Roulette by the Numbers

 

To stress the importance of knowing numbers, I usually begin my game protection sessions in table games with a simple gambling question. “What is the mathematical house advantage on your double-zero roulette game?” I start out explaining that anyone who has been in the casino gaming field for more than five years can easily be considered a professional and should be able to answer a basic question such as the exact mathematical house edge in roulette.

I’m not surprised when no one can come up with the correct answer, which is 5.26 percent, because people in our profession rarely take time to learn the different percentage numbers of the very precious edge casinos hold over the player. I find it amazing that in a field ruled so much by numbers, most people, executives included, have only a general idea, if that. The standard reply: “I don’t know exactly, but I’ll bet it’s pretty high.” ggbmagazine.com

How do I come up with the percentage 5.26 percent? Roulette is easy to calculate because it’s straight mathematics. You can figure it out using a hand calculator, but I personally prefer using an Excel spreadsheet.

First, one needs to develop a clear picture of the logic behind the math. On a double-zero roulette wheel there are 38 possible pockets for the ball to land (36 numbers plus the zero and double-zero). If a person were to wager on one number straight up to hit, that person has one opportunity for success and 37 chances to fail. If the ball were to fall into the losing pockets, the person loses one chip, while a ball dropping into the wagered number’s pocket provides the player with a 35-chip windfall.

Chart 1 illustrates how the 5.26 percent mathematical house advantage is calculated. The “probability” numbers are the decimal point equivalent to 1/38 and 37/38. It’s simple to see that by multiplying the payout result by the probability, one can calculate the return. By adding the two returns together, the positive and negative return numbers will produce a total return when one unit is wagered. This decimal result is easily converted to a percentage by moving the decimal point two positions to the right and adding the percentage sign.

Chart 1-Advantage of 1 Number Wagered

What about the other wagers on the double-zero wheel which are subject to a host of different payouts? Believe it or not, all but one of the possible wagers experience the same mathematical edge.

Chart 2 recaps several of the other wagers including the five-number wager when covering the 0, 00,1, 2 and 3. The five-number wager is an “odd fellow” compared to all other roulette wagers, in which payouts are symmetrical to the probabilities. When examining the properties of a single-zero wheel, this same unconforming wager situation does not occur.

How then does this common mathematical advantage apply to the actual situation on the game itself? Basically, no matter where you wager your chips (bar the five-number wager), the house advantage remains the same. There is no difference between the player who sticks to precise bet placements and the player who tosses a handful of chips onto the table and has the dealer place them as close as possible to the wager in which they landed.

Question: Since all wagers (bar the five-number bet again) are mathematically the same, what constitutes a “tough” roulette player? If all bets are subject to the same house advantage, there is no such thing as a tough roulette player. Usually, the casino executive making this comment is referring to a person who used some type of money management scheme and is rated “tough” since it takes a long time to grind him or her out of their money.