Roulette Win Ratio

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Written by Yana Sliusar

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Why can you not win in online roulette? In this article, we present a mathematical proof of the negative mathematical expectation on the course when you play in roulette. We shall also explore the Mathematical evidence of ineffectiveness while using the winning strategies. So, why is it impossible to win at roulette? The basic line is that there are 37 numbers on the field (0-36) and payments are paid 36 to 1. So, every time you bet in, statistically, you are losing 2,7% from the betting amount (even if you have won in the current spin). If you want to check our mathematical explanations, read further.

Why cannot you succeed in roulette via using strategies?

Let's consider all possible common bets in roulette as the mathematical proof of the impossibility to win in roulette and determine their ME (Mathematical expectation) result.

In the general case, I of any bet in roulette can be calculated using the classical formula (1):

, (1)
  • Where is xi– event I,
  • Pi– The probability of the event I,
  • К – The total number of events forming a complete group.

The mathematical expectation of the European version:

The formula (1) for ME of any bets on 'European roulette' can be converted taking into the full probability, not collaborative events, that is Pwin.+ Ploss.=1, to the view with the game for N sectors (rooms), is equal to:
... (2)

Since the probability of winning Pwin in 'European roulette', while you are playing for N sectors (rooms), is equal to:

, that finally, we obtain the expression for ME for ANY bet in 'European roulette', when you are playing for N sectors (rooms), is equal to:... (3)
Let's calculate ME for each 'simple' (basic) bet in 'European roulette' (a wheel with one zero). The result of ME calculation for average basic bets is presented in table 1.

The mathematical expectation for the bets:

Table 1. Calculation of ME for 'simple' bets.

№

«Simple» bet

Winning

Loss

Calculation

МО, у.е.

Payout

Probability

Probability

1.

Straight-Up

35:1

1/37

36/37

=35×1/37-36/37= -1/37

2.

Split

17:1

2/37

35/37

=17×2/37-35/37= -1/37

3.

Street

11:1

3/37

34/37

=11×3/37-34/37= -1/37

4.

Corner

8:1

4/37

33/37

=8×4/37-33/37= -1/37

5.

Six Line

5:1

6/37

31/37

=5×6/37-31/37= -1/37

6.

Column & Dozens

2:1

12/37

25/37

=2×12/37-25/37= -1/37

7.

Even Chance

1:1

18/37

19/37

=1×18/37-19/37= -1/37

As can we see from the table – ME is exactly equal to the value obtained by the formula (3). Let's sum up the results.

The player always loses even when he wins

If the gambler is playing at 'European roulette', (no matter where and how much he puts), he ALWAYS loses 1/37 part of the bet (bets). At the same ME of the game, it is not dependent on the outcome of the spin; that is, the player loses even when he wins. Or in other words, the player ALWAYS loses when he makes a bet at 'European Roulette' regardless of the outcome of the current spin.

Using the strategies of the bets:

For the mathematical proof of the winning's impossibility at 'European roulette' or 'American Roulette,' it is enough to expand any betting strategy on the 'basic' bet. As ME result of all bets is negative and equals -1/37 the size of the stake, then the total expectation of the game result will be negative and equal -1/37. The sum of all bets made by the player or -1/37 from the value of the average stake multiplied by the number of spins played by a gambler.

Assessing the ME of any strategy is enough to determine the value of the average bet while you are playing according to this strategy and taking into consideration all the rules of the transition from bet to bet, and multiplying the result by -1/37. The value of the average bet and sum of all of the bets are positive values; therefore ME is always less than zero, that is ME£0 and less than ME£-1/37 if used the progression because the average rate is bigger than 1.

Dispersion

Let's calculate the variance for any bet in 'European roulette', depending on how many sectors N (rooms) puts the gambler. Use the variance to determine the optimal Bank Kelly criterion for playing 'European roulette'.

Information

Bank on Kelly's criterion shows what should be the gambler's bank to the total balance of all games aspired to infinity.

In the general case, the variance of the player who is playing at the 'European roulette' in N sectors (rooms) can be calculated by the expression:

. (4)

The formula (4) for the variance D of any bets on the 'European roulette' can be converted taking into the full probability, not joint events, that is Pwin.+ Ploss.=1, to the mind:

. (5)

Since the probability of winning Pwin in the 'European Roulette' while you are playing for N sectors (rooms) is equal to:

, finally, we get the expression for the dispersion D of any bet at the 'European roulette' when you are playing for N sectors (rooms), is:. (6)

The magnitude of dispersion D has a positive value throughout the range of games in N sectors. That is an important detail.

Where it is possible to calculate the required bank for the game at 'European roulette' using Kelly's criterion:

. (7)

Using the expressions (3) and (6), we finally obtain the expression:

(8).

The formula (8) shows that the optimal amount of the bank, according to Kelly's criterion for playing at 'European Roulette' is a negative value.

