Comparing House Edges in Online Casino Roulette
Published on: November 3, 2009
The three variants of roulette available in online casinos are American roulette, European roulette and French roulette. The American roulette wheel has 38 numbers, 18 of which are black, 18 of which are red and 0 and 00 which are green. The European roulette wheel has 37 numbers, 18 of which are black, 18 of which are red and 0 which is green. The French roulette wheel is identical to the European roulette wheel. However the game differs because players are returned half the wagers placed on even money bets if 0 is called.
These differences can be used to compute the house edges of the different online roulette variants and thus come to a conclusion as to which is the most user-friendly game. In order to illustrate the process of computation of the house edges it will be assumed that the player places a $1 wager on any red number being called. In the context of this wager three outcomes are possible. A red number can be called, a black number can be called or a green number can be called. By considering the probabilities of each of these outcomes and their payouts it is possible to compute the house edge.
Let us first consider American roulette. There are 18 red numbers and a total of 38 numbers therefore the probability of obtaining a red number is 18/38. If a red number is called the player wins $1 and therefore his expected payout is $(1 x 18/38). There are 18 black numbers and a total of 38 numbers therefore the probability of obtaining a black number is 18/38. If a black number is called the player loses $1 and therefore his expected payout is $(-1 x 18/38). There are 2 numbers that are green and a total of 38 numbers therefore the probability of obtaining a green number is 2/38. If a green number is called the player loses $1 and therefore his expected payout is $(-1 x 2/38).
Hence the expected payout in the case of American roulette is:
(1 X 18/38) + (-1 x 18/38) + (-1 x 2/38) = -0.053
For ever $1 wagered on Red in American roulette the player expects to lose $0.053 to the online casino.
In European roulette there are 18 red numbers and a total of 37 numbers. If a red number is called the player wins $1 and therefore his expected payout is $(1 x 18/37). There are 18 black numbers and a total of 37 numbers. If a black number is called the player loses $1 and therefore his expected payout is $(-1 x 18/37). There is 1 green number and a total of 37 numbers. If a green number is called the player loses $1 and therefore his expected payout is $(-1 x 1/37).
Hence the expected payout in the case of European roulette is:
(1 X 18/37) + (-1 x 18/37) + (-1 x 1/37) = -0.027
For ever $1 wagered on Red in European roulette the player expects to lose $0.027 to the online casino.
In French roulette there are 18 red numbers and a total of 37 numbers. If a red number is called the player wins $1 and therefore his expected payout is $(1 x 18/37). There are 18 black numbers and a total of 37 numbers. If a black number is called the player loses $1 and therefore his expected payout is $(-1 x 18/37). There is 1 green number and a total of 37 numbers. If a green number is called the player loses only $0.5 and therefore his expected payout is $(-0.5 x 1/37).
Hence the expected payout in the case of French roulette is:
(1 X 18/37) + (-1 x 18/37) + (-0.5 x 1/37) = -0.014
For ever $1 wagered on Red in French roulette the player expects to lose $0.014 to the online casino.
Therefore is can be seen that on the basis of the house edges for even money bets French roulette offers the maximum advantage to the player.
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