Open AccountJoinDeposit 
DepositMy Bets
Join usDeposit
CasinoLive CasinoPromotionsSports

Roulette Spins - Independent Events with a Statistical Connection

Roulette has been a popular casino game for centuries, drawing in an untold number of players who allow the spinning wheel to determine their fate. Due to the nature of the game, questions have arisen about the nature of roulette spins and whether what has gone before can help predict what will come next. Here we will look at whether roulette spins truly are independent from one another and how this should inform your approach to the game.

What are Independent and Related Events?

Before discussing roulette spins, it's essential to understand what independent and related events are in the context of probability. Independent events are those whose occurrence does not affect the probability of other events happening, while related events are those that can influence each other. An example of an independent event would be tossing a fair coin while an example of a related event is drawing cards from a deck without replacing them.

The Basics of Roulette

To better understand the nature of roulette spins and how they influence your betting strategy, it is worth first going over the basic rules of the game. European Roulette consists of a wheel with 37 pockets, numbered 0 to 36, and a betting are where players can place their bets. The pockets are alternately coloured red and black, with the exception of the 0 pocket, which is green.

The croupier spins the wheel in one direction and releases a small ball in the opposite direction. As the wheel loses momentum, the ball drops into one of the numbered pockets, determining the winning number and colour.

In European Roulette, players can place various types of bets, each offering different odds and payouts. Bets are divided into two main categories: inside bets and outside bets.

Inside Bets:

  • Straight-Up: A bet placed on a single number, offering the highest payout of 35 to 1.
  • Split: A bet placed on two adjacent numbers on the table, with a payout of 17 to 1.
  • Street: A bet placed on a row of three numbers, offering a payout of 11 to 1.
  • Corner (or Square): A bet placed on four numbers that form a square on the table, with a payout of 8 to 1.
  • Line: A bet placed on six numbers that comprise two adjacent rows, offering a payout of 5 to 1.

Outside Bets:

  • Column: A bet placed on one of the three columns on the table, covering 12 numbers and offering a payout of 2 to 1.
  • Dozen: A bet placed on a group of 12 numbers (1-12, 13-24, or 25-36), with a payout of 2 to 1.
  • Odd/Even: A bet placed on either all odd or all even numbers, offering a payout of 1 to 1.
  • Red/Black: A bet placed on either all red or all black numbers, with a payout of 1 to 1.
  • High/Low: A bet placed on either the high (19-36) or low (1-18) group of numbers, offering a payout of 1 to 1.

Roulette Spins as Independent Events

Classical probability theory considers roulette spins as independent events. This means that the outcome of one spin does not affect the outcome of subsequent spins. The spinning of the wheel and the release of the ball are random processes, with each number having an equal probability of being landed on.

For instance, in European roulette, the probability of the ball landing on any given number is 1 in 37 or approximately 2.7%. This probability remains constant for each spin, regardless of previous outcomes.

The Gambler's Fallacy – Misunderstanding Related Events

The Gambler's Fallacy, also known as the Monte Carlo Fallacy, is a cognitive bias that leads people to believe that past events can predict future outcomes. This fallacy often arises from a misunderstanding of the law of large numbers and the nature of randomness. Players may incorrectly assume that deviations from the expected outcome are corrected over time, leading to the belief that a particular outcome is "due" after a series of opposite outcomes.

A famous example of the Gambler's Fallacy occurred at the Casino de Monte-Carlo in 1913 when the roulette wheel landed on black 26 times in a row. Many gamblers believed that red was "due" to come up and continued to bet on red, losing substantial sums of money in the process.

The Gambler's Fallacy arises due to several psychological factors, such as the belief in the “law of averages” and the tendency to look for patterns in random sequences. By understanding the independence of roulette spins and resisting the allure of the Gambler's Fallacy, players can avoid falling into a trap and potentially losing a great deal of money.

Roulette Spins as Related Events

Despite the standard view of roulette spins as independent events, there is a perspective from which the spins can be seen as both independent and related in a statistical sense. Each spin is an independent event with a fixed probability of occurrence, but when analysed as a group, spins exhibit statistical relationships.

For example, the probability of black appearing 100 times in a row is extremely low. However, this statistical observation does not alter the probability of black appearing in the next spin, which remains 18/37.

While this is unlikely, such events are not unheard of. At the Rio Hotel and Casino in Las Vegas, the red number 19 landed seven times in a row. The odds of this happening are 1 in 114 billion.

The Impact on Roulette Betting Strategies

Various betting strategies have been created for roulette, with many based on progressive betting systems that aim to manage losses and capitalise on winning streaks. While these strategies do not inherently assume that past events influence future results, some players may misunderstand the nature of independent events and fall into the trap of the Gambler's Fallacy. Some popular strategies include the Martingale System, Labouchère System, Fibonacci System, and the Paroli System.

  • Martingale System: This strategy involves doubling the bet after each loss, aiming to recover all previous losses with a single win. While the system is designed to recoup losses when a win eventually occurs, some players may incorrectly believe that a specific outcome (e.g., red or black) is “due” after a series of opposite outcomes. It is important for players to understand that each spin is an independent event, and the probability of red or black appearing remains constant, regardless of previous outcomes.
  • Labouchère System: This strategy is a progressive betting system in which players create a sequence of numbers representing bet amounts. After each loss, the player adds the amount of the lost bet to the end of the sequence, while after each win, the player removes the first and last numbers in the sequence. This system aims to recover losses over multiple wins. However, as with the Martingale System, some players may fall prey to the Gambler's Fallacy, erroneously believing that previous outcomes can influence future results.
  • Fibonacci System: This strategy involves following the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, etc.), increasing the bet size after each loss according to the sequence. After a win, the player moves back two steps in the sequence. The idea behind this system is to recover losses gradually over multiple wins. However, like other progressive betting systems, it cannot guarantee long-term success due to the independent nature of roulette spins and potential table limits.
  • Paroli System: Also known as the Reverse Martingale, this strategy involves doubling the bet after each win and returning to the initial bet size after a loss or a predetermined number. Once again, the strategy can be helpful as long as players do not continue to bet with funds they don’t have in the mistaken belief that a certain result is “due”.

Embracing the Complexity of Roulette Spins

The enigmatic nature of roulette spins is what makes the game so exciting. Recognising that spins can be both independent and related in different contexts will deepen your understanding of the game and heighten your strategic thinking. The importance of approaching roulette with a clear understanding of probability and the game’s unpredictable nature will ensure that you do not fall for the Gambler’s Fallacy. It is highly unlikely that you will be carrying out the type of statistical analysis that requires viewing spins as related events, so simply remember, the outcome of one round has no bearing on the outcome of the next, even if the wheel has produced black for the last 10 spins in a row.

Related Articles