Before we can get into the particulars of our two major wheel types, we should first note that “odds” and “probability” are NOT the same thing. If you remember this portion of your fifth-grade math class—or weren’t playing a mini Ferris Bueller that day—feel free to skip ahead to “Wheel of the People” below. If, on the other hand, your recollection of fractions, odds and probability is a little sketchy, we suggest you read on.
In the simplest terms, odds are the likelihood of an event occurring expressed as the number of desired outcomes over the number of undesired outcomes. “Desired” in this sense only means, “What are we asking?” It doesn’t mean “desirable,” or whether you want a thing to happen. So, for example, if you were trying to determine the odds of winning a coin flip in which you chose heads, you would have to count the possibility that the coin will land on heads as the “desired outcome” and count the possibility of it landing on tails as the “undesired outcome.” If, however, you were determining the odds of losing the same flip, you would have to count the possibility of tails as “desired” over the possibility of heads. In either case, the odds for the coin flip would be 1 to 1, but take a look at what happens if we use a more complex set of variables, say a six-sided die: In a scenario in which you can only win if you roll a six, your odds of winning are 1 to 5, and your odds of losing are 5 to 1!
To further complicate matters, you won’t always hear the question posed in the same way. In casinos, for instance, odds are always posted in terms of the house winning, while if another player asks you, “What’re the odds?” he could just as easily mean his own odds of winning since you’d sooner square a circle than find a gambler looking to lose. In any case, then, just assume the house’s posted odds are the topic of conversation, and if you’re asked, refer to them. (That way you can avoid a long and tiring conversation with a player who’s too dull or too sweet on the cocktail waitresses to really get what you’re telling him).
Now, as for those odds posted by a casino, they are almost always the “payoff odds,” not the real odds. This is essentially how the casinos get that 5.26 or 2.7 percent advantage in roulette you keep hearing about and how they keep their coffers full. All they do is subtract the odds of the zero and/or double zero from their own odds of winning, and suddenly, they get to keep their increased chances of cleaning up, while only paying you out as if you were playing against a smaller wheel.
But to help you better understand how this works, let’s look at an actual roulette scenario: Say, for the sake of argument, that you bet $10 on 14 on a Double-Zero layout. Because there are actually 38 pockets on the wheelhead, your odds of losing are 37 to 1. But, assuming you do win this wager, the dealer will only pay you at a 35 to 1 ratio. So you’re total winnings on a $10 bet would be $350 instead of the $370 payoff that matches your actual risk.
The final sticking point to understanding roulette vigs, though, has more to do with probability than odds. Remember, we keep talking about a “percent advantage” here, and that’s because most people who pick apart games of chance do so using statistics. The reason for this is that probability is not a fractional ratio but an expression of the total possible outcomes. As a result, it can be converted into a percentage and these percentages can be multiplied to determine the probability of a string of events.
But to give it to you in plain English, probability is the number of desired outcomes over the total number of possible outcomes. So, if we go back to our six-sided die, you would have a 1 in 6 probability of winning because there is one possible way you can win and six total possible ways a die can land. This ratio can also be viewed as the fraction 1/6 or, if we divide one by six, the decimal .1666…. Also, we can find the percentage probability of an event by multiplying the decimal by 100—“percentage” literally meaning “per 100.” Doing that, we find out that the probability of winning our die roll is 16.66 percent or about 17 times out of 100.
So going back to that ever-confusing roulette vig, you can now see where all these percentages come from: If we figure that on an American Roulette wheel there are two pockets in 38 that aren’t counted in the payoff odds, we can divide that two by 38 and get .05263…. Then, by simply multiplying by 100, we find that the percentage probability of the ball landing in one of these pockets is 5.263!
This, of course, is only the crust on the casserole as far as roulette’s math goes, and we’ll definitely be giving you more numbers to crunch in later sections. For now, though, we figure all this arithmetic is probably turning your stomach, so we’re just going to leave you with a few finer points to consider:
- A Word to the Wise: As you may have noticed, different terms are used when speaking of odds and probability. The word “To,” for instance, always signals odds or a payoff and should be treated as a “versus.” “In,” on the other hand, means probability, or its colloquial cousin, “chance.”
Sometimes you will also see the word “for” used in connection with a payoff, as in “36 for 1.” This means that “for” every so many units you bet the house will return the total number listed, including your bet. (So, for a straight-up bet with “for” in the payoff, if you bet one unit and win, you get 36 units back all-tolled). It does not mean that the casino has upped the payoff rate, merely that they are counting your bet as part of your winnings.
Beware, however, of casinos that use “for” along with the same payoff you’d find in a “to” ratio. In this case, they are paying out at an even lower rate than the standard and trying to trick you into ignoring the fact. Generally, gaming-control commissions frown on such practices but can do nothing to stop them because that “for” is posted front-and-center where everyone can see it. And while, more often than not, a casino that uses such methods is usually into all kinds of underhanded behavior—including ignoring payoffs, gaffing wheels and short-changing players at the buy-in—the governing GCC just hasn’t caught them yet. The best thing for you to do, then, is to simply leave any table where you see that ever suspicious “Straight-Up: 35 for 1,” and hope the law will eventually take its course.
- Efficiency: No, not your apartment or some lunacy your boss is always raving about, “efficiencies” in gambling simply mean the payoff once all losses, multiple-unit bets and the vig have been accounted for. It is important to know this because, often, playing a system will entail placing bets on several propositions with the expectation that most of those bets will not win. As we will explain later, this kind of play is very useful in that you can use specific betting ratios to ensure a profit no matter which option hits, meanwhile upping your total probability of winning to over 50 percent. But to be able to do so, you must first make sure the efficiency remains in your favor.
To determine an efficiency, all you have to do is take the amount you stand to win on a given prop, minus the amount you would lose on all the other props you’re betting at the same time. So say, for instance, you’re betting 15 units on Red and ten units on the second column on an American Roulette layout (See: bets chart in "Wheel of the People"). If the second column wins, you would win 20 units but lose 15, making the efficiency for that bet 5 to 10 or 1 to 2. If, on the other hand, you won the bet on Red, the efficiency would be 5 to 15 or 1 to 3 because you would win five units for every ten you lose on the column bet.
Efficiencies can also be called “real payoffs,” and for the sake of simplicity—and cutting through all the jargon—we’ll use this term and do all the mathematical legwork for you from here on in.
- K.I.S.S.: The “keep it simple, stupid” law of mathematics is our bread-and-butter here at GP, so rather than writing out fractions—which can get pretty complicated and confusing—we’re instead going to use fractional notation throughout the rest of the article. For odds, this means using a colon (:), and for probability, a slash (/). Odds can also be expressed using a dash (-), but we’ll be using this punctuation for odds-derived payoffs instead.
As we said before, we'll simplify all fractional expressions as far as we can get them. But during the course of your roulette-playing career you’ll find that we definitely haven’t covered everything. (To do that, we’d need a hellova lot more space than we’re willing to bet you’d read). To make sure we're not entirely throwing you to the wolves, then, we're winding up this section with a short explanation of how to simplify fractions on your own:
To simplify a fraction, all you do is divide the top number (known as the “numerator”) by the bottom number (the “denominator”) by the biggest number that will go into both of them evenly. You then set you answer from dividing the numerator on top of the fraction and your answer from dividing the denominator on the bottom. A simple example of this would be the fraction 2/10. Because the largest number you can divide both numbers by is two, the simplified version of this fraction is 1/5. Pretty easy, huh?
Read Section III: Wheel of the People
- Phill Provance