Whatever the game, if money and chance are involved, there are some basic gambling truths that can help the happy statistician stay happy.
Although this chapter is full of hacks aimed at particular games, many of them games of chance, there are a variety of tips and tools that are useful across the board for all gamblers. Much mystery, superstition, and mathematical confusion pervade the world of gambling, and knowing a little more about the geography of this world should help you get around. This hack shows how to gamble smarter by teaching you about the following things:
The Gambler's Fallacy
Did you ever have so many bad blackjack hands in a row that you increased your bet, knowing that things were due to change anytime now? If so, you succumbed to the gambler's fallacy, a belief that because there are certain probabilities expected in the long run, a short-term streak of bad luck is likely to change soon.
The gambler's fallacy is that there is a swinging pendulum of chance and it swings in the region of bad outcomes for a while, loses momentum, and swings back into a region of good outcomes for a while. The problem with following this mindset is that luck, as it applies to games of pure chance, is a series of independent events, with each individual outcome unrelated to the outcome that came before. In other words, the location of the pendulum in a good region or bad region is unrelated to where it was a second before, andhere's the rubthere isn't even a pendulum. The fickle finger of fate pops randomly from possible outcome to possible outcome, and the probability of it appearing at any outcome is the probability associated with each outcome. There is no momentum. This truth is often summarized as "the dice have no memory."
Examples of beliefs consistent with the gambler's fallacy include:
Avoid fallacies like this at all costs, and gambling should cost you less.
Casinos and Money
Casinos make money. One reason they make a profit is that the games themselves pay off amounts of money that are slightly less than the amount of money that would be fair. In a game of chance, a fair payout is one that makes both participants, the casino and the player, break even in the long run.
An example of a fair payout would be for casinos to use roulette wheels with only 36 numbers on them, half red and half black. The casino would then double the money of those who bet on red after a red number hits. Half the time the casino would win, and half the time the player would win. In reality, American casinos use 38 numbers, two of them neither red nor black. This gives the house a 2/38 edge over a fair payout. Of course, it's not unfair in the general sense for a casino to make a profit this way; it's expected and part of the social contract that gamblers have with the casinos. The truth is, though, that if casinos made money only because of this edge, few would remain in business.
The second reason that casinos make money is that gamblers do not have infinitely deep pