Last updated on May 6th, 2022.

From being a waiter on a cruise ship, earning a cumulative $2 million through professional gambling, and then losing it all in a high stakes poker game, Archie Karas then turned his life into a legend. After losing all the money mentioned above, with only $50 USD left, he drove to The Mirage casino in Las Vegas, met an old friend, and persuaded him to ask for a loan of $10,000 USD. Karas used the borrowed money to play Razz (a type of Poker) with a bet limit of $200/$400 USD, earning $30,000 USD; he gives his friend $20,000 back and keeps $10,000. Then from this money, he won a total of more than $40 million USD within 3 years thanks to gambling, including the famous players of the gambling village at that time [1].

Karas’ winning streak and rewards are recorded as the longest and largest in casino gambling history, still inspiring many gamblers around the world. But the secret of inspirational stories is that they are… rare, their appeal comes from the fact that it is a dream contrary to the reality of the majority. In fact, the most common is the beginning of the story, “someone loses all of his accumulated possessions until there are only a few silver coins left in his pocket”, followed by a series of miserable tragedies. . The suffering gambling brings to the majority of those involved is undeniable, but it does prompt us to a more interesting question: what makes the obvious risk from gambling unstoppable? The human system is constantly engaged in it? The answer lies in the risk and returns ratios, as well as the way our minds perceive them emotionally.

In fact, everyone is gambling, betting on an unknown future. Opening a store, investing in children to study abroad, and spending money to learn a new skill… are all risky activities, though not as high as gambling. So we are all potential gamblers, possessing a mechanism that is ready to bet on uncertainties, just need a good enough incentive. I would be willing to spend billions of dong to send my children to study abroad if I think it will live up to my expectations. If this amount is too large for what I have, then I will expect to receive more before I do it, like believing that my child will become a successful businessman, earn a larger amount of money, live a better life. easier and bring more honor to the family by studying abroad. If the amount is too small, I probably wouldn’t put too much of a romantic claim on the outcome, simply choosing the best option for my child and hoping that it turns out. Similarly, you can accept the purchase of 5 lottery tickets, which will almost certainly result in a loss of $5 USD, because the prize money is a million times higher than the original amount is a very good outcome. can meet anyone’s expectations, helping you to make quick decisions without too much calculation. You won’t quantify it into real events like “I just spilled two cups of coffee,” though you’ll most likely be confused tomorrow morning about whether to buy a $2.5 or $1.5 cup of coffee.

Therefore, the gambling games themselves are not attractive because of their appearance, but from the risk-reward ratio that activates the motivational chemicals within each of us. You can’t find a gambler to the point of playing “eat porridge and eat tea” all day, because it doesn’t give you enough dopamine; just as adults rarely participate in children’s “one thousand two thousand” games because the expected profits do not meet their expectations, while the children are still very excited because their expectations are met. response. Meanwhile, people are willing to sit from dusk to dawn to engage in extremely simple games, like guessing whether the coin will be heads or tails, as long as the expectation of return is met.

Although it shares the same mechanics with so many other normal activities, gambling is called gambling because of its very characteristic features of stakes, odds, and bonuses [2]. In particular, we do not have too many children and time to try again and again the bet “for children to study abroad”, besides there are too many unknown factors affecting the results of bets such as However, gambling makes things simpler: the outcome cannot be predicted but the probability can be predicted, the scenario is predetermined; more importantly, you can always keep playing as long as you have money left.

So, when learning about gambling, we need to look deeply at the 3 factors above: stake, win rate, and bonus.

## I. If you have to do something long enough, care about the minority (if you have to do something with the minority, do it long enough).

### 1. Statistical probability.

Statistical probability is the most applied mathematical application to gambling, but it was not mathematicians who figured out how to gamble effectively, it was the gamblers who promoted the birth and development of this discipline. Blaise Pascal and Pierre de Fermat, two famous mathematicians, jointly developed the foundations of modern probability theory by taking on the bet division challenge posed by gambling philosopher Antoine Gombaud [3]. . It is no coincidence that the coin and dice, two symbols of gambling, are also two symbols of probability.

Returning to the essence of gambling games, with coins, dice, 52-card decks, or other types of spins … long-lived also thanks to being carefully designed to ensure that the element the chance is maximum, the probability of winning is equally divided among all players, and there is no definite advantage for anyone (or insignificant advantage, for example being the first to act in around). This fair design is also based on the calculation of probabilities. For example, a fair coin will guarantee the same number of heads when tossing infinity. Therefore, a gambler would not favor a heads or tails, as the potential of both options is the same. Guessing the tails of a coin or guessing the number of dice is a pure game of chance. They are often complicated by changing the rules (like increasing the number of coins), or changing the odds (discussed later), but the outcome is still a pure chance.

Unlike coins or dice, the statistical probability is a bit more complicated. It is said that the deck has “memory”. For example, with three consecutive tosses, if the first one heads and the second lands tails, then the probability of the third coin tailing is still – although many people would think that “there is a high chance it will head up.” “. Coins that are tossed in a row simply have no relation to each other, so the odds are still ½, even if you have rolled 100 heads in a row, the chances of it continuing tails is still equal to heads and equals bằng. However, when drawing consecutive cards, the probability of drawing an Ace is 1/13, but the probability of drawing the next Ace is only 1/17, the third is 1/25 and the fourth is 1/49. If your goal from the start is to draw 4 Aces, the probability of getting it is: 1/13 x 1/17 x 1/25 x 1/49 = 1/270725. We will return to this information later.

In short, almost every gambling game, although it is impossible to predict a specific outcome, predicts the process and the final outcome based on its design, thanks to statistical probability. For example, you can’t tell if the next coin toss will be heads or tails, but you know that the number of tails will be equal to the number of heads, so if you play long enough and keep your stake (assuming you have enough money to play “long enough”), the result is always breakeven. Meanwhile, if the coin cheats, just enough to head 55% and tail 45%, if you bet heads continuously, in the end you will profit about 10% of your capital (for example, playing 1000 times will win about approx. 550 times). And vice versa.

### 2. The house always wins.

Adjusting the balance of dice, coins or other items is a common practice of gambling fraud. Cheating is taboo in this risky sport. A person can lose their fortune to bad luck (or stupidity), and still accept it, but it is rare for anyone to sympathize with cheating even if it affects only 10% of the outcome like the example above. on. Therefore, it is common to change coins, smash dice (and dishes or ancillary tools), and change… after a certain number of turns to make sure there is nothing shady behind past results. both future. Until now, cheating has always been a shadow over the gambling industry, players think that the bookie is cheating, the bookie is afraid to welcome swindlers, and people are often skeptical about the authenticity of gambling after losing all property. But the magic of gambling, of good players or casinos, is finding a way to survive even without cheating. Since taking advantage of a trick is as dangerous as gambling without reason, it is risky and short-term, opening the door to a high probability of an inevitable catastrophic failure. No one dares to invest millions of dollars to open a casino with a gambling mentality, in fact, it is more like opening a coffee shop. Their way of working is based on an absolute win (ie positive profit after balancing all factors) that has been calculated in advance.

First, let’s go to pure binary luck games, like guessing coin results, choosing parity, binary options (predicting the up and down results of currencies / stocks / virtual currencies / commodity prices) at a specific set time, for example every 30 seconds) or competitive sports betting (with win/lose options or even-numbered results). In this type of game, the house can make money by charging a transaction fee, as the rule states that the winner will only receive 95% of the bet, while the loser loses 100%. In this way, they do not need to care about the results, because the random ratio ½ will ensure that after operating long enough, with enough rafters, the house will always receive a stable % of profit. The job now is to attract as many players as possible and maintain it for as long as possible.

In games like sports betting, the balance of the odds will be balanced by the margins, which constantly change depending on the amount bet on each side. For example, team A is rated stronger, is believed by many to have a higher win rate, so more bets are placed, will be ranked as the upper hand, and the winner will receive a low % bonus. more (sometimes 10 to 1 or even 100 to 1). The lower the team and the fewer bets, the higher the bonus. Therefore, it is still basically a balanced bet in the eyes of the house. Another way that many bookmakers apply is to arrange the upper – lower bets using algorithms or a system of experts. Now the problem will be the accuracy of the system they use to balance the bet, if the algorithm ensures a high number of accurate predictions, then in a long enough time, when they put their trust in their system, they still get a positive profit.

Inside casino casinos, almost every gaming machine follows this principle. Casino owners never cheat, they don’t have to, but just cleverly insert a certain percentage of profits into their bonus calculation mechanism. For example, with roulette, a circle has a total of 38 cells, with 36 cells numbered 1-36 and colored alternately (eg 1 red, 2 black, 3 red… and so on. such slot) with two special blue boxes of 0 and 00, the way the house makes money is as follows:

- If you bet on red/black or over and under and win, you will receive a bonus of 100% of your capital, 1 to 1.
- If you bet any number and win, such as 23, you will receive a bonus amount of up to 3500%, which is 35 times the stake.

(and a few other bets with comparable margins).

