In the exploration of decision-making and risk, there is probably no better arena to examine than that of Gambling. Gambling is defined as “the act or practice of risking the loss of something important by taking a chance or acting recklessly.” Chance is “the absence of any cause of events that can be predicted, understood, or controlled.” Gambling sounds risky and unpredictable, so why would anyone ever do it?
As you would guess, lots of people do it. The American Gaming Association estimated the gross gaming revenue of regulated commercial casinos at $37.3 billion in 2012. Their definition of gross gaming revenue (GGR) is “the amount wagered minus the winnings returned to players.” That is just the tip of the iceberg. In 2015, NBA basketball commissioner Adam Silver raised eyebrows in a New York Times op-ed piece writing, “…some estimate that nearly $400 billion is illegally wagered on sports each year.” The reality is we simply don’t know. Most of this activity is unregulated. What we do know is that a lot of people spend a lot of money gambling every year.
In his book, Bringing Down the House: The Inside Story of Six M.I.T. Students Who Took Vegas for Millions, Ben Mezrich explains how a small group of college students won millions of dollars by counting cards in blackjack. During the week, they were normal college students, but on the weekend they were skilled card sharks gaming the gaming industry in Las Vegas. This story was made into a movie staring Kevin Spacey called 21. The technique they used to win big at the tables is called card counting. Although this practice is not illegal, it does help to tip the scales of probability in favor of the player and away from the “house” or casino. When members of the group were eventually identified, they were banned from the casinos.
What exactly is card counting and why do casinos hate this legal activity? Let’s begin by looking at the game of blackjack. This table game has the best odds of winning for the player, because the house only has a <1% edge in most casinos. Like all games of chance blackjack is a game of probabilities. The player isn’t competing against the other players at the table, but rather the house itself. However, cards dealt to other players influence the probabilities of the next card dealt.
The blackjack player has several decisions to make, but the two most basic and important are whether or not to take another card and how much to bet on any given hand. On the surface, it may seem as if the outcome of these decisions are random, but in reality they are somewhat predictable through the understanding of probability and statistics.
The beautiful Las Vegas hotels and casinos were built on the gut feeling decision-making of most gamblers, but the M.I.T. crew proved that mathematical strategies of probability are actually the key to the game. While a player does not know for sure which card she will next receive, she can calculate the probability of her hand winning and bet accordingly. It’s basic statistics, which is probably why M.I.T. students were ideal card counters. They bet more money when the probabilities were in their favor and less money when they were in the dealer’s favor. Statistically, they would win money over time (and they did). In other words, this game of chance becomes less risky when you understand and play the probabilities over the long haul.
Counting cards is a method of determining which cards have already been dealt in order to predict the probability of the next card. For example, if you know that all the eights have been dealt, the probability of anyone at the table receiving another eight is zero. If you don’t know how many eights have been dealt, you don’t know the true probability of another eight coming from the dealer’s deck. The card counter’s advantage is in using this information to formulate more accurate probabilities, which affects her decision-making.
Contrary to popular belief, counting cards does not require the player to memorize the cards that have been dealt with Rain Man precision. The basic card counting strategy, called the Hi-Low method, requires the player to keep a “running count” of the cards that have been dealt. This is done by assigning each card a point value: low cards (1 – 6) = 1; neutral cards (7 – 9) = 0; high cards (10 – Ace) = -1. So, if these cards have been dealt (2, 10, Ace, 6, 9, 7, 4, Queen, 2, 3, 8) the card counter’s running total would be two. The counter would translate those cards like this: 1 + (-1) + (-1) + 1 + 0 + 0 + 1 + (-1) + 1 + 1 + 0. When all of these values are added, the total is two.
The purpose of the Hi-Lo approach is to predict the ratio of high cards versus low cards remaining in the deck. Statistically, when the deck has more high cards, it favors the player. Conversely, when the deck has more low cards it tips the scale in favor of the dealer. Because most casinos use multiple decks when dealing blackjack, the “true count” is determined by dividing your running count by the number of decks left to be played (usually estimated to the half-deck). When the true count is a positive number, bet more (the higher the count, the more you bet). When the true count is negative, only bet the table minimum.
Like everything else in life, it takes practice to master card counting. In addition to the skill itself, the player must learn to deal with the time pressure involved in a fast-moving game, the suspicious gaze of the pit boss, the all-seeing eye of casino security, waitresses, other players and the myriad of buzzers, bells and other distractions in a casino.
So, if black jack is a game of statistical probabilities, why do most gamblers lose money?
Because they make decisions based on emotion. They’re riding a streak or making false assumptions based on the notion of luck. On the other hand, the M.I.T. students were solving a math problem… over and over and over again. They didn’t win every hand, but they played the probabilities to win more than they lost. Much more than they lost. In their case, they worked effectively as a team by distracting the casino workers from the fact that they were counting and by signaling each other to locate the more advantageous tables.
We all fall somewhere on the spectrum of risk tolerance. Some of us love to take risks, while others only go for sure things. Unfortunately, in the real world, there are very few sure things. There is always the risk of failure. Depending on your risk tolerance, sometimes that perception of risk can be amplified too high or dimmed too low. Casinos, like all businesses, are in business to make money, so they obviously frown on the practice of card counting. While it is not illegal, some people find it unethical.
I don’t find gambling particularly entertaining or enticing, so I don’t have a strong opinion either way. But, why would it be unethical to allow people to calculate the statistical probabilities in a game based on statistical probabilities? At any rate, the M.I.T. students taught us that when emotion and fear is removed from a decision, even in games of chance, risk can be reduced to a metric of probability—a mere statistic. And, that rational decision-making can win the day.
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