Roulette Odds Are Fixed

Because roulette is a game of independent events, it is highly predictable from a statistical point of view. The roulette odds are fixed. They never change, regardless of how many spins have been made, what results occurred in the past, or how many wagers are piled on the table.

The European version of the game features 37 possible outcomes, from single zero to 36, on every turn of the wheel. The American version adds a double zero to the wheel, upping the number of potential results to 38. For the examples in this article, the European version, with a lower house edge, will be used.

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The basic 36 numbers on the roulette table layout can be bet in groups of 18 (even money bets, such as black, red, odd, even, 1~18 and 19~36) or as groups of 12 (dozens or columns). They can also be bet in groups of 6 (six-line or double row), 4 (corners or blocks), 3 (streets or rows), 2 (splits or pairs) and straight up (bets placed on a single number.

Combinations including the zero include the zero block (0-1-2-3), trios (0-1-2 or 0-2-3), and splits (0-1, 0-2, 0-3). The zero may also be bet straight up.

You will want to remember two basic formulae used for computing roulette odds. The first yields the likelihood of any winning outcome (P) for all numbers bet (B) on any given spin. It is expressed by the formula: P = B/37.

Using this formula, you can calculate that the likelihood of a zero coming up is 1/37 or 2.70 percent. This is also the amount of the house advantage, owing to the addition of the zero to the basic 36 numbers.

Similarly, the probability of a winner coming up among a pair of numbers is 2/37 or 5.40 percent. In a group of three numbers, it is 3/37 or 8.11 percent, a block of four numbers is 4/37 or 10.81 percent, and so on up to the even-money wagers, such as black, even, and high (19~36), which occur 18/37 times or 48.65 percent on any single spin of the wheel.

The second formula computes the probability of a winning outcome (P) for all numbers bet (B) over the course of any number of spins (N) in a series. It is expressed by the formula: P = 1 – {(37-B)/37}N.

You can use this formula to see that the probability of a red number coming up at least once in six spins is 1 - {(37-18)/37}6 or 98.17 percent. Or calculate the odds of a winner in 13 spins using the Birthday Strategy (repeatedly betting your two birthday numbers, such as July 13 = 7 and 13): 1 - {(37-2)/37}13 or 51.44 percent.

Knowing roulette odds can give you an appreciation of how good or bad some of your bets are. The Birthday Strategy, for example, gives you only a 5.40 percent chance of winning on any given spin, but it becomes a better than 50-50 proposition if you repeat it for 13 spins. Have you been giving up on it too soon?

Since a split pays 17-to-1, you can actually afford to play your birthday numbers up to 17 times before giving up and saying, “Today’s not my birthday.” Calculate the probability of your numbers coming up in 17 spins and you’ll get 61.1 percent. That means you should be getting a birthday present almost two-thirds of the time.

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