# The Role of Mathematics in Online Roulette: Probability and Expected Value

Online roulette is a popular casino game that has captivated players for centuries. While it may seem like the game is all about luck, math plays an important role in understanding the underlying mechanics and making informed decisions. This article explores the role of mathematics in online roulette, focusing on probability and expected value, and how these concepts can be applied to betting strategies.

## Roulette Probability: The Basics

Understanding Roulette Betting

In roulette, players can place various bets on the outcome of a single spin of the wheel. Tariffs can be divided into:

• Inside Bets: Bets on individual numbers or small groups of numbers.
• Outside Bets: Bets on larger groupings of numbers such as odd/even or red/black.
• Different bets have different payouts depending on the probability of winning them.

## Calculation of probabilities in roulette

There are 37 cells in a standard European roulette (numbered from 0 to 36). The probability of a certain outcome can be calculated by dividing the number of successful outcomes by the total number of possible outcomes. For example, the odds of getting one number (upright bet) is 1/37, and the odds of getting an even number (outside bet) is 18/37.

## Expected value in roulette

How expected value works

Expected Value (EV) is a statistical concept that is the average outcome of a random event over a large number of trials. In roulette, EV helps determine the long-term results of betting strategies and helps players decide which bets have the highest earning potential.

## Calculation of expected value in roulette

To calculate the EV of a roulette bet, you multiply the probability of each possible outcome by the corresponding payout and sum the results. For example, the EV of a straight bet in European roulette can be calculated as follows:

EV (1/37 35) (36/37 -1) -0.027

Negative EV means that, on average, a player loses approximately 2.7% of their bet on every spin.

## Applying Probability and Expected Value to Betting Strategies

Various betting strategies have been developed to try and beat the roulette wheel. Some of the more famous systems are:

## Martingale wagering system

This structure involves multiplying the bet after each failure. The idea is that when you finally win, you will recover all past failures and create a win equivalent to your unique bet. Although it may seem tempting, the Martingale scheme has a negative numerical assumption and can lead to serious setbacks in the long run.

## Betting system Labouchere

Also known as the cancel system, the Labouchere system requires players to create a sequence of numbers, where each number represents a unit of their bet. Players place bets on the sum of the first and last numbers in the sequence. If they win, they remove those numbers from the sequence. If they lose, they add the sum to the end of the sequence. The goal is to cancel all the numbers in the sequence, which will result in a profit. However, like the Martingale system, the Labouchere system also has a negative mathematical expectation.

## D’Alembert betting system

The d’Alembert system involves increasing the bet by one unit after a loss and decreasing it by one unit after a win. This system is less aggressive than the Martingale system, but it still has a negative expected value in the long run.

## Casino advantage in online roulette

The house edge is the built-in advantage of the casino over the players, which ensures their profit in the long run. In European roulette, the house edge is approximately 2.7%, while in American roulette with extra pocket 00, the house edge increases to 5.26%. This means that no matter what betting strategy a player uses, the casino will always have the edge in the long run.

## The role of chance and luck

While understanding the mathematics behind roulette can help players make better decisions, it is important to remember that each spin of the wheel is an independent event and the outcome is ultimately determined by chance. No betting system or strategy can guarantee a permanent win or change the odds in favor of the player.

## Increase your chances of winning

To maximize your chances of winning at online roulette, consider the following tips:

• Choose European roulette over American roulette as it has a lower house edge.