Gambling

The word "gambling" can vary greatly in context, whether it refers to betting on whether there is an even or odd number of steps when walking up the stairs or playing Mahjong with relatives during Lunar New Year. By definition, anything involving the act of taking risks and trying to earn money (or have a positive income) is considered gambling. However, today we are focusing on the act of gambling in a casino.

I am sure that everyone has heard of a casino or may have even been to one. The closest casinos you can get to from Hong Kong are the Sands Casino (in Macau) or the Venetian Casino (in Macau), depending on whether you are taking a boat or car to Macau.

Background of Macau's Gambling

Currently, the Macau government has limited the number of casinos in Macau by granting permission for only six major casinos to legally host gambling. They are Wynn, Sands, Galaxy, MGM, Melco (Studio City), and SJM (Lisboa). Only these six oligopolies can host legal gambling and sell their licenses to others. Although these six are all competitors, they share the same types of games, such as Big Small, Blackjack, and Baccarat. Have you ever thought about why these games?

Gambling "Games"

All these games are designed for players to take risks and win money from the casino. This might seem strange because you have never heard of a casino shutting down because someone won too much. This is because it is all based on a rule known as the Kelly criterion.

The Kelly criterion is a mathematical way to show long-term expected value (EV), which can be either a positive or negative number. A value greater than 0 means it is likely to win money, while a value less than 0 indicates that, over the long run, you will lose money. The more negative the value, the more you will lose in the long run.

 

This is the formula for the Kelly criterion, which can only be used to measure two outcomes, similar to a binomial distribution. If we take the example of playing Roulette and calculating the expected value (EV) when betting on red, you might think that the chance of winning is 50% and losing is 50%. However, the presence of a 0 or, in some casinos, a 00, makes the EV no longer greater than 0 (or zero).

In the case below, we plugged in $b = 1$, $p = \frac{18}{37}$, and $q = \frac{19}{37}$. This gives us -0.027, which is less than 0. Or, if you think that betting on an individual number might give us a positive number, let's try $b = 35$ (the casino pays you 35x when you win on a single number), $p = \frac{1}{37}$, and $q = \frac{36}{37}$. It is still -0.00077. Although this number is smaller (or closer to zero) than betting on colors, you still won’t win, as the value is still negative, and it takes more rounds for a winning time to come compared to the color bets.

If we use a binomial distribution to find the number of wins for a straight-up bet, we denote this as $X \sim B(35, \frac{1}{37})$ and let $P(X > 1)$ represent the probability of earning money. Here, $n = 35$ because the payout is 35x, and $\frac{1}{37}$ represents the probability of hitting the winning number. The case where $X \leq 1$ (which means no earnings) is not included, and it turns out to be 0.244. In other words, there is a 24.4% chance of winning and getting more than you paid, while there is a 75.6% chance of losing all your money. This situation starts to go wrong as it is not just a 50:50 outcome, as you might have thought.

I asked ChatGPT to simulate an additional binomial distribution of the outcomes for 5 sets of data, each containing 35 numbers. I requested one more number (simulating a human choice), and I got 26. When comparing the number 26 with the sets of data, it turns out there are 0 occurrences in the third set. From these 5 sets of data, not a single set allows you to win money.

Summary

In summary, casinos have set all sorts of gambling games to have a negative expected value (EV). If you really want to "win" from a casino, the only way is to opt out and stop playing once you win money. However, you might not win at all or even lose all your money before you have your first win.

Remember, what we discussed today is all mathematics; nothing is certain. You might get all red for the next 100 spins and still not get a black. Mathematics is mathematics, and reality is reality; you must control yourself when betting.

The best quote—and what you should take away after reading this is...

"Do not go to the casino, as all the "games" are designed to make you lose." 2025. Ian Lam

Publisher: ianlam.us.kg

Author: Ian Lam

Citations:
Kelly criterion Formula

https://encrypted-tbn0.gstatic.com/images q=tbn:ANd9GcTlXzbn9Pn0EaYFrlBw2UWtvuIQq9LeHbR0rw&s

Roulette Layout

https://www.primeapi.com/cmscdn/cdn/cms/GZ/European_Roulette_Table_f731217615.webp

Number Simulation Generator

https://poe.com/

Binomal Calculator

https://www.igchkshop.us.kg/test