Mathematical Systems That Govern Roulette

Roulette is arguably the most well-known casino game, whether people enjoy it at a land-based casino or at an online casino. This is because like many classic games it blends some mathematical complexities with an in-game format that is simple and easy to get a grip on. These are the mathematical systems and sums that make this classic casino game tick, and which will also debunk some Roulette myths that the numbers do not support.

Odds – Otherwise Known at Probabilities

Odds are a vital part of being able to understand how a Roulette table works, because every place on the felt where a player can position a chip comes with its very own applied odds.

For example, if a player places a chip, so that it straddles two numbers, it is called a Split bet. In the case that the ball stops on either number it does so at odds of 17/1 for the player.

Obviously, the more numbers that any bet covers means a reduction in odds. This can be seen with what is called a Corner bet, where four numbers are covered by a chip and the odds are automatically lowered to 8/1.

Percentages

While many casino players like to think in fractions and decimals, there are those who are altogether more comfortable dealing in percentages, as they go about trying to decipher how to approach Roulette.

Often a percentage can also give a clearer indication of the potential ramifications of a certain bet. For example, a bet placed on red or black has slightly less than a 50% chance of beating the house, whereas those percentages are much lower if a player wishes to select a sole number, with such a bet having around a 2.60% chance of coming good.

Numbers spin in more ways than one at the Roulette table

House Edge

Both odds and percentages combine to explain so many of the overriding mathematical factors that are at play on a Roulette table, whether it is a virtual one or a table operating in real life.

One of these is the house edge. This refers to the fact that the odds and percentages involved in any game of Roulette always slightly favour the house.

However, what is important to note is that house edge varies slightly depending on the specific Roulette variant that is being played.

The house edge is achieved by the presence of the 0 in European Roulette and the 00 in American Roulette.

The approximate house edge in the European version of the game is 2.7%, whilst American roulette puts the house edge at 5.26%.

The house edge calculation is determined based on the difference between the probability of winning and the payout odds.

Although all Roulette varieties are equally enjoyable to engage with, players should take these factors into account as each comes with its own distinct mathematical quirks.

Game Theory

Some players go one step further with their mathematical strategies, with the aim to, in theory, manage the outcomes to reduce losses or improve wins. However, it’s important to note that although they utilise probability and risk management, nothing guarantees a win in Roulette (or any gambling activity!).

Martingale System

This mathematics system is known as a negative progression system which requires the player to double their bet after each loss on the Roulette wheel.

The aim is for a player to recover their losses from the previous hands in hope that the next spin of the wheel results in a win.

Although you should never chase your losses in any form of gambling, as long as you are betting within your pre-determined budget, the Martingale system can work.

It works on the law of large numbers theory, which suggests that over a sustained time everything is pretty even based on the probability of its occurrence i.e if you spin a Roulette wheel 200 times, it will roughly land on a red 100 times and a black number 100 times.

The issue with this approach, though, is that it doesn’t account for table limits (meaning you can’t always double your bet after a loss) and doesn’t factor in that each spin of the Roulette wheel is an independent event.

Quick bit of history for you: the reason behind the name Martingale is because a former London casino owner, John Martindale – the ‘d’ and ‘g’ aren’t a typo, but we are as perplexed as you by the naming outcome.

Anyway, although not Martindale’s idea (it originated from France in the 18th century), the casino owner was famous for going round his casino floor and encouraging players to double their bets after a loss.

Paroli System

Whilst the Martingale system is a negative progression system, the Paroli approach is a positive one based on the fact a player increases their stake after a win – basically: when your luck is in, you are in!

That being said, most players using the Paroli system set a maximum number for consecutive number of wins, with this most commonly being four. Therefore, if a player does win four games in a row, they will then reset to the initial bet and begin the process again.

Example of the Paroli System

• 1.Bet $5 on black; black comes in, you now have $10.
• 2. Bet $10 on black; black comes in, you now have $20.
• 3. Bet $20 on black; black comes in, you now have $40.
• 4. Bet $40 on black; black comes in, you now have $80.
• Pocket your profit ahead of the next hand and return to the $5 initial bet.

Debunking Roulette Myths

A strong understanding of maths allows a Roulette player to debunk some of the myths that have always hovered around casino games such as Roulette or Blackjack.

One of these is that a streak of red or black numbers that a Roulette wheel makes somehow affects the way in which a player should approach playing the game, implying that the mathematical rules are continuously altered as a game progresses.

Of course, as this article has shown, this is simply not the case. On the contrary, odds, equations, percentages, and house edge always remain rigidly the same no matter how many times in a row the ball lands on red or black.

In fact, some believe that betting systems like the Martingale (chasing your losses by doubling your bet after a loss) will guarantee eventual success. However, these systems do not alter the house edge, and work on the assumption that a player has an infinite pot of money and that table limits are not something that exist.