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Calculating Odds in Roulette

By Charles D.

Level: Apr 29th 2010
So much of life is dictated by odds. It really is. Have you ever bought an insurance policy? Of course you have. Well, in that transaction, the insurance company is making what amounts to a bet that the premiums you pay them over the course of time (plus of course, interest they can earn on it), will wind up exceeding the amount of money they pay out to actually cover you over the course of the policy. Will they win with you? Maybe not. But when you put everybody together, they have figured out a way to turn the numbers very much in their favor.

They do this through the calculation of odds. What are the odds of developing some catastrophic? They've investigated the chances. They have the actuaries. It's all about the probability of things happening.

It operates much that way in the casino world as well.

To be able to truly comprehend the concept of roulette strategies or roulette systems you have to first understand what the odds of this casino game are, not to mention your odds of winning. There is obviously a direct relationship between the probability of events occurring and the odds that play such a critical part of the game.

We can use a very simple formula to arrive at the answer we want to know.

To calculate your odds of winning roulette games, it is....

Probability of winning
1 - Probability of winning

Let's illustrate. Say for instance that there is a 10% chance of something occurring. We can easily express that in terms of a decimal (.10).

Knowing this, we can plug it into the formula, like this:

.10 divided by (1 - .10) = .10/.90 = 1/9

That's a 1-9 chance for it to occur, or you can flip it over, in effect, to arrive at the chances AGAINST such a thing happening. So in other words, you're talking about 9/1 odds against when the chances are 10%.

An easier way of calculating this might be to use another, simpler equation:


If you have a 10% chance to win, that would mean there are nine ways to lose and one way to win. So the odds can be expressed literally as a fraction, 9/1, and maybe that's a lot more convenient.

These would be the true odds you would expect to be paid if the house did not "take a cut," so to speak.

Of course, it is reasonable to expect that the house is going to make some money; so it is no surprise that it would fall short of paying off precisely according to the odds of something occurring. Remember that the house is in the business of "booking" bets, and they naturally take a fee for that. You're not going to get paid at the so-called "true odds" because that is how the casino survives. It's as simple as that.

On a roulette wheel (of the American variety), you've got 38 different possibilities for the ball, virtual or otherwise, to land in on any given spin. That means there are 37 numbers that WON'T come up.

If we plug it into the formula as we detailed above, Ways to Lose (37) are divided by Ways to Win (1) which brings us to 37/1. Those are the odds that we will win a bet that is made on a single number. As far as percentages are concerned, there is a chance of .0263 that you will win this kind of bet.

The house pays 35/1 on straight bets that win. That would be equivalent to your having a .0277 chance to win. So the casino carves itself out a little room in between.

Its what is known as the "house edge."

In the next installment, we're going to take a look at how that edge is actually derived.
Lesson 1: Roulette History
Find out the beginnings of the game
Lesson 2: Roulette Rules
How to play this incredible game
Lesson 3: The Roulette Wheel
The first playing tool, learn how to read it.
Lesson 4: Roulette Systems
Betting systems to maximize your playing time and winnings
Lesson 5: Roulette Strategy
How to play Roulette smart
Lesson 6: Roulette Betting
The different types of Roulette bets detailed
Lesson 7: The Roulette Table
The second playing tool, where to place your bet, and how to read the table
Lesson 8: Roulette Tips
Simple rules of thumb to help your game

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