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Probabilities, Payouts and Strategies

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Probabilities, Payouts and Strategies

 

Last time we gave you a rundown of the various bets that can be placed and where to place your chips on the layout. Now, we know you’re itching to put this knowledge to use, but there are a couple of important factors left to consider: the odds of individual bets and the various betting systems. In the final instalment of our roulette strategy guide good we analyse both and see whether there’s a good way to make inroads on the house edge.

Probabilities and Payouts

Let’s start with the American double-zero roulette wheel and the probabilities of a winning bet. As you will see, the house edge is always the same, no matter the bet, unless you bet on 0, 00, 1 and 2 (known as the top line) where you’re the house edge goes up to 7.89%. For those who don’t know what we mean by the house edge: it is the amount that a player loses on average relative to any bet made.

BET

PAYS

PROBABILTY OF WIN

HOUSE EDGE

Red

1

47.37%

5.26%

Black

1

47.37%

5.26%

Odd

1

47.37%

5.26%

Even

1

47.37%

5.26%

1 to 18 (Manque)

1

47.37%

5.26%

19 to 36 (Passe)

1

47.37%

5.26%

1 to 12 (1st 3rd )

2

31.58%

5.26%

13 to 24 (2nd 3rd)

2

31.58%

5.26%

25 to 36 (last 3rd)

2

31.58%

5.26%

Six numbers (Double Street)

5

15.79%

5.26%

Top Line (First 5 numbers)

6

13.16%

7.89%

Corner (4 numbers)

8

10.53%

5.26%

Street (3 numbers)

11

7.89%

5.26%

Split (2 Numbers)

17

5.26%

5.26%

Straight (a single number)

35

2.63%

5.26%

A Bit More Maths

The house edge for a single-zero European-style wheel is around half that of an American wheel at 2.7%. As such for every £1 bet placed on a double-zero wheel you can expect to lose 0.053 pence over time and 0.027 pence on a single-zero wheel. The average return of any bet can be worked by using the following equation:

Roulette Payout Equation

where n  is the number of squares being bet on. If there were 36 numbers to bet on (n = 36) the expected value of each bet would be zero, it is the 0 or 0 + 00 that gives the house its advantage.

Betting Strategies

It’s often alleged that Albert Einstein claimed: “No one can possibly win at roulette unless he steals money from the table while the croupier isn’t looking.” For once, it seems, Einstein was incorrect. There have to date been numerous instances of single players or teams cheating the system and overcoming the house edge without resorting to flagrant thievery, particularly in the case of biased wheels and casinos where bets can be placed after the ball is rolling.  For example, in 2012 mathematician, Doyne Farmer, revealed the secrets of how he beat the house edge with the world’s first wearable computer in the 70s. However, as we revealed in the first instalment of this guide, the chances of cheating the house are slimmer than ever these days with biased wheels nigh on impossible to find. The latest American attempt at cheating the house took place in Cincinnati, Ohio, where four men tried to swap their $1 chips for $25 counterfeit ones.

Over the years, several even-money betting systems have been championed as capable of beating the game. An even-money bet is one with a payout of 1 to 1: even/odd; red/black; 1 to 18/19 to 36. Most systems are predicated on the Martingale system, whereby the gambler doubles his bet after every loss so that any eventual win will cover all previous losing bets. At some point the Martingale player is likely to win, but if enough bets are lost in a row their bankroll may run out or they may hit the table limit for a bet. Last year, in Vegas, a roulette wheel reportedly came up with 19 seven times in a row. As an example, if you had been using the Martingale system and wagering £50 a time on black, by the 6th effort you would be stumping up £1600 which could well be more than the maximum bet allowed, and if you lost that bet you’d be £3150 down.

Another widely-used strategy was the D’Alembert system, or montant et demontant as it is called in French. It is another system applied to even-money bets and involves a simple progression: a loss means you add one unit (say £1) to your next bet and a win means you deduct one unit. This is a manifestation of the “gambler’s fallacy” where it is said that a player is more likely to win following a loss, and vice versa. The most complex of the basic strategies is the Labouchère system: you make a list of positive numbers that sum to the amount of money you wish to win; the amount of your first bet is the sum of the first and last numbers on the list; if you lose you cross off the numbers, if you lose you add the amount bet to the end of the list. However, the Labouchère system, like many others, has an overall negative value, meaning over time you will lose money.

The Last Word

A final word of caution: Be wary of online betting strategies that claim to know the secret workings of a roulette wheel and charge a high price to part with it. The authors of a legitimate guide, like ours, will tell you that there is no such thing as a strategy that always pays out. Roulette is the epitome of a game of luck: it’s all about the excitement of winning (and losing) and ceding control to fate. Practically no one can predict unaided where the ball will land and the adrenalin rush as it comes to rest on its square, whether a winning one or not, is the main reason is reason so many people love it.

And so concludes this roulette strategy guide. We hope we’ve provided you with some useful information and a few invaluable lessons to take away. Good luck on the tables!

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