The Mathematics of Roulette
The mathematics of roulette are easily learned. On the double-zero wheel with 38 positions, the player should be able to pick the winning number an average of once every 38 spins. Although the odds are 37 to 1 that you will select the right number in one spin, the payoff odds are only 35 to 1, and the casino edge derived from this difference of two units is 2/38 or 5.26%.
If you place a single bet on two numbers, you are, in effect, betting half on each number, and, in the long run, 38 spins of the wheel two wins as compared to 36 losses. Therefore, true odds are 36 to 2, or 18 to 1, and as the casino pays 17 to 1, or 34 to 2, the house, again, comes up with the same two-unit-average advantage. The arithmetic is similar for all the inside bets except the five-number wager.
Unless "surrender" or "en prison" is offered, the outside even payoff wagers are not better. If you bet on the 18 red or 18 black numbers, the 18 even or 18 odd numbers, or the 18 high or 18 low numbers, you have 18 chances to win but the green zeros must be added to give you 20 chances to lose, and the house still ends up with a two-unit edge. With the three columns, and the three dozen bets, you have 12 ways to win, and including the zeros there are 26 ways to lose. The odds are 26 to 12 against you, but the payoff is only 2 to 1, or 24 to 12, once again yielding the casino the identical two units.
Surrender:
For Atlantic City, The New Jersey Control Commission Rules of the Games state, "If the roulette ball comes to rest around the wheel in a compartment marked zero (0) or double zero (00), wagers on red, black, odd, even, 1 to 18, and 19 to 36 shall not be lost, but each player having such a wager shall surrender half the amount on such bet and remove the remaining half." This rule cuts the casino advantage in half, from 5.26% to 2.63% on all the even money bets, giving the same result as the European "en prison" rule, where the outcome on all even-money bets after the appearance of a zero is determined by the following spin. Atlantic City casinos are the only gambling houses in the United States offering the gaming public this feature, although "offering" is probably not the best word, since the state law requires it.
Single-Zero Game:
An even better game being offered at many casinos features roulette with a single zero. Unfortunately, the surrender rule does not apply, but even so, the casino advantage is reduced to 2.70%, not just for even-money bets, but for all wagers, inside and outside. True, the game is not as favorable as correct play at blackjack or the line bets in craps, but for the gamer who likes to play roulette, it is acceptable. The only thing difficult understand is why anyone but the even-money-bet players would patronize the double-zero wheels.
Now that you are familiar with the rules and procedure of the game, and understand how to bet with the very least disadvantage, you must consider that in the long run your hourly cost will be a little more than 2½ percent of the average total amount of money you place on the table in an hour. Only you can decide how much you are willing to pay for the pleasure of playing this exciting game. Of course, with intelligent money management you can control your losses, and, who knows?...you may come up a big winner.