Sanderson M. Smith

ROULETTE:
A FUN CASINO GAME, BUT YOU WON'T GET RICH PLAYING IT.

"Thanks to Sean Connery, black 17 is the most commonly played number. Why? Because that's the number James Bond, 007, always plays." (Harry Anderson)

Betting on the spin of the wheel is an old form of gambling. In American Roulette, the wheel contains thirty-eight pockets. Thirty-six of the pockets are numbered 1, 2, 3, ..., 36, one pocket is is 0, and the last is 00. As the diagram below indicates, there are 18 red numbers, 18 black numbers, and two green numbers (0 and 00). The wheel is spun and a small ball is thrown against a rim that surrounds the wheel. The ball eventually falls into the wheel and comes to rest in one of the numbered pockets. Prior to the rolling of the ball, players can bet on a number, a group of numbers, or a color which they hope will be a winning choice.

The possible roulette bets are shown below. A 1:1 bet means that if you bet one dollar, you get a dollar if you win, and lose your dollar if you don't win. Note that when you win, you keep your original dollar. If you have a chip on a 1:1 bet, and you win, the dealer simply matches your chip, and you end up with 2 chips. If you win a 35:1 bet, and you win, the dealer gives you 35 chips, and you also keep the chip you bet. When you lose, you simply lose your chip

The purpose here is not to show how to place the bets. (It's easy to make any of the bets indicated.) It is important to note that the numbers 0 and 00 are not considered to be even numbers when you bet on even.

1:1 BETS

• Bet or RED
• Bet on BLACK
• Bet on EVEN NUMBER
• Bet on ODD NUMBER

2:1 BETS

• Bet on TWELVE NUMBERS

5:1 BETS

Bet on SIX NUMBERS

6:1 BETS

• Bet on FIVE NUMBERS

8:1 BETS

• Bet on FOUR NUMBERS

11:1 BETS

• Bet on THREE NUMBERS

17:1 BETS

• Bet on TWO NUMBERS

35:1 BETS

• Bet on ONE NUMBER

 0 00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

The following table details expected gains and losses over 38 games. (Remember that there are possible numbers, including 0 and 00 ... and each number has a probability of 1/38 of being a winner.)

 EXPECTATIONS PER 38 GAMES (FOR \$1 BET) Payoff Type of Bet games player wins game casino wins dollars won by player dollars won by casino casino expectation (38 games) casino expectation per game 1:1 Bet RED 18 20 \$18 \$20 \$2 \$.0526 1:1 Bet BLACK 18 20 \$18 \$20 \$2 \$.0526 1:1 Bet EVEN 18 20 \$18 \$20 \$2 \$.0526 1:1 Bet ODD 18 20 \$18 \$20 \$2 \$.0526 2:1 Bet TWELVE NUMBERS 12 26 \$24 \$26 \$2 \$.0526 5:1 Bet SIX NUMBERS 6 32 \$30 \$32 \$2 \$.0526 6:1 Bet FIVE NUMBERS 5 33 \$30 \$33 \$3 \$.0789 8:1 Bet FOUR NUMBERS 4 34 \$32 \$34 \$2 \$.0526 11:1 Bet THREE NUMBERS 3 35 \$33 \$35 \$2 \$.0526 17:1 Bet TWO NUMBERS 2 36 \$34 \$36 \$2 \$.0526 35:1 Bet ONE NUMBER 1 37 \$35 \$37 \$2 \$.0526

As indicated above, there are many different bets you can make in Roulette. What is particularly interesting is that, with one exception, the casino edge is 5.26%. The one exception is the five-number bet, where the casino has an edge of 7.89%.

We can, of course, calculate expectations without constructing a table. For instance, if you wager \$1, your expectation, in terms of dollars, is

• 35(1/38) + (-1)(37/38) = -2/38 = -.0526 if you make a ONE NUMBER bet.
• 6(5/38) + (-1)(33/38) = -3/38 = -.0789 if you make a FIVE NUMBER bet.
• 1(18/38) + (-1)(20/28) = -2/38 = -.0526 if you make a RED bet.

In a nutshell, for every dollar a player "invests" in Roulette, the casino expects a return of at least 5.26%. It's easy to understand why the casinos want their dealers to play as many games as possible during a specific time period. The dealers are always friendly and polite, but I'm sure you have noticed that they don't slow down to have a friendly chat with you.