Jul

28

2016

# How to Calculate House Edge in Roulette

A couple of months ago, I walked through the arithmetic for the house advantage on the pass line in craps.  It’s quite a lengthy calculation with a number of factors, but enough readers followed along that it brought a few questions. Here’s one:

“Thank you for your explanation of how to calculate the house edge on pass in craps. Could you do the same in roulette, maybe for red or black?”

Calculations are much simpler in roulette than on the craps pass line. For one thing, there’s no comeout roll and need to repeat numbers as in craps.

For red/black, odd/even or first 18/last 18 – the roulette wagers with even-money payoffs, we start with the number of possible wins or losses. There are 38 numbers, including 0 and 00, on an American double-zero wheel.

Twenty of those numbers are winners for the house; 18 win for the player. So our probabilities are 20/38 for a house win and 18/38 for a player win.

Subtract 18/38 from 20/38, and you get 2/38, representing the two more expected wins for the house than for the player per 38 spins. Do the division, and 2/39 comes to .0526. Multiply by 100 to convert to percent, and the house has a 5.26 percent edge.

The calculations differ slightly on other bets because we have to factor in bigger payoffs. Take the four-number corner bet, which returns 8-1. Out of 38 numbers, four are winners and 34 are losers.

If we bet \$1 on each of 38 spins and every number comes up once, then on each of the four winners we keep the \$1 bet and get \$8 in winnings. That’s \$9 per win, so four wins mean that in an average 38 spins, we wind up with \$36 of our original \$38, and the house keeps \$2.

That brings us right back to the house keeping 2/38 of the money, or 5.26 percent.

The number of wins per 38 spins and the payoff per win vary, but the house edge still comes to 5.26 percent on everything except the 7.89 percent on 0-00-1-2-3.