This odds sound fair, as the odds of return seem to be equal to the risk, two odd 50/50 selections offer a double bonus, so how does the bookie make the money? Remember the two special squares, 0 and 00. If the ball lands on these two boxes, the dealer wins, all bettors lose money, regardless of color, specific number or over and under. The odds of the ball falling into these 2 boxes is 1/19. That is, if you bet red and maintain 1000 turns continuously, you will lose about 550 turns, including 500 turns of the ball falling to the black box and 50 turns of the ball falling to the two dealer cells, similar to the player who placed black or Set any number.

This figure of about 5% is known as the house edge, which is often inserted into nearly every game without hiding it, because it is small enough for the player to find it acceptable [3]. So, from a personal perspective, on a lucky day maybe you will earn from the house 10 times the bonus and leave, or go to any slot machine and win 3 times in a row. Play again, you will feel very happy. But if you keep playing, long enough and often enough, you will always lose money. With a house edge of about 5%, a player brings to the casino $1,000,000 USD and plays continuously, the house always takes from him at least $50,000 USD. In the eyes of the house, either they need a lot of players, and the number of gamblers losing will be more than the number of winning, or they need a player to play a lot, and the losses will be more than the winnings. Therefore, the story now is to attract many players and entice them to stay for a long time. Building casinos as light-filled entertainment centers, often integrating it with multi-room hotel systems, continuously serving free wine and fruit, clockless and windowless design, building structure in the form of mazes, scents, sounds from slot machines… are all designed for the purpose just mentioned. Luck is now an ally of casino owners. Because of pure chance, there are no other factors to interfere, probability ensures that all possibilities will play out according to the scenario, and the house will always earn a certain profit thanks to the house edge.

Therefore, professional gamblers rarely sit on casino slot machines, as those are certain losers. They like to participate in player-versus-player games (sometimes the house is also the player) to make money from their opponents, accepting to pay a little service fee to the house, such as poker. or blackjack.

Although the big casinos are highly likely not to cheat, because it is high risk, and because they have no reason to do so. But a series of big and small bookies everywhere. For example, in binary options games, where predicting the price of a volatile commodity at a certain point in time, the most common scam is data fraud. In addition to the service fee, the house now also chooses the winner based on the bet amount: whichever side has the smaller bet amount, that party wins. But the problem with cheaters is that they aren’t straightforward in the first place, so you shouldn’t consider yourself wise and think that simply looking for the less popular option will lead to a war. win. Binary options scams around the world are often linked to criminal organizations, and they also want to take money from the winners (which they choose) by impeding withdrawals and disappearing. some fine night. Despite being valid in nature, binary options have been banned and restricted in most countries around the world due to their vulnerability to abuse.

### 3. A professional player.

Movies about professional gamblers who make money on figuring out how to win the house, whether based on true stories or purely composed, are frequently sponsored by casinos. The movie 21, for example, based on the true story of a group of MIT students using legal techniques to beat the house at blackjack, is seen by casinos as an inspiration to players everywhere. But the type of audience that is gambling-inspired by a TV series, is likely to be those who will go to the casino to play for fun or show, or clumsy imitation of the techniques that lead to an even higher achievement. Even worse than leaving it to chance.

This optimism of the casinos is well-founded. Although games like blackjack (blackjack is a variation of blackjack), poker (sixth poker) or gin rummy (phham) always have a valid strategy for winning, they are often complex, requiring concentration , the ability to memorize and high discipline. There aren’t too many people like this in a gambling group. Before going into specific strategies to gain an advantage in the games just mentioned, perhaps we should go over a few common myths about a professional gambler.

First, a professional gambler cannot influence the element of luck, so they have no advantage in games of pure chance. The only way to win these games is to cheat, or get lucky and stop at the right time. We’re not talking about cheaters here, nor are we talking about luck. Second, a professional gambler doesn’t actually gamble anymore, because the core is no longer based on luck, while the profits usually remain stable but not too large. In the end, the real pros rarely run into each other and seem to avoid the loss of time and the risk of going up against people with equal or better skills. Instead, they tend to go to places that include people with a lot of money just playing for fun, playing purely on emotions or with unskilled skills. Specifically, how do they create an advantage over the rest of the players? As they know that a lot of gambling, the factor of luck does not play a decisive role, especially in card games.

In almost all gambling with imperfect information, luck can help you win (like you draw good cards while everyone else has bad cards), but it cannot keep you winning all the time. . In particular, “bad cards” and “beautiful cards” often have many levels, the value of your hand depends on what other people’s cards are holding. As in the game of progress, in the endgame, a 4 is also a good hand if all the other player has is a 3. So for professional players, what they are looking for is an advantage over their opponents. , not luck. This advantage usually comes from gathering information and seizing opportunities that give a sure advantage, such as in a forward game, a player who memorizes the cards that have been played, calculates what percentage of the odds are. self ability will be cut off by the rest. Normal players also process information, but they stop at holding 3 Aces and know that… someone is holding the remaining Ace slice. A more professional player will take into account the possibility of seemingly everything, and play based on that. That is basically.

