HOW BAD LUCK WORKS: OR WHY YOU ALWAYS LOSE GAMBLING (PART I)

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.

From being a waiter on a cruise ship, accumulating $2 million through professional gambling, and then losing it all in a high stakes poker game, Archie Karas 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 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 returned his friend 20,000 and kept 10,000. Then from this money, he won a total of more than 40 million USD within 3 years thanks to gambling, going against famous players of the gambling world 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 story is the beginning of the above story, “someone loses all of his accumulated possessions until only a few coins are left in his pocket”, and then followed by a series of miserable tragedies. The suffering that gambling brings to the majority of those involved is undeniable, but it does prompt us a more interesting question: why the obvious risk from gambling cannot stop humans from constantly engaging in it?

The answer lies in the risk and return 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 our children for their education, 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 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 an easier life 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 and hoping that my childs turn out okay. Similarly, you can accept the purchase of 5 lottery tickets, which will almost certainly result in a loss of 10$, because the prize money is a million times higher than the original amount is a wonderful outcome that 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 poured two cups of coffee down the drain” though you’ll most likely be weighing tomorrow morning about whether to buy a 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 playing no-stake games all day, because it doesn’t provide dopamine; just as adults rarely participate in children’s penny games because the expected profits do not meet their expectations, while the children are still very excited because their expectations are met. 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.

Despite sharing the same mechanics with so many other normal activities, gambling is called gambling because of its very characteristic features of stakes, odds and rewards [2]. In particular, we don’t have enough children and time to try again and again the bet “sending my children abroad”, besides there are too many unknown factors affecting the results of such bets, but 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.

So, when learning about gambling, we need to have insights at the 3 factors above: stake, win rate and reward.

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 pushed 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… They ensured their existence thanks to being carefully designed to guarantee 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 action in a round). This fair design is also based on the calculation of probabilities. For example, a fair coin will guarantee the same number of heads and tails when tossing to infinity. Therefore, a gambler would not favor heads or tails, as the potential of both options is the same. Guessing the heads and 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 pure chance.

Unlike coins or dice, the statistical probability in cards is a bit more complicated. It is said that the deck has “memory”. For example, with three consecutive tosses, if the first one and the second are both tails, then the probability of the third coin showing tails is still ½- although many people would think that “there is a high chance it will go heads”. 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 tails in a row, the chances of it continuing tails is still equal to heads, ½. 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, you can always predict 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 break-even. Meanwhile, if it’s a loaded coin, just enough to bring it to 55% head and 45% tail, if you bet heads continuously, in the end you will profit 10% of your betting money (e.g. playing 1000 times you will win about 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. Therefore, it is common to change coins, smash dice (and dishes or ancillary tools), change dealers… after a certain number of turns to make sure there is nothing shady behind both past and future results. Until now, cheating has always been a shadow over the gambling industry, players think that the bookie is cheating, the bookie is afraid to receive swindlers, and people are often skeptical about the authenticity of gamble after losing their fortune. But the magic of gambling, of good players or casinos, is finding a way to survive even without cheating. Since depending all your wealth on a trick is as dangerous as gambling for the sake of gambling, 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 (i.e. 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 heads or tails, binary options (predicting the up and down trend of currencies/stocks/cryptocurrencies/commodity prices at a specific set time, for example every 30 seconds) or sports betting (with win/lose options or total score betting). 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 their winning, 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 bet, 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 adjusted 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 as more bets are placed, they will be ranked as the upper hand, and the winner will receive a lower % bonus (sometimes 10 to 1 or even 100 to 1). Lower the team is ranked 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 after a long enough time putting their trust in the system, they will always net a 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 slots numbered 1–36 and colored alternately (e.g. red, black, red… and so on) with two special blue boxes of 0 and 00, the way the house makes money is as follows:

- If you bet red/black or even/odd and win, you receive 100% of the money you put in, meaning 1 to 1

- If you bet on a random number and win, let’s take 23 for example, you get back 3500%, meaning 35 times your betting money.

(and a few other bets with similar margins).

These odds sound fair at first, as the return seems to be equal to the risk, even/odd with 50/50 chance offers 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 slots, the dealer wins, all bettors lose money, regardless of color, specific number or even and odd. The odds of the ball falling into these 2 boxes is 1/19. That is, if you bet red and maintain it for 1000 turns continuously, you will lose about 550 bets, including 500 turns of the ball falling to the black slot and 50 turns of the ball falling to the two dealer slots, the same goes with the player who placed his bet black or any specific number.

