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All About Calculating Roulette Odds, Expectation & Optimal Bet Sizing

Posted on July 30, 2018 | 1:59 pm

If you are looking to play some live roulette, and you have a bankroll ready to play with, it might be best that you take a little time to familiarise yourself with a few details of the game. Take a look at how to calculate the odds for roulette, the expected player returns and how to manage your bankroll through optimal bet sizing.

When it comes to roulette this might be more important than with other live dealer games as you can look at the probability of winning with each bet. First off, there are different odds relating to the various games of roulette. The American version of roulette has a higher house edge, with European and French roulette offering better odds to the player and the La Partage and En Prison options allowing for a greater chance of winning.

Probabilities within Roulette

Whichever style of roulette you play, the probabilities will remain the same. The spaces are all the same size and as such the ball it as likely to land on one space as another. The probabilities work out as follows therefore:

  • With 37 spaces, the probability that the ball lands on one particular space is 1/37
  • 18 red spaces mean there is a probability of landing on red of 18/36
  • 20 black or green spaces mean a probability of anything but red of 20/37
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Bet Type
Payout Odds
European Roulette Odds To Win
French Roulette Odds To Win
American Roulette Odds To Win
Red/Black
1 to 1
48.65%
48.65%*
47.37%
Odd/Even
1 to 1
48.65%
48.65%*
47.37%
1 to 18/19 to 36
1 to 1
48.65%
48.65%*
47.37%
Dozen Bets
2 to 1
32.43%
32.43%
31.58%
Column Bets
2 to 1
32.43%
32.43%
31.58%
Double Street
5 to 1
16.22%
16.22%
15.79%
Top Line*
6 to 1
N/A
N/A
13.16%
Square
8 to 1
10.81%
10.81%
10.53%
Street
11 to 1
8.11%
8.11%
7.89%
Split
17 to 1
5.41%
5.41%
5.26%
Straight Up
35 to 1
2.70%
2.70%
2.63%

 

Understanding Random Variable and Expected Value in Roulette

The net winnings that you make when placing a wager on a game of roulette can be looked at as a discrete random variable. If you place a wager of £1 on red, and the ball lands on red, you win £1 on top of the return of your wager of £1, or a net win of £1. If you place the same bet but the ball lands on green or black, you lose that pound and have a net winning of -£1.

The expected value is a measurement of the average results, indicating what you can expect to happen if you continued to place the same wager over the course of a long time. If you placed only £1 wagers on red, you might win a few bets in a row over a short period of time, but on average you would expect to lose about £0.05 every time you play. The house edge always gives the advantage to the casino in the long run.

Roulette Payouts

There are a vast number of wager options when playing roulette, but the majority of bets are straightforward. You must make sure that your chips are placed exactly in the right spot on the table for the bet you wish to make, the last thing you would want to do is place them in the wrong spot (in real life or at a live online casino) and miss out on a big payout as a result. The odds are x to 1, so for every pound you wager you’ll win x pounds back, plus your bet. So for instance, the single number bet provides you with a payout of 35 to 1. If you bet £1, you’ll receive £36 in return, including your original £1.

What are the Odds and Payouts on Inside Bets?

Away from the outside bets there are inside bets that you can choose to make. These bets are less likely to succeed, but if you do you will receive a much greater payout than with an outside bet. Inside bets relate to bets made on a single number or a small group of numbers, which can be split into the following wagers.

Straight-Up – This is a simple bet placed on a single number on the table. If your bet comes in you’ll receive a payout of 35 to 1.

Split-Bet – If you place the chip on the line between two adjacent numbers you are covering both of those numbers. If the ball lands on either number you’ll receive a payout of 17 to 1.

Square (Corner) Bet – This wager is made on a corner, placing chips on four numbers to make a square. The payout is 8 to 1.

Street Bet – The street bet in roulette covers three numbers. In order to make this bet you place your chips on the line outside of the three numbers that are together in a row. The payout on a street bet is 11 to 1.

Double Street Bet – With this wager you cover two rows that are adjoining, covering 6 numbers. The payout on a successful bet is 5 to 1.

Basket (Five-Number Bet) – This is perceived by many as the worst bet you can make in roulette, and you can only make one of them. It is a wager on the numbers 0, 00, 1, 2 and 3, with the chip placed on the outside corner of the line between 1 and 0. The payout for a successful wager is 6 to 1, but it has a higher edge than any other bet you can make. The Basket bet is only available in American Roulette.

