On this page we'll show you how to calculate the expected outcome for the roulette bets. You will see what determines the house edge.
Let's assume the American roulette rules, so we have 38 numbered wheel (1-36, 0, 00) and 11 possible bets. We can bet on a number, a group of numbers, or a color which we hope will be a winning choice.
The outcome of every spin is independent, that is not determined by prior spins. Even if you have ten black numbers after ten spins, the chance of getting red in the next spin is the same as to get black.
The probability of hitting the single number is 1 in 38, or 37 to 1. In other words, if you bet $1 chip on this number 38 times you will win only once. The payoff for this bet is 35:1. So, the dealer will give you $35 and you also keep the dollar you bet. In total, after 38 spins you will lose two dollars that is 5.26% of 38 wagered dollars. So, the house edge on the single bet is 5.26%.
The house edges on all possible bets for American roulette are in the table below, it details expected gains and losses per 38 games for $1 bet. Each number has a probability of 1/38 of being a winner
|Bet||Bet on||Payoff||Odds||Games player wins||Games casino wins||Dollars won by player||Dollars won by casino||Casino expectation (38 games)||House edge|
|Straight up||one number||35:1||38:1||1||37||$35||$37||$2||$.0526|
|Split Bet||two numbers||17:1||38:2||2||36||$34||$36||$2||$.0526|
|Street Bet||three numbers||11:1||38:3||3||35||$33||$35||$2||$.0526|
|Five Numbers||five numbers||6:1||38:5||5||33||$30||$33||$3||$.0789|
|Line Bet||six numbers||5:1||38:6||6||32||$30||$32||$2||$.0526|
|Red or Black||eighteen number||1:1||38:18||18||20||$18||$20||$2||$.0526|
|Even or Odd||eighteen number||1:1||38:18||18||20||$18||$20||$2||$.0526|
|Low or High||eighteen number||1:1||38:18||18||20||$18||$20||$2||$.0526|
With one exception, the casino edge is 5.26%. It is the five-number bet, where the casino has an edge of 7.89%.
We can, of course, calculate it in another way. The mathematical formula for expectation:
Expectation = [Number of the favorable results / Total number of the possible results] X The payoff for the favorable result + [Number of the unfavorable results / Total number of the possible results] X The bet
So, if you wager $1, your expectation, in terms of dollars, is:
Straight up (one number bet) = (1/38) x 35 + (37/38) x (-1) = -2/38 = -0.0526 or (-5.26%)
Five numbers = (5/38) x 6 + (33/38) x (-1) = -3/38 = -0.0789 or (-7.89%)
Red bet (18 numbers) = (18/38) x 1 + (20/38) x (-1) = -2/38 = -0.0526 or (-5.26%)
The results above are negative because we calculated the "player expectation". Revers these to positive and you will get the "casino expectation" or "house edge".
What does the expectation (house edge mean)? For every wagered dollar (we can say "invested" by the player) the casino expects to get at least 5.26%. And it's no wonder that casinos want their dealers to play as many games as possible during a specific time period.