How to Calculate the Roulette House Edge
Outside Bets Edge
Outside bets will always lose when a single or double zero comes up. Zero is not red or black, is not even or odd etc. When the green zero comes up, the croupier wipes all the chips on the outside of the table.
Inside Bets Edge
The house also has an edge on inside bets because the payouts are always set at 35 to 1 when you mathematically have a 1 out of 37 (1 out of 38 for American roulette with 2 zeros) chance at winning a bet on a single number.
To demonstrate the roulette house edge, let's suppose you place chips and bet on every single number on the table, including the zero. Of course, you will win with one of your perfect bet, but you will win only 35 chips and invested 37 to cover the table.
European Roulette House Edge
If a player bets $1 on black, his chances of winning $1 is 18/37 since there are 18 black numbers out of 37.
However, his chance of losing $1 is 19/37. Therefore, the expected value of the house edge may be calculated as follows:
Expected Value = ($1)(18/37) + (−$1)(19/37)
Expected Value = 18/37 − 19/37
Expected Value = −1/37
Expected Value = −2.7%
Therefore, the house edge is 2.7%
American Roulette House Edge
If our player bets $1 on black, his chances of winning $1 is 18/38 since there are 18 black numbers out of 38.
However, his chance of losing $1 (i.e., winning −$1) is 20/38. Therefore, the expected value may be calculated:
Expected Value = (1)(18/38) + (−1)(20/38)
Expected Value = 18/38 − 20/38
Expected Value = − 2/38 = −1/19
Expected Value = −5.26%
Therefore, the house edge is 5.26%, very close to 2 times the house edge of the European roulette.
Other Roulette Bets House Edge
Check this Roulette Table of Odds. this table shows that all roulette house edge bets have the same expected value. The only exceptions are the five numbers bet where the house edge is considerably higher, 7.89% on an American wheel.
(4.3 / 5)
(4.2 / 5)
