How Casinos Use Math When You Gamble Online

Gambling is a game of chance, staking money on the uncertain outcome of an event, hoping that the wheel of luck turns in one’s favor. However, casinos have a business model that aims at maintaining a profit just like any other business. They apply complex mathematical principles to ensure that the odds remain in their favor in the long run.

Traditional land-based casinos combine many factors, including attractive interiors, impeccable services, and complimentary treats in their model. Since an online casino lacks this advantage, it will have to develop other ways to keep its edge in the business. Besides offering higher odds than the land-based casinos, here are other mathematical principles used by online casinos when you gamble.

Definite probabilities

All casino games have absolute probabilities that depend on the size of the sample spaces or the total number of possible outcomes. For example, tossing a six-face die has a sample space of 6 and a 1 in 6 chance of landing on any side. That said, these games have, by design, some of the lowest probabilities of winning. In poker, drawing a royal flush has a probability of 0.00000154.

This leaves very slim chances for any gambler to win any money from the casino. Only the skilled players can understand the sample space of each game and take it into account when estimating their odds. This guides their choices in play but does not guarantee any wins.

Expected Value

The expected value is mathematically defined as the total amount a gambler can expect to win from a particular event. It is the sum of all the probabilities multiplied by their related gains or losses. Casinos take advantage of this value by maintaining it negatively for any given events or combination of circumstances. This guarantees an advantage over the gamblers and is commonly known as the ‘house edge.’ The expected value derives from the central limit theorem. Interestingly, the more you play, the more chances you will lose more money to the casino—the more reason to encourage to play one more time. 

For example, when you play a straight-up bet in roulette, the maximum payout is 35 to 1. This is based on the sample space of numbers1 to 36 on the board. However, the inside of the board has extra numbers 0 and 00, making the real chance 1 to 38 and the actual possible payout 37:1. That is the ‘house edge’ in roulette, and it ensures that even when you win, the casino still makes money.

The ‘house edge’ represents the average gross profit the casino expects to make from the game. The casino expects profit ranging from 1% to 2% from the games with the smallest house edge’. From the higher paying games such as the slots, the expected profits can be as much as 20% to 25%. The ‘house edge’ on a roulette table with the 0 and 00 numbers is around 5.3%. 

Volatility Index. 

The volatility index is the gambling term for standard deviation, and it refers to the difference between the expected value and the actual value. Casinos set the expected values with a profit margin. This means the odds are always exaggerated in favor of the casino, and the implied odds are not the actual odds. To the skilled gambler, this difference quantifies luck by telling them the odds of winning more than the expected value for a specific number of events. Higher volatility games present a greater chance of winning above the estimated value. Casinos have crafted the application of this possibility to lure in gamblers. 

Some other factors that online casinos include in their strategy are the length of play and the size of the stake. Casinos have rules and regulations that govern each game. These rules are mathematically calculated to extend the advantage of the casino. Online casinos offer attractive bonuses aimed at keeping the gamblers playing and attracting new customers.   


Bookmakers always include a profit margin in the odds to ensure the house wins in the long run. The odds on display are not always the actual probabilities of the outcome of the events. This means that in the case of a win, the payoff is always lesser than what it could have been with the actual probabilities at play. With this in mind, a bet would only be valuable if the assessed probability for an outcome is higher than the probability implied by the bookmaker.