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Explore how maths powers the gambling world
- 2 days ago
- 2 min read
Written by Trang Ninh
Most gamblers walk through the door of casinos and hope that they would win by luck. However, are casinos built just through luck? In fact, casinos are rigorous business models rooted in mathematics, where probability and statistics turn uncertainty of gambling into a highly predictable stream of revenue. Thus, despite gamblers winning all the time, how do casino models remain profitable?
Probability measures the likelihood of an event occurring, expressed as a value between 0 (impossible) and 1 (certain), or as a percentage from 0% to 100%. The most common mistake gamblers make is confusing independent events with dependent events—a misunderstanding that costs them millions.
Consider coin flipping: if a fair coin lands on tails 5 times in a row, what is the probability of getting heads on the sixth flip? Many people incorrectly believe tails is "due" or that heads are "more likely now." However, the correct answer is still 50%. Each coin flip is an independent event and the coin has no memory of previous results. This misconception is called the gambler's fallacy, and it leads players to make irrational betting decisions based on patterns that do no't actually exist.
Furthermore, not only probability, but expected value is also utilised by Casino to articulate the chances of gaining profit. Considering the American Roulette wheel which has 38 spaces: numbers 1 to 36, 0 and 00. If you bet 1$ on one number, the chance of winning would be $38 as you gained $35 with your $1.
Using the formula:
E(X)=(X P[X])
Expected value shows the average outcome of a random event. It is the sum of the product of each outcome and its probability.
Expected Value on American Roulette (1/38 chance of winning and 37/38 chance of losing) is predicted as follow:
E(X) = (5 138) + (-1 3738) = -0.05
This means that for every dollar bet, the player would be expected to lose $0.05 (5 cents). This is used in casinos as a “house edge”. Through this mathematical calculation, the casinos’ profit is guaranteed through thousands of dollars of bet from players.
So, why would the casinos only focus on the 5 cents edge rather than individuals' bet? Moreover, how is this applicable if some players still win? This could be explained by the “Law of Large number”, which claims that the accuracy of the calculation would increase as the sample size becomes bigger. In a day, there could be thousands of bets happening in the casino, which makes its sample size extremely big and its profit is much more guaranteed.
Casinos do not need luck because they have mathematics. Understanding these principles will not make you rich gambling, but it will make you mathematically literate which is that is far more valuable. These concepts extend far beyond gambling. Expected value guides investment decisions, insurance pricing, and risk management. Probability and statistics are the languages of uncertainty—master them, and you'll make better decisions in every area involving risk and chance.
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