The European Roulette: Not A Fair Game To Play

Introduction

Different method of playing the roulette and the payout “Luck” by the definition from Cambridge, “the force that causes things, especially good things, to happen to you by chance and not as a result of your own efforts or abilities” but the mathematics there is no such things as “Luck” to play the roulette, probability is used to replace “Luck”. In this mathematics internal assessment, I have decided to centre my exploration on the topic of European Roulette. Roulette is a casino game named after the French word meaning little wheel. In the game, players may choose to place bets on either a single number, various groupings of numbers, the colors red or black, whether the number is odd or even, or if the numbers are high (19–36) or low (1–18).

To begin with, I looked at the different ways of playing European Roulette at trustworthy EU casinos. To determine the winning number and color, a croupier spins the wheel in one direction, then spins a ball in the opposite direction around the circular track running around the outer edge of the wheel.

The European roulette wheel has 37 slots, where numbers from 1 to 36 and 0 can be found. Numbers from 1 to 36 are alternately colored in red and black, while the single zero is marked in green. The main objective for the player itself was to predict, which numbered slot the roulette ball is going to settle into. To do that, all players must make bets on a particular number, after which the dealer turns the roulette wheel in one direction and spins the roulette ball in the opposite. Once the ball finds its way into the pocket with that particular number, the players get paid by the way they play. I started to research on the different types of roulette and the ways of playing the game. There are totals of 10 ways to play the game, Reds and Black, Evens and Odds, Lows and High, Dozens, Columns, 6 Numbers (6 line), 4 Numbers (square), 3 Numbers (street), 2 Numbers (split) and 1 Number (straight). Each way of playing the game has a different payout and chance of winning.

To do my calculation, I did a primary data and collected 200 different results from the Roulette when I spin it. I will be using the data that has been collected first hand to calculate the expected gain for the gambler and whether the European Roulette is a fair game to play, the expected value, comparing the experimental probability vs theoretical probability and the expected mean of the game.

The expected outcome for the random variable X is the mean result 1. In general, the expectation of the random variable X isIn gambling, we say that the expected gain of the player from each game is the expected return or payout from the game; less the amount it cost them to play. The game will be fair if the expected gain is zero. In order to collect my data, I will be performing the spinning the roulette myself since this is a primary set of data. First, I will need a roulette ball. Secondly, I will need to spin the rotor and each trial must be use the same amount of power to spin the rotator in order to get a fair result. Thirdly, I will spin the roulette ball in the opposite direction of the rotor around the ball track. Lastly, I will have to wait for the roulette ball to be landed on one of the number pockets.

Expected Gain

The formula for expected gain is stated belowThe expected gain of the game would be calculated with the money that the player is willing to pay, in this case, we will set the price to pay the European Roulette at $10. Types of Bet Calculation Expected Gain Red Colour E(X)=E(Y) - $10 = - $10 = Black Colour E(X)=E(Y) - $10 = - $10 = Even Numbers E(X)=E(Y) - $10 = - $10 = 9 Odd Numbers E(X)=E(Y) - $10 = - $10 = 8 Lows E(X)=E(Y) - $10 = - $10 = -0.5 Highs E(X)=E(Y) - $10 =- $10 = 17.5 Dozens E(X)=E(Y) - $10 = - $10 = -3.5 E(X)=E(Y) - $10 = - $10 =.5 18.5 E(X)=E(Y) - $10 = - $10 = 20.5 Columns E(X)=E(Y) - $10 = - $10 = 7.5 E(X)=E(Y) - $10 = - $10 = 8.5 E(X)=E(Y) - $10 = - $10 = 9.5

The result shows us that the European Roulette is not a fair game because of all the different methods of playing the game, most of the expected gain is either higher or lower than 0 which makes the European Roulette not a fair game, to have one of the types of bet to be fair the expected gain of that bets must be equal to 0, as we can see from the result above only one bet is consider to be a fair game, which is the lows, it is not considered as a fair game as the expected gain of that bets is -0.5 which is less than 1 but not close to 0, it could still be considered as a fair game. When the player tries to play the European Roulette, putting the bets on the highs and lows would consider you have a chance of earning some money back.

Experimental Probability vs Theoretical Probability

Theoretical probability is what we expect to happen, where the experimental probability is what actually happens when we try it out.

To compare the experimental probability to the theoretical probability, the theoretical probability must times itself by 150 times since the probability is shown are only the chances of 1 times playing the roulette. The result shows that we can see that when the player is putting his bet on to the colour section, odds/evens number section or lows/highs, the player will expect to have 73 times out of 150 times that the ball is landed on that section. There are 4 times that was not shown on the graph because that 4 times was expected to land on the 0 and 0 does not lie on the colour section, odds/evens number section or lows/highs section. The experimental probability has a similar result with the theoretical probability except for the dozens and the columns.

Normal Distribution

Using the value of the expected mean, and the 150 times of data collected, I can calculate the standard deviation and created a normal distribution graph using excel. The bell curve shown above has a mean of 17.7(3 sf) and a standard deviation of 11.1 (3 sf).

Conclusion

This investigation explored the different types of bets in the European Roulette and which bets (colours, numbers, highs/lows, dozens and columns) would be a fair game to play with? Area involves in the investigation are probability and normal distribution. The big question about this game is that “Can mathematical theory on probability help you to predict the game or win the game?”

Firstly, the expected gain from the different bets, most of the bets are either higher or lower than 0, which the rule for the game to be fair the expected gain must be equal to 0, the closest bet that could be considered as a fair game would be the lows, it has an expected gain of -0.5 and for highs it has an expected gain 17.5. From this 2 numbers, we can see that when players pay the bets on the lows, they will lose a small amount of money, for example, if the player pays 10 dollars they will only gain 0.5 dollars and when place bets on the highs the player is expected to lose 17.5.

Secondly, the game has a similar probability for the theoretical probability and the experimental probability. For the colours, numbers, and highs/lows it is expected to have an outcome of 75/150 times and in experimental probability around 73 times, the ball has landed on its spots. From this result, we can create a statement that mathematics theory probability can help you to predict the game or even win the game?

The weakness of this investigation would be that the data would be collected by hand as there could be an error in the data. When I throw the ball into the rotating roulette, the power that was used to push the ball into the roulette would be different each time, so it would affect the result. To minimize the error, I could build a machine, which is capable to push the ball into the rotating roulette with the same amount of power used to push the ball every time. This will not able to use the same power to push the power, it could also minimize the error that human create.

The most valuable lesson I have learnt from this investigation is the idea “probability” can be used in the European Roulette, as we can see from the result, and the data analyze that the probability of the theoretical, and the experimental has a similar outcome, even though the European Roulette turns out to be an unfair game, it is possible to still play the game base on the 2 different types of probability that I have calculated but if you want to win and earn money by playing the European Roulette, I would recommend not to play this game as the European Roulette is a kind of casino game, when you lose once, you will want to keep playing till you can earn some money, but when the time you have finally earned and win some money back you may have lost a lot of money and start to gain debt which may result you to lose your life. If you want to earn money, thy best way is to go the right way and not going into a shortcut to earn money that may kill you.