**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?