Optimal Bet Sizing and the Kelly Criterion

Now you’ve had a look at the odds and payouts relating to live dealer roulette you should think about optimal bet sizing. Your odds of winning are always lower than the payout amounts, due to the casino enjoying a house edge of 5.26% in American Roulette. In European and French Roulette the house edge is a more enticing 2.70%.

There are of course strategies out there to help you manage and build your bankroll, with optimal bet sizing key. The most popular is the Kelly Criterion, which can be used within multiple gambling and sporting arenas. The formula is as follows:

F = bp – (1-p) / b

f = fraction of current bankroll to bet

b = net odds

p = probability of winning

Roulette is considered one of the games where the Kelly Criterion works best, if you use it with certain types of bets that are available within the game. To use the Kelly Criterion wisely you should stick to placing wagers on red or black.

The key is to avoid under-betting. Over-betting can kill your bankroll quickly, but under-betting can have worse long-term affects. Under-betting takes place when you continue to wager the same amount every single time. You should of course be cautious so as not to waste your bankroll quickly but the Kelly Criterion can help you work out your optimal bet size.

How it works is that if the wager has a 51% chance of winning and the price is even (as with a red or black bet) you should bet your edge of 2%. If the chance to win rises to 53% then you should bet 6%, and so on. It helps you to build your bankroll in a carefully managed way, without risking through over or under-betting.

What this means is that roulette is best approached, as a game to have fun with, not one that you can build a long-term strategy that will successfully make you millions.

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What Are The Odds For The Same Number Being Spun Several Times In a Row?

Below you can take a look at the odds for the same number coming up on a single zero (European & French) and double zero (American) roulette.

The current record that has been covered by mainstream media is the number 19 being spun 7 times in a row at the Rio in Las Vegas.  The odds of this happening are 94 billion to one!

Funnily enough, if you would place a £1 wager on 19 and keep your winnings for the entire 7 spins, this would be worth £64,339,296,875 (of course this is just a fun fact, you could not actually place a straight up bet this big due to the limits).

The more interesting numbers that you can take away from the table below are the odds for the same number coming up two and three times, as this is a fairly common occurrence.

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Same Number To Come Up In a Row
American Roulette
European and French Roulette
1
37 to 1
38 to 1
2
1,369 to 1
1,444 to 1
3
50,653 to 1
54,872 to 1
4
1,874,161 to 1
2,085,136 to 1
5
69,343,957 to 1
79,235,168 to 1
6
2,565,726,409 to 1
3,010,936,384 to 1
7
94,931,877,133 to 1
114,415,582,592 to 1

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What About Outside Bets in Roulette?

If you like to play it safe with your live dealer roulette play, you’ll most likely stick with the outside bets. These have better odds of winning, with the most popular known as ‘even money’ bets as they cover half of all possible outcomes on your wager. If the ball lands on 0, or 00 in American Roulette, you’ll lose on any outside bet that you make.

What are the outside bets in roulette?

Red or Black – This wager pays out 1 to 1 as an even odd bet if the ball lands on the colour you choose.

Odd or Even – Again, with odds of 1 to 1 on a successful wager, you choose whether the ball will land on an odd or even number.

Low or High – Another even money bet with 1 to 1 odds. You choose whether you think the ball will land low (between 1-18) or high (19-36).

Dozens – This outside bet allows you to bet on whether the ball will land in the first dozen (1-12), the second dozen (13-24) or the third (25-36), with a payout of 2 to 1.

Columns – The numbers are laid out on the table in three columns of twelve numbers. If the ball lands on the column you’ve placed a wager on there is a payout of 2 to 1.

Odds For Multiple Equal Even Money Bet Outcomes

Try showing this to believers of the Martingale betting system!

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Number of Equal Outcome Spins
Odds of Happening
Odds in Ratio
1
48.6%
1.06 to 1
2
23.7%
3.23 to 1
3
11.5%
7.69 to 1
4
5.6%
16.9 to 1
5
2.73%
35.7 to 1
6
1.33%
74.7 to 1
7
0.65%
154 to 1
8
0.31%
318 to 1
9
0.15%
654 to 1
10
0.074%
1,346 to 1

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