Roulette Mathematics - Independent Events and Probability

$Roulette wheel and betting areas$ Roulette is one of the most popular games that are currently available at both land-based and online casinos all over the world. It is a game of numbers and chance that is exciting to watch, but the thrill of actually participating in the gameplay is even more exhilarating.

The fact that roulette is after all a game of chance and players do not really know where the ball will land, makes the anticipation among betters one of the main reasons why this casino game is so preferred in casinos worldwide. Unfortunately, the game also has some great disadvantages. The outcome of a spin is hardly possible to be predicted, not to mention the fact that eventual expectations are associated with a complex set of mathematics that could be too hard to understand, especially for beginners.

Independent Events

As a game of chance, roulette is based on independent events. This basically means that no event is influenced by the preceding events and does not predetermine the events following it in any way. This is exactly the opposite thing of the dependent events which are associated with other casino games such as blackjack for example and which outcome is affected by the ones before it.

When it comes to roulette, this would basically mean that the outcome of the wheel’s spin cannot be influenced by the previous spins and cannot affect the upcoming spins in any way. Due to the very nature of independent events, the game’s outcome cannot really be predicted.

Of course, this has not stopped a great number of players to try cracking the roulette game by using mathematics for the purpose. This is also one of the main reasons why some of the most popular roulette systems are actually based on mathematical sequences.

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Roulette and Mathematics

In fact, it is exactly mathematics that seems the most obvious solution for every player to beat the dealer, and the house edge, respectively. Unfortunately for them, predicting any result in the game of roulette is simply a matter of probability and no mathematical sequences and strategies could determine the actual outcome of the spin.

As already mentioned, the entire game is based on independent events that are not interrelated. These events occur at the spinning of the wheel and the landing of the ball, but they are not influenced by any previous events, neither do they affect the ones that are to come in the future.

Some specialists believe that if players understand the basics of probability theory, then it would be quite easy for them to test betting systems mathematically.

Simple bet is every bet that is made when chips are placed on the roulette table in a unique way. You can find the odds for all major simple bets in both European and American roulette.

European Roulette Mathematics

The payout ratio for placing a bet on one number in Roulette is 35:1. This basically means that if players manage to win, they will get their initial bet multiplied by 35. If a player makes a bet on either red or black, the payout ratio for this bet is 1 to 1 due to the fact that the probability of such an outcome is much bigger, and this automatically lowers the ratio.

When making their wagers, player must always be aware of that the larger the probability, the lower the payout. Many players choose to place an even-money bet in order to get better chances of winning.

Simple Bet	Probability (Odds)	Payout
Straight Up bet	2.70% (36:1)	35 to 1
Split bet	5.40% (17.5:1)	17 to 1
Street bet	8.10% (11.3:1)	11 to 1
Corner bet	10.81% (8.2:1)	8 to 1
Line Bet	16.21% (5.1:1)	5 to 1
Column bet	32.43% (2:1)	2 to 1
Dozen bet	32.43% (2:1)	2 to 1
Colour	48.64% (1.0:1)	1 to 1
Even/Odd bet	48.64% (1.0:1)	1 to 1
Low/High bet	48.64% (1.0:1)	1 to 1

American Roulette Mathematics

A total of 36 red and black slots are available on the roulette wheel when it comes to playing American roulette. There are also two green slots, representing the 0 and 00 positions on the wheel.

The probability of landing the ball on Red can be calculated by dividing the number of red slots by the total number of slots. In this case that would be 18/38, which makes 0.47, or 47%.

Simple Bet	Probability (Odds)	Payout
Straight Up bet	2.63% (37:1)	35 to 1
Split bet	5.26% (18:1)	17 to 1
Street bet	7.89% (11.6:1)	11 to 1
Corner bet	10.52% (8.5:1)	8 to 1
Line Bet	15.78% (5.3:1)	5 to 1
Column bet	31.57% (2.1:1)	2 to 1
Dozen bet	31.57% (2.1:1)	2 to 1
Colour	47.36% (1.1:1)	1 to 1
Even/Odd bet	47.36% (1.1:1)	1 to 1
Low/High bet	47.36% (1.1:1)	1 to 1