#### Blackjack

Specifically, in blackjack, a group of MIT students used card counting techniques to increase their advantage over the dealer, thereby ensuring their victory. The techniques themselves are quite complicated, but I’ll show you a simplified version so you guys get the hang of it.

Blackjack rules are quite simple, each player is dealt two cards, allowed to keep or draw more, so that the total value of the number of cards drawn is higher than 15, as high as possible but must be below or equal to 21. reaching 21 points with only 2 cards, you definitely don’t lose; while the total value of the last hand is more than 21, it definitely does not win. Each card contains a value equal to the number written on it (1-10), the letter card (J Q K) has a value of 10 and card A has a value of 1 or 11 depending on the player’s choice. For example, if you were dealt an Ace and a 6, you could consider it 17, or keep drawing, for example drawing a 10, you might consider the Ace as 1 and the value of the card now as 17. One table Blackjack usually consists of one, facing five to seven players. Players do not compete with each other but directly compete with the hand, they will win if the score is higher than the card, and are entitled to increase the bet or surrender (accept immediate loss and lose half of the bet). ). This is one of the house games with the lowest edge, but why is that?

Let’s go back to the draw probabilities, as you know above, we always know how many possibilities we have to draw the desired card and how they change over time. Combined with the rules of blackjack, you always know which cards you want, especially thanks to information from a face-up card of the dealer and other players. Therefore, in specific cases, you will calculate how much your advantage is over the house, thereby deciding to withdraw or stop, bet more or surrender. Specifically, in the classic game rules, there are from 4 to 8 decks of cards: The face up card of the one is 5.

- Player has 15 points: do not withdraw more.
- Player has 12 points: draw more.
- Player has 10 points: double bet and draw more.

(see detailed table)

This is the basic strategy to follow, the opposite means depending on luck and lack of professionalism. When in the 15 point case, of course the player still believes he has the ability to draw 1-2-3-4-5-6 cards, but this is less likely than drawing the high cards, and choose The custom of picking gave them an advantage over the other. If the hand is played over and over again, making the decision to draw more will result in more losses than wins, which means the player is losing. This strategy helps you to reduce the probability of losing, even increase the probability of winning to positive 1-2%. But of course that is not enough for the blackjack players to get the money. American mathematician Edward O. Thorp invented a method to make winning more certain, called card counting [4]. In it, a popular strategy is Hi-Lo (High and Low) to divide into 3 groups of cards +1, -1 and 0. After dividing the group, you calculate the score on the whole table and make an appropriate decision. This group is specifically:

- +1: Cards 2 -> 6, called low cards.
- 0: Cards 7 -> 9, called neutral cards.
- -1: 10, J, Q, K, A are called high cards.

Know that we have statistical evidence that high cards are in the player’s favor, while low cards are in favor of the cards (they affect specific scenarios, one of which is the draw of cards). lower will help the one less likely to go over 21 points). So based on the number of cards dealt (casinos often deal cards from a hand that is shuffled by many different decks, and the dealt cards don’t return to the hand), you can get an idea of the odds How much is your probability of winning in the next game (including your advantage and the house’s advantage). For example, in a hand of 4 decks, and 3 decks have been played, the total count is -12 (based on the total number of cards dealt), so now the real score is -4 (take the number count divided by the number of decks played), the probability that the next card is a low hand is higher than the probability that the next card is a high hand. Combined with the set of basic rules mentioned above, you will know what percentage of cards you need to draw, and what percentage of the hand draws unwanted cards, from here adjust. the odds. The higher the score, the positive, which means the more low cards have been drawn, which means the more high cards are left in the hand – this is just a matter of normal probability, like the example of drawing 4 Aces at the beginning. This is important information.

The technique of counting cards does not require a genius mind, just concentration and speed. The software even calculates exactly how much money to bet in each situation, helping players always leave with a certain amount of bonus if they play disciplined. Although legal, card counting players can be banned from casinos, Ben Affleck is an example, as discontinuing the service is also a legal action. In addition, casinos also have many ways to prevent card counting, such as using a multi-hand hand (making counting less accurate, requiring players to play longer), betting limits ( results in negligible), constantly shuffling the cards by machine… or they even design their own special rules. Blackjack today is recorded as having about 100 variations.

## Bottom Line

You can dig deeper on your own to get an edge in blackjack games with friends. I am only covering some basics, intended to talk about the power of statistical probability in gambling, not a complete guide.