House Edge in European Roulette

House edge is the percentage of each bet that is expected to go to the online casino in the long run. Therefore the higher the house edge the less favorable is the game to the player. It is not always easy to calculate the house edge in online casino games. Roulette however allows easy calculation of house edges. This article describes the process for some bets in roulette.

The simplest bet in roulette is the single bet. In European roulette it can be placed on any of the numbers 1 to 36 or on 0. A player who wagers $1 on this bet will get $35 if he wins. He will forfeit the $1 if he loses. Out of 37 outcomes the player will win on one outcome and therefore the probability of winning is 1/37 or 0.027. Out of 37 outcomes the player will lose on 36 outcomes and therefore the probability of losing is 36/37 or 0.973.  The players expectation for the $1 wagered is calculated as (35 x 0.027) – (1 x 0.973), which is -0.027. Hence for every $1 wagered on any single number the player will expect to lose $0.027 or the house will expect to retain $0.027. Expressed as a percentage this is 2.7%.

The neighbors of zero bet, is one of the complicated European roulette bets, that follows a continuous sequence of numbers on the roulette wheel of which zero is at the center. The 17 numbers covered are 22, 18, 29, 7, 28, 12, 35, 3, 26, 0, 32, 15, 19, 4, 21, 2 and 25. The wager has to be placed as multiples of $9. The minimum $9 wager is placed as follows. $2 are placed on the 0, 2, 3 trio; $1 is placed on each of the 4, 7, the 12, 15, the 18, 21, the 19, 22 and the 32, 35 splits and $2 are placed on the 25, 26, 28, 29 corner. The calculations are as follows.

If any of 0, 2 or 3 is called the player will win $22 at a payout of 11 to 1. He will lose the remaining $7 and hence his net win will be $15. The probability of this happening is 3/37 or 0.08. If any of 25, 26, 28 or 29 is called the player will win $16 at a payout of 8 to 1. He will lose the remaining $7 and hence his net win will be $9. The probability of this happening is 4/37 or 0.11. If any of the numbers from the five splits are called the player will win $17 at a payout of 17 to 1. He will lose the remaining $8 and hence his net win will be $9. The probability of this happening is 10/37 or 0.27. If any of the 20 numbers not in the given sequence are called then the payout is zero and the player loses $9. The probability of this happening is 20/37 or 0.54.

The players expectation for the $9 wagered is calculated as (15 x 0.08) + (9 x 0.11) + (9 x 0.27) – (9 x 0.54), which is -0.243. Hence for every $9 wagered on the neighbors of zero bet the player will expect to lose $0.243 or the house will expect to retain $0.243. Expressed as a percentage this is also 2.7%. In fact all bets in European Roulette have a house edge of 2.7%.

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