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A Mathematical Guide to Master Roulette & Crack Its Codes!

Mastering the Odds: Understanding the Mathematics of Roulette

How many of you enjoy playing Roulette? We bet many of you do, as it’s fun to engage in with its timeless appeal, attractive stakes and simple-to-understand instructions. With popular casinos like bringing the magic of it within homes, it today enjoys more recognition than ever. However, being a game of chance, gamblers need to grow familiar with the chances of winning. Once you master the calculation, you can influence the winnings in your favour and know which wagers to place.

Let’s start by understanding the odds in this game.

What Is Meant by Odds?

By odds of this casino game, gambling experts imply winning chances on placing wagers. Let’s take the case of its American version. Here, the chances of hitting a single number when a straight-up bet is placed is 37 to 1, where the total number is 38. However, players receive 35 to 1 on winning as the house retains a part of the stakes for its profit. This is called the house edge.

Before we move forward to elaborate a bit on the house advantage of this table game, let’s understand the concepts of inside and outside bets.

Roulette Bet Categories and Their Differences

Speaking of its bets, you are most likely to come across two types – inside and outside. While the former comprises wagers on either single numbers or clusters of adjacent numbers on the table, the latter denotes bets on larger groups of numbers, which could be odd, even or a specific range. The two differ from the perspective of payout. Although outside bets have lower payouts, as compared to inside ones, the chances of winning here are higher.

It’s mostly the column or dozen outside bets that provide better payouts. The rest offer only 1:1 for stakes. Enclosed are the chances of winning and potential payout ratios when players wager on outside bets of both American and European versions.

Roulette outside bet type Payout potentialOdds of American variationOdds of European variation 
Dozen2:131.6%32.4%
Column2:131.6%32.4%
Red or Black1:147.37%48.65%
High or Low1:147.37%48.65%
Odd or Even1:147.37%48.65%

Now that you know outside bets have higher chances but lower payout potential, except for column or dozen, let’s demonstrate how inside bets are distinct.

Roulette inside bet type Payout potentialOdds of American variationOdds of European variation 
Double street5:115.8%16.2%
Basket6:113.2%NA
Corner8:110.5%10.8%
Street 11:17.9%8.1%
Split17:15.3%5.4%
Straight35:12.6%2.7%

As depicted above, this table game features a fixed set of payouts and odds. However, during payout, the casino game hands over less than the chances captured above. Wonder why? As explained before, it’s due to the house advantage.

What is the House Edge of Roulette?

It’s essential to wrap your brain around house advantage since it helps players make informed decisions when betting on the table game. So, here are a few things to note before testing your luck at it:

  • The house edge of this gambling game is higher for inside bets than outside bets;
  • American version has a higher house advantage due to the double zero slot on its wheel;
  • Outside bets have a lower house edge when compared to inside bets;
  • The house advantage in European version for wagers placed is 1.35%. The same figure is 2.70% in American table layout.

When figuring out the mathematics of this game of chance, a fair bit of idea about house edges is hardly enough. Therefore, the next section is all about probability and how it influences the game.

What Role Does Probability Play in Roulette?

Every number on the wheel has an equal chance of winning, but the outcome of the game is determined through probability. This ‘probability’ varies depending on the type of bet placed by players. Take, for instance, a straight bet. Here, the likelihood of winning is 1 in 37 for European roulette and 1 in 38 for its American counterpart.

Since a bet could be of two types, the probability of winning on red or black, high or low and odd or even is higher for an outside bet. Consider the case of European style, and you will be sure of the statement. Here, the winning probability on an outside bet is 48.65%, whereas it’s slightly lower (47.37%) for the American version.

Finding inspiration to learn about probability? It’s simple! You get to determine the likelihood of winning various bet types. How? Let’s say a gambler placed stakes on two adjacent numbers. The individual can determine the chances of winning through a mathematical calculation:

Number of possible winning outcomes÷ aggregate number of potential outcomes

Learn How to Calculate the Roulette Payouts

Refer to the tables depicted in this write-up and check out the payout potential. The figures are in ratios of x:1. Wondering what that implies? It denotes that for every $1 bet, the player will win x dollars. Let’s explain things from this table demonstrating different roulette bet types:

Roulette bet typesExamplesPotential payoutsOdds of American variationOdds of European variation 
Single number735:12.60%2.70%
Two numbers19 or 2017:15.3%5.4%
Three numbers28, 29 or 3011:17.9%8.1%
Four numbers5, 6, 8 or 98:110.5%10.8%
Five numbers0, 00, 1, 2 or 36:113.2%13.5%
Six numbersAny number between 4 to 95:115.8%16.2%

Consider the single number bet from the chart. If you bet $1 on it, you will win back the dollar along with $35. The math behind it is simple. Let’s say you placed a bet on a three numbers bet. Since it has 36 numbers, divide it by the number of squares (36/3=12). Then, subtract by 1 (12-1=11). The payout comes to around 11:1, implying that a $10 bet could draw $110 on winning.

How to Improve the Odds of Winning at Roulette?

This table game belongs to those where you can never lower the house edge or influence the odds in any way. However, you can always maximise the winnings. Shared below are the tips on how to nail such a table game:

Prepare Yourself First Before Placing Bets

Research about this table game, and when you do so, you will notice that the odds of different wagers are varied. Check them out individually to boost your bankroll. All online games feature them for players to refer to, but if it does not, keep this write-up open to take a cue.

Choose Between the Roulette Game Types

As you know, the table game can be American, European or French. Before you commence, look through the different odds for every variation and figure out the house advantage. It’s advisable to play the variation that offers the lowest house edge. Try betting on European type of the game for generous payouts!

Invest More Time in Outside Bets

No bet pays out as lavishly as outside! It’s frequent and safe when you wager on minimum bets. However, if you want to lower the risk while enjoying a decent chance of grabbing payouts, it’s recommended to place two equal outside bets. Such a betting style may not increase your winnings dramatically, but it will at least promise you an enjoyable time without the risks of losing big sums.

Try Your Luck at a Game of Roulette in SpinCity!

Now that you have explored the mathematics behind it, evaluate your understanding by placing stakes on numbers. Check if your winning chances have improved, and play more rounds if necessary to master the game. SpinCity is the ideal destination to practice your strategies and win real money if you are lucky.