This 5% figure 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 10 times your money from the house and leave, or go to any slot machine and win 3 times in a row and stop, 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 as long as possible. Building casinos as light-filled entertainment centers, often integrating it with multi-room hotel systems, continuously serving free drink 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. Chance 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, career gamblers rarely sit on casino slot machines, as those are sure to lose games. They like to participate in player-versus-player games (sometimes the house is also the player) to make money from the 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, wins. But the problem with cheaters is that they don’t play fair in the first place, so you shouldn’t consider yourself wise and think that simply betting for the less popular option will lead to a 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 in the first place) by impeding withdrawals and disappearing after 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 gambler

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 being a clumsy imitation of the techniques that lead to an even worse performance than leaving it to chance.

This optimism of the casinos is well-founded. Although games such as blackjack, poker or gin rummy always have a valid strategy for winning, they are often complex, requiring practice, memory ability 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 even though not too fruitful. 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 unskilled. Specifically, how do they create an advantage over the rest of the players? Because they are experts in many different types of gambling games, the factor of luck does not play a decisive role anymore, 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 forever. In particular, “bad cards” and “good 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 Vietnamese Killer 13 card game, a player who memorizes the cards that have been played, calculates the odds they will be cut off by the rest. Normal players also process information, but it’s only at holding 3 Aces and know that… someone is holding the remaining Ace. A more professional player will take into account the possibility of seemingly everything, and play based on that. 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 a sense of how they work.

Blackjack rules are quite simple, each player is dealt two cards, allowed to keep (stand) or draw more (hit), so that the total value of the number of cards drawn is higher than 15, but must be below or equal to 21. Reaching 21 points with only 2 cards, you win; while the total value of the last hand is more than 21, you lose. 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 hand now is 17. One table Blackjack usually consists of a house, facing five to seven players. Players do not compete with each other but directly compete with the house, they will win if their score is higher than the house, and are allowed to increase the bet or surrender (accept immediate loss and lose half of the bet). This is one of the games in which the house has 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 house’s face up card is 5.

- Player has 15 points: do not draw more.

- Player has 12 points: draw more.

- Player with 10 points: double bet and draw more

(Details in table below)

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 choosing to draw gives them a disadvantage over the house. If the hand is played over and over again, making the decision to draw will result in more losses than wins, which means the player is losing. This strategy helps you to reduce the probability of losing, and even increase the probability of winning 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 the deck into 3 groups of cards +1, -1 and 0. After dividing, you calculate the score on the whole table and make an appropriate decision. Specifically:

+1: 2 -> 6, called low cards.

0: 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 house (they affect specific scenarios, one of which is drawing low cards will help the house less likely to go over 21 points). So based on the number of cards dealt (casinos usually deal cards from a deck that is shuffled by many different decks and the dealt cards don’t go back to the deck), you can get an idea of winning probability in the next game (including your advantage and the house’s advantage).

For example, in a game play with 4 decks, and 3 decks have been dealt, the total count is -12 (based on the total number of cards dealt), so now the real score is -4 (take the counted number divided by the number of decks in played), the probability that the next card is a low will be higher than the probability that the next card is a high. Combined with the set of basic rules mentioned above, you will know what percentage you get the card you need, and the percentage the hand draws unwanted cards, from here you adjust your betting. The higher the score, a.k.a positive, means the more low cards have been drawn, which means the more high cards are left in the deck — this is just normal probability math, like the example of drawing 4 Aces at the beginning. It is important information.

Counting cards does not require a genius, just concentration and speed. Softwares can even calculate exactly how much money to bet in each situation, helping players always leave with a certain amount of bonus if they maintain their discipline. 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-deck (making counting less accurate, requiring players to play longer), betting limits (making the reward insignificant), constantly shuffling the cards by machine… or even designing their own special rules. Blackjack today is recorded as having about 100 variations.

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.

(to be continued…)

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References:

[1] Wikipedia Contributors, “Archie Karas,” Wikipedia, May 27, 2021. https://en.wikipedia.org/wiki/Archie_Karas (accessed Jun. 26, 2021).

[2] “gambling | Definition, History, Games, & Facts | Britannica,” Encyclopædia Britannica. 2021, Accessed: Jun. 26, 2021. [Online]. Available: https://www.britannica.com/topic/gambling.

[3] “probability and statistics | History, Examples, & Facts | Britannica,” Encyclopædia Britannica. 2021, Accessed: Jun. 26, 2021. [Online]. Available: https://www.britannica.com/science/probability.

[4] Wikipedia Contributors, “Card counting,” Wikipedia, Jun. 23, 2021. https://en.wikipedia.org/wiki/Card_counting (accessed Jun. 26, 2021).