Conclusion:

Roulette win odds

Roulette Win Ratio Calculator

If the optimal value of the gambler's bank following Kelly's criterion is negative, then playing at 'European roulette' is generally not necessary, since the overall result of the balance of all players` games approach to zero, or the player has to lose all his money during the long game.

To assess the 'attractiveness' of the gambling, you can use generalised criteria, which is obtained as the ratio of required the gambler's bank following Kelly's criterion to the mathematical expectation of the game result that is:

(9).

This expression (9) can be understood that the smaller size of the gambler's bank at the mathematical expectation, the 'better' will be a game for the player. This optimal criterion can be interpreted as the criteria of minimal specific player's bank per unit of profit from the game.

The optimal criteria of the Кoptima game can only be used for evaluation of games with a positive expectation! If the game has a negative MT, it will not attract the attention of the gamblers. For 'European roulette' MT -1/37, that is less than zero, so 'European roulette' as the game is not 'attractive' for gamblers. That is why it is impossible to win in roulette, regardless of which betting strategies and tactics selection of items you use.

Note: the formula (3), (5) and (8) can be obtained for 'American roulette' with two sectors of zero: 0 and 00.

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Written by Yana Sliusar

Roulette Win Ratio Chart

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The European roulette consists of the rotating barrel with 37 cells on its perimeter, where each cell corresponds to a number from 0(zero) to 36, and the playing field is intended for making money betting.

The player on his own choice makes bets on the roulette game field. The names of different types of bets and explanations to them are given in the table below. To confirm the rates and the beginning of the spin you can by pressing the Spin/”Spin” button. Then the bets cannot be changed anymore.

Roulette win ratio chart

Spin is the process that begins from the start of the ball on the side of the barrel to the falling out of certain winning number. All bets on the playing field participate only in the sequential spin. The losing bets are removed from the field, and the winnings are paid out according to the table of bets and are returned to the player.

To repeat the bet of the previous spin, just click the “Re-bet”. In order to double the bet, simply click the “x2”. In this case if the doubling of bet will exceed the maximum, the rate will increase to the maximum. The spins without betting are allowed, and the number of such spins is unlimited.At will, the player can disable the rotation animation of the ball in the menu “Options”. One click on the area of the European roulette wheel will disable or enable the animation. When you direct the mouse on the roulette wheel, the tool tip will prompt you to turn off the “animation off” or to turn on the animation “animation on” with one click of the mouse.

While making a bet, the player can set the number of desired spins and play european online roulette in auto mode, pressing the button “AUTO”. For idle spins and for european casino roulette on the FUN the function of the auto spins is not active. The minimum bet size on the field and on the chances is 0,1 USD/FUN. The maximum bet size is listed in the table below.

The payouts on the european online roulette for guessed numbers are corresponded to the type of the made bet. The less is probability that the selected rate will play, the more there will be payouts. By the rules of the roulette there are certain types of bets and payout odds for them.

Types of European Roulette Bets

The number – is a bet on a single number (number).You can bet on zero (zero).The chip or chips are placed in the sector of one number.The win ratio 35:1

SPLIT – is a bet on two adjacent numbers (numbers).You can bet on a combination of zero and number for choice in the front row.The chip or chips are placed on the border between the numbers.Win ratio 17:1

STREET is a bet on a horizontal row of three numbers.The chip or chips are placed on the border of the row and external area.Win ratio 11:1

DOUBLE ZERO is a bet on zero plus two numbers (number) of first rows.The chip or chips are placed on the border of three sectors (zero, plus a couple of selected numbers).Win ratio 11:1

KARE is a bet on a square of adjacent numbers.The chip or chips are placed in the center of the square.Win ratio 8:1

LINE BET is a bet on the entire first horizontal row of numbers plus zero.The chip or chips are placed on the border between the first row and zero.Win ratio 8:1

Six-line is a bet on two adjacent horizontal rows of numbers.The chip or chips are placed on the external border and the border between the selected rows.Win ratio 5:1

COLUMN is a bet on a selected vertical row of twelve numbers. The chip or chips are placed in the space provided for such rate sector. Win ratio 2:1

DOZEN is a bet on a sector of twelve numbers (numbers): numbers 1-12 first sector; numbers 13-24 the second sector; the numbers 25-36 in the third sector. The chip or chips are placed in a specially designated sector, indicating a dozen. Win ratio 2:1

The simple options:

COLOR the color can be red or black. In the bet there involved 18 numbers of the same color. The chip or chips are placed in the designated sector. Win ratio 1:1

ODD – EVEN (Even/Pair Odd/Impair) is a choice of even or odd value numbers. There are 18 numbers of the same value involved in the bet. The chip or chips are placed in the designated sector.

MORE LESS is a choice of one of two sectors: less numbers (numbers) 1-18; more numbers (numbers) 19-36. The chip or chips are placed in the designated sector. Win ratio 1:1