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# Application Of Statistics To Predict Winning In Casino

Gambling is a kind of game in which valuable things are betted to win or lose. It is also a kind of entertainment for human beings. Gambling so requires three elements: consider (a bet amount), risk (opportunity), and a prize. The application of statistics in gambling mainly revolves around these three points. The probability of winning or losing is calculated, and the amount of bonus obtained is the result of statistics. All kinds of games have been designed to benefit the casino, which is an important means of profit for the casino. But for every customer, these disadvantages are very weak. How much is the rate of return in gambling, whether it can improve the probability of winning, and whether it should be increased in a certain situation. Roulette is a common gambling game in casinos. Roulette usually has 37 or 38 numbers. Roulette originated in France in the 17th century and is generally considered to have been inspired by the famous mathematician Blaise Pascal when he studied the principle of perpetual motion. In 1842, the French Blaise Pascal added No. 0 to the original roulette to increase the banker’s advantage (in turn, to reduce the possibility of imprisonment), and later to the United States, the Americans added No. 00 to the roulette (which was replaced by the eagle pattern in the early days). The casino is responsible for beating beads at the edge of the rotating wheel. The number on which the beads fall is the winning number. Because roulette betting is a way and customers like to bet on more than one number, American roulette tables usually use their unique color chips to bet on different customers, but in many casinos, cash chips can also bet. Because color chips cannot be directly converted into cash, customers will change color chips back into cash chips when they leave the table. Roulette is a fascinating and exciting game. It consists of a roulette, an ivory ball and a gambling table. The disc revolves around the axis and is divided into 38 slender grooves. The 36 channels are numbered 1 to 36, half red and half black. The other two green ditches are marked 0 and 00 respectively. Players can buy a single number or a combination of numbers on the gambling table. When all players bet, the dealer will release a small ball, and the number that stops in the digital slot is the final result. All American casinos follow the following rules. The advantage of all betting casinos is 5.26%, except for the 0-00-1-2-3 betting portfolio, which has a 7.89% advantage.

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In roulette gambling, unless there is a draw, players will win 36 chips for every 38 chips they put in. No matter how you bet, the average is unchanged. Therefore, in every 38 chips, the casino wins 2 chips, and the casino’s profit is 5.26%. In addition to betting on a specific number, players can also bet on the color of the number that appears. In this case, the casino’s profits are halved. The rules of roulette stipulate that if the number of players betting is black or red, the final color of green is a draw. The casino receives half of the bet and the other half is returned to the player. The profit margin of the casino is 2.63% when the player bets on the number color. Prove this view: According to the rules of roulette, if players bet two chips on the red number, they may lose two chips, or they may change the two chips into four. Of course, 2/38 of them may encounter a green number. At this time, two chips will become one, and three possible may get 0, 1, 4 chips. Suppose our roulette rule changes to this: if a green number appears, players have a quarter of the chance to recover four chips, and three quarters of the chance to get nothing. This rule does not change the player’s game revenue, but when calculated, the player’s return will only appear 0 or 4. The probability of green is 2/38. In the case of 2/38, the player’s return when the probability of a quarter to four, on the other three-quarters of probability is 0. The comprehensive consideration is the result of the player’s return is 73/76（1/4*2/38*73=73/76）to be 0. The player’s have 75/76 (1/4*2/38*75=75/76) get 4 chips. 2.63% is the difference between the two values. Our hypothesis does not affect the results of the game, but it can simplify the calculation.

We according to the analysis of st. Petersburg paradox can win come to the fantasy, If the first throw is successful, the player will get a bonus of \$ 2 and the game will end; if the first throw is unsuccessful, the second one will get a bonus of \$ 4and the game will end; thus, if the throw is unsuccessful, the player will continue to throw repeatedly until the game is successful and the game is over. If the nth throw is successful, the n-th power of the bonus is 2, and the game is over. According to the calculation method of probability expectation value, the expected value of the reward value of each possible result can be obtained by multiplying the probability of occurrence of the result. The expected value of the game is the sum of the expected values of all the results. With the increase of n, the probability of future results is very small, but the reward value is getting larger and larger. The expected value of each result is 1. The sum of the expected value of all possible results, that is, the expected value of the game, will be ‘infinite’. According to the theory of probability, the results of many experiments will be close to their mathematical expectations. But the actual throwing results and calculations show that the average value of the results of multiple throws is several dollars. In the same way, if the casino does not set the upper limit of betting and allows players to credit, can provide a winning gambling scheme, you only need to bet red numbers in roulette, if you lose the bet double, until the first win, once you win, the bet will be restored to the original amount, start again. But the strategy relies on two unfounded assumptions: that casinos do not allow credit and that casinos require maximum bets. Suppose the upper limit of the casino’s bet is 100 chips. And your goal is to use the strategy offered to win a chip. You have a great chance of success. You can use this strategy to bet seven times. If you lose all seven times, you may fail. The probability is (18/38)^7 =0.5%. Suppose the upper limit of the casino’s bet is 100 chips. And your goal is to use the strategy offered to win a chip. You have a great chance of success. You can use this strategy to bet seven times, and you may fail if only seven times all fail. The probability is less than 1%. You can achieve your goal once in the next place, and the success rate is more than 99%. Although the success rate is over 99%. But even if the successful income is just a chip, but the failure, the loss is much greater, in fact, no matter what strategy is used to bet, the result is beneficial to the casino.

Combined with the above data, we get the gambler fallacy. The gambler’s fallacy refers to treating random events that are independent of each other as related events. For example, when tossing coins, no matter how many times they are tossed, they are independent of each other and do not affect each other.The reason is simple and easy to understand, but sometimes it will be confused. For example, when you toss the front five times in a row, by the sixth time, you may think that the probability of the front will be smaller (< 1/2), and the probability of the back will be greater (> 1/2). Others will think backwards, thinking that since all five times are 1, it may continue to be 1 (also known as the hot-hand fallacy). In fact, both ideas fall into the pit of ‘gambler fallacy’. In other words, independent events are treated as interrelated events. If gamblers have the mentality of ‘gambler fallacy’, they will lose even worse. For example, the famous Martingale system in casinos takes advantage of this mentality: gamblers bet \$1 for the first time, \$ 2 for the second time, \$4 for the second time, and so on, until they win. The gambler mistakenly thinks that after losing many times in a row, the probability of winning will increase, so he is willing to double and double the bet, knowing that the probability is unchanged. The gambling machine in the casino has no memory, and will not give you more chances to win because you lost.

14 May 2021

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