractive option for real money players.
A key difference is the la partage and en prison rules. In the majority of current-day American and European games, zero goes to the dealer by default – ie. if you make any bet that doesn’t include 0 or 00, you lose outright if the ball lands on a zero. In French roulette however, if you make any ‘even money’ bet (red or black, evens or odds, 1 to 18 or 19 to 36) and the zero comes up, you will usually have two options: enact the ‘half back’ rule, where you reclaim half of your wager and forfeit the rest (la partage), or ‘imprison’ the bet by leaving it in place to play the next spin (en prison, as you would of guessed).
If an imprisoned bet wins on the next spin, it effectively pays for itself – ie. you recover your stake without adding any winnings. If zero happens to be spun again on the second spin, different casinos will hold different rules for imprisoned bets: they may be treated as wins, loses, la partage or en prison again.
This system has a huge impact on the house edge for all even-money bets, as you get two bites of the cherry on a wager that already has more than a 48% chance of winning. This cuts the house’s advantage in half, from 2.70% to 1.35%. As such, these rules are rarely used in brick-and-mortar gambling venues outside of Monte Carlo (although there are establishments in Atlantic City that use a similar method for double-zero games).
Payouts and odds table
As mentioned, the payouts for winning wagers are all but universally standardised across all major forms of roulette.
- Below is a list of all the bets on European and American tables and their respective payouts.
- We have columns (one Euro and one U.S.) for the ‘odds against winning’ in their simplest form (x to 1) so as to easily see the discrepancy between such odds and their respective payouts, as well as in parenthesis, their non-simple form, which is ultimately the amount of non-winning numbers compared to the amount of winning numbers’).
- We have columns (one Euro and one U.S.) for the probability of the bet winning in percentage format (to two decimal places).
- And we list the house edge for U.S. (double zero) and European/French (single zero) versions.
This is the most in-depth and comprehensive roulette odds/payout table you will find on the Internet:
| Bet Type | Payout (Same for Euro and US) | European Odds Against Winning | European Probability In % | European House Edge | US Odds Against Winning | US Probability In % | US House Edge |
|---|---|---|---|---|---|---|---|
| Single Numbers | 35 to 1 | 36 to 1 | 2.70% | 2.70% | 37 to 1 | 2.63% | 5.26% |
| Split | 17 to 1 | 17.5 to 1 (35 to 2) | 5.41% | 2.70% | 18 to 1 (36 to 2) | 5.26% | 5.26% |
| Street | 11 to 1 | 11.43 to 1 (34 to 3) | 8.11% | 2.70% | 11.667 to 1 (35 to 3) | 7.89% | 5.26% |
| Trio (European only – 0, 1 and 2, or 0, 2 and 3) | 11 to 1 | 11.43 to 1 (34 to 3) | 8.11% | 2.70% | NA | NA | NA |
| Basket American (0, 1, and 2; 0, 00, and 2; or 00, 2, and 3) | 11 to 1 | NA | NA | NA | 11.667 to 1 (35 to 3) | 7.89% | 5.26% |
| Basket/First Four European (0, 1, 2, and 3) | 8 to 1 | 8.25 to 1 (33 to 4) | 10.81% | 2.70% | NA | NA | NA |
| Corner | 8 to 1 | 8.25 to 1 (33 to 4) | 10.81% | 2.70% | 8.5 to 1 (34 to 4) | 10.53% | 5.26% |
| Top Line/First Five | 6 to 1 | NA | NA | NA | 6.6 to 1 (33 to 5) | 13.16% | 7.89% |
| Six Line | 5 to 1 | 5.17 to 1 (31 to 6) | 16.22% | 2.70% | 5.33 to 1 (32 to 6) | 15.79% | 5.26% |
| Columns | 2 to 1 | 2.08 to 1 (25 to 12) | 32.43% | 2.70% | 2.167 to 1 (26 to 12) | 31.58% | 5.26% |
| 1st 12, 2nd 12, 3rd 12 | 2 to 1 | 2.08 to 1 (25 to 12) | 32.43% | 2.70% | 2.167 to 1 (26 to 12) | 31.58% | 5.26% |
| Red & Black | 1 to 1 | 1.06 to 1 (19 to 18) | 48.65% | 2.70% | 1.111 to 1 (20 to 18) | 47.37% | 5.26% |
| 1-18 & 19-36 | 1 to 1 | 1.06 to 1 (19 to 18) | 48.65% | 2.70% | 1.111 to 1 (20 to 18) | 47.37% | 5.26% |
| Odds & Evens | 1 to 1 | 1.06 to 1 (19 to 18) | 48.65% | 2.70% | 1.111 to 1 (20 to 18) | 47.37% | 5.26% |