4. Odds and Probabilities

Throughout this book, I am going to use terms like "odds" and "probabilities." These terms can be expressed as ratios, percentages or fractions and each has a slightly different meaning. Just in case you slept though your course Statistics 101, or even managed to escape the experience altogether, I am going to attempt to clear things up.


A general definition of probability is the likelihood that a given event will occur. When we apply this concept to gambling, we usually end up with a specific expression like 1 out of 2 or 1:2. When probability is expressed as two numbers, the first number represents the expected frequency of a specific event occurring.

The second number is the total number of possible events or outcomes, including the specific event and all other events that can occur.

Let's take a look at the concept of probability applied to coin flips. Consider this question - "What is the probability of a head showing on the next coin flip?

Since there are two possible outcomes (heads or tails) and we are looking for only one event (heads), this probability can be expressed as 1 out of 2, 1 to 2 or 1:2 or even 1/2.

This two number expression can also be converted to a percentage by dividing the first number by the second number, which, in this case, will give us: 1 divided by 2 equals 0.50, which can also be expressed as 50%.

Therefore, the probability of getting heads on the next coin flip is 1 to 2 or 50%.

Let's apply this concept to the game of roulette. The American version of the game has the numbers 1 to 36, plus a zero and a double-zero, for a total of 38 numbers. This gives us 38 possible outcomes on any spin of the wheel. If your favorite number is 17, and you wanted to know how likely this was to show on the next spin of the wheel, you could express this as 1 out of 38, 1 to 38, 1:38 or 1/38.

To determine this probability as a percentage means - 1 divided by 38 equals 0.026 which is 2.6% as a percentage.

Interpretation? There is a 2.6% probability or chance of your wager on the number 17 winning on the next spin of the roulette wheel.


The definition of odds is the likelihood (or probability) of a given event occurring, compared to the likelihood of that same event not occurring.

Odds, like probabilities, can be expressed as two numbers in the form of a ratio. The first number represents the expected frequency of a specific outcome occurring, which is the same as with probabilities. However, unlike probabilities, the second number states only the number of all the other possible outcomes.

This figure excludes the specific event - that is, the first amount. Going back to our coin toss, we can ask "What are the odds of a head showing on the next coin flip?"

If we decide to pick "heads" as our bet selection, we know that on a two-sided coin heads can only show one way. The only other option is a tails. We can show the odds of a heads showing on the next coin flip as 1 to 1, 1:1 or 1/1.

Unlike probabilities, which can also be expressed as percentages, odds are always shown as ratios.

Now, let's calculate the odds of number 17 showing up on an American roulette wheel, with 38 numbers. Our number, 17, represents just one number. The remaining numbers, excluding the number we chose, are 37, making the second figure in the ratio thirty-seven. The odds of a 17 showing on the next spin, or any other single number showing on the next spin of the wheel, is expressed as 1 to 37, 1:37 or 1/37.

If we reverse this ratio, we will show odds against a 17 showing. The odds against a 17 showing on the next spin of the roulette wheel are 37 to 1 or 37:1.

The House Edge in Roulette

The house gains its edge over the player because of the appearance of a zero and a double-zero on American roulette wheels. European wheels have only one zero, giving the player a better chance of winning.

Let's calculate how the casino's edge affects the payoff of a wager on our favorite number, seventeen. We have already calculated the probability of the number showing, which is 1 out of 38 or 1 to 38. If the house did not have an edge over the player, the correct payout for winning the wager would be the real odds against winning the bet, which is 37 to 1. However, the house gains an edge by shortchanging the player on the payoff of a winning bet and only pays the wager at 35 to 1. The house keeps 2 out of the 38 numbers for itself. These numbers are the zero and double zero. The house edge over our bet on the number 17 can be calculated as follows:

Wheel with zero and double-zero - 2/38 = 0.0526 or 5.26%

Wheel with one-zero - 1/37 = 0.027 or 2.70%

As we shall see later, some LIVE dealer roulette casinos use a special rule for roulette's outside bets which allows the wager to stay up for an additional spin after a zero appears. In this case the bet is said to be imprisoned. This rule lowers the house edge even more.

The Gambler's Fallacy

Many gamblers place wagers based on a poor grasp of the law of averages. They believe that because an event has not occurred for a while that it is due.

In one incident, when I first started playing roulette, I came up to a table and starting watching before I began wagering. One man was wagering on red, which showed three times in a row while I was watching. I exchanged my cash for chips and starting betting black since I knew that long streaks of a single repeating number are fairly rare. I wagered $5 on black, feeling somewhat superior to the man who keep wagering on red. Red showed again. Next spin I wagered $10 on black, feeling more confident that black was "due" to show. The ball landed on red again.

I continued to double my wagers until I had lost six bets in a row. At this point I backed off and watched as red showed on eleven consecutive spins.

If I had not backed off wagering I would have run into the house betting limit before I eventually won a bet.

There are a couple of lessons to be learned here. First, no number or event is ever due in a game of chance. This includes all wagers in the games of roulette, craps and baccarat. We will talk about bet selection a lot in this book, as it will become an integral part of the Maximum Advantage Roulette Strategy.

However, in general, bucking the trend is not a good idea. The trend is your friend in roulette just like it is when playing the stock market.

The second lesson is that it often pays to be flexible in selecting your wagers in roulette. Gambling probability is defined as the "likelihood" of an event occurring. It does not mean "definite" and it certainly doesn't mean that the event will happen on the next spin or even the next two or three spins.

Approach Gambling with a Winning Attitude

People have different reasons for gambling. For most people it is the excitement of the game, the escape from the humdrum of day-to-day existence, and the possibility of a potential cash windfall.

The price of this "casino entertainment" is the almost certainty of losing money. Surveys of visitors to Las Vegas show that most persons believe they are going to win. The reality is that most of them lose. Approaching gambling with a positive attitude is important. You need to believe that you are going to win. However, in order to win consistently and not just once in a while, subject to the whims of blind luck, you have to have a total plan for winning.

This book will give you a complete plan for winning. However, even with a "blueprint" for success, you can still influence the outcome with your attitude. It pays to have a positive attitude as well as a proven way of winning.

With this combination, you will be able to consistently gamble and win. As you read this, there are players using the Maximum Advantage Roulette Strategy to amass small fortunes. If you want to skip ahead to the chapters describing the system itself, go ahead. However, don't forget that winning consistently requires not only the "mechanical means" that the system provides, but the attitude, skill and discipline to follow the roulette system. That's why if you do skip ahead, you should still come back and read all of the material you skipped. It will pay you in spades, trust me.

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