Casino Game Probability 101

Casino Game Probability 101

Posted on 07/07/10 - by Theodor Mavrodis Features

Do you understand probability? If you’re going to gamble in a casino, you should make sure that you understand probability first. Why? Because probability is the engine that powers the casino.


Without probability, casino gaming would not even be possible.

casino game probability

What Is Probability?

Probability is simply the likelihood that something will happen. We use probability every day in our daily lives. When we decide whether or not to cross the street against the light we are measuring the likelihood that we will get hit with an oncoming car vs. the benefits of getting across the street faster.

When we gamble, we are estimating the likelihood that an event will happen in order to formulate a bet. In these cases we are estimating probability.

Probability Example

Let's say you have a bag containing three blue balls and one red one. The likelihood of you picking the red ball out without looking is 1 in 4.

There are a number of ways to express this probability. We can say there is a 1 in 4 chance of red. We can also say there is a 3-to-1 chance against red, because on average we will pick three blue balls for every one red one.

Thus we can say the odds of picking red are 3-to-1 against.

We might also say our odds or probability of picking red are 25 percent, since there is a 100 percent probability of picking a ball of any color and four balls, and 100 divided by four is 25.

Our probability of picking a blue ball is 75 percent, since there are three of them with a probability of 25 percent.

Probability in Casino Games

Casinos work by offering you odds of winning that are not quite as good as the probability of the chosen outcome.

For example, in the ball picking example, the casino might offer to pay you 2-to-1 if you pick the red ball. If you bet $5, then over four trials on average you will pick the blue ball three times, losing $5 each time for a total loss of $15, and you will pick the red ball the fourth time and win $10, for a net gain to the casino of $5.

Of course, on any individual trial anything can happen. You might pick the red ball four times in a row and win $40, or pick the blue ball four times in a row and lose $20. However over the long term, you can expect to lose $5 for every four trials.

This difference represents the house edge.

Probability in Roulette

If we look at a single-number bet on an American roulette wheel, your odds against winning is 37 to 1. There are 37 slots, including the zero and the double zero, and you have picked one number.

If you win, you'll get 35 to 1.

Again, the difference between the chance of winning and the actual payout represent the house edge.

So if you play roulette online - or any other casino game for that matter - make sure that you understand the game's probability and your chances of winning.