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Apr 7th 2007
To clarify, the odds are stated as A to B, meaning for every B dollar that you bet, you win A dollars. For example a 35 to 1 bet means you win 35 dollars for each 1 dollar bet.

Imagine that you are making a simple \$1 bet on the roulette table, on and individual number. You are having 1 to 38 chances to hit the number you bet on with an American roulette. Also, you could express it as 37 to 1 odds. Now, let's say you would win the bet. In this case the casino would pay you only 35 to 1 and as it was explained before, you should be paid 37 to 1. Over 38 spins then, you will stand to win on a number once, and lose 2 full dollars on this win. Two dollars is 5.25% of \$38.

Through the 5.26% house edge of American roulette you should understand that over the long run, the casino will take in 5.26% of what is played through the table. You can work that number out intuitively as we did above, or you can work it out with the mathematical formula for expectancy.

Expectancy is a number that represents the percentage of your wager you expect to win or lose for a given bet. If the bet is a 'positive expectation' one, the expectancy will be a positive number, and you should expect to make money from the game. If the bet is a 'negative expectation' bet, as almost every casino bet is, you should expect to lose money from the game.

Expectancy = [odds of winning X money won] + [odds of losing X money lost]

For example, let's run through the single dollar bet example from above.

Expectancy = [1/38 X 35] + [37/38 X -1]
= [0.921] + [-0.9736]
= -0.526 or a 5.26% negative expectation

This is the same as saying that this roulette bet has a house edge of 5.26%. The strange thing about roulette is that every bet has a house edge of 5.26%, on an American wheel. To illustrate this, let's look at a more complicated bet. If we put \$10 down on red, \$10 down on the number 8, and \$10 on the third column, what would the house edge be?

E = {[18/38 X \$10] + [20/38 X -\$10]}
and {[1/38 X \$350] + [37/38 X -\$10]}
and {[12/38 X \$20] + [26/38 X -\$10]}

E = [47.368 + (-52.631)]
and [9.210 + (-9.7368)]
and [6.3157 + (-6.8421)]
= -5.263 and -5.268 and -5.264

So, as you can see, the horrible house edge of 5.26% can't be avoided. The combination of bets also has an edge of -5.26, which we can see logically. 5.26% of each bet, combined, would work out to be 5.26% of the total bet.

Now, of course, you can hedge your bets if you like. Say you were betting on black, you could hedge that bet a little by betting on the third column. The third column has 8 reds and only 4 blacks, so a bet there covers almost half of the red numbers. Almost half of the red numbers covered, and all of the black numbers covered gives you pretty good coverage. In the end though, each bet still has a 5.26% house edge.

Now, don't be completely disappointed. After all these explications about how this house edge cant be avoided I will offer you better news. There are two things you could do to improve your house edge with the double zero wheel.

First it would be to look for an American roulette game played with a rule called "Surrender". Surrender is a rule whereby outside, even-money bets, are not lost instantly on a zero or a double zero hit. When a green pocket comes up you only lose half of your bet. Since those zeros play a large role in the edge, this rule plays a large counter-role. With this rule in effect, the house edge on outside even-money bets is dropped right down to 2.63%.

The second and actually the best ideea it would be to look for single zero wheels. This single decision brings the house edge from 5.26% to 2.70%.

And there's more. After you choosed a better house edge with the single zero wheel, you can do even more to lower your house edge. What? Look forward and play single zero wheels with the rules called En prison rule or the La partage rule.

If you can find a table that offers a single-zero wheels with the la partage rule, things couldn't get any better for roulette players. The reason for this is that the 'la partage' rule lowers the house edge of 2.7% to a more attractive 1.35%. What happens is that if the ball lands on zero, the players only lose half of their money on outside bets. In all, you still have the same chances of winning your bet, but the amount of money you could lose is less.

With the en prison rule is almost like getting a second chance. If the ball lands on zero, nothing happens to your bet; it stays 'in prison' until the next time the ball is rolled. Whatever happens then is exactly the same that would happen was the bet just placed on the table. The rule eliminates the threat of losing your bet if the ball lands on a zero. Just as with the 'la partage' rule, this one also lowers the house edge to 1.35%.

In the end as you can see after reading this page, even roulette holds a horrible house edge, especially the American roulette you still can find ways of improving your odds. There's always a difference between knowing how to play a game and knowing how to play smart and to win. Good luck!

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