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The Mathematics of Gambling

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Staff member
Jul 11, 2008
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When people think of casino games, they always know that there’s a certain degree of luck that’s involved. But more than just luck, it’s actually a lot about mathematics. After all, the software that runs slot machines and the games that you would find in an Australian online casino are run by mathematical equations and algorithms. So, there’s no arguing that casino games are powered by math. And, as it turns out, you can increase your chances of winning at these games by understanding the mathematics of it all.

In this article, we are going to go over some of the most basic aspects of gambling and break them down in terms of probability and mathematics.

Six-Sided Dice Roll

The die is one of the most popular symbols of a casino, especially because of its connection to the game craps. With dice, there are only six possible results: 1, 2, 3, 4, 5, and 6. That means that the probability of any specific number coming up is one out of six or 17%. But what if you need to calculate the probability of getting either one of two different numbers? It’s all a matter of adding fractions. So, if you’re shooting for either a 1 or a 2, this is how that computation would go:

Both numbers have a 1/6 chance. That means that you just have to add 1/6 and 1/6 to come out with 2/6. This can further be simplified to 1/3 or a 33% chance of getting either one of those two numbers.

Blackjack Cards

Let’s say that you’ve been dealt an ace as the first card of your blackjack round. What are the chances that you will get an ace in the second round too?

Since you already have one ace, that means that there are only three other aces in the deck out of 51 remaining cards. That means that the probability of you getting an ace is 3/51, which can be further simplified to 1/17. That equates to a little under a 6% chance of securing your ace.

Roulette Wheels

For the purposes of this article, let’s go with the American roulette wheel, which has 38 pockets on which a ball can land. That means that the chances of a ball landing on a particular pocket is 1/38 or 2.6%. These chances can also be expressed by saying that you have 37 to 1 odds of landing the ball in a specific spot. However, the casino pays off only 35 to 1 if you do win. This is why casinos are often referred to as having a house edge.


There are so many different casino games out there that have varying levels and depths of probability and mathematics. Even a strategy-based game like poker will rely a lot on probability in terms of decision-making and betting. At the end of the day, you need a lot of luck when it comes to winning at casinos. And you can amplify that luck with your mathematical knowledge.

Jeffrey Wilkins

New Bettor
Oct 14, 2022
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Good note. Many casinos now offer to play the game Aviator by Spribe. Do you have any information about the mathematical model of this game? Any information would be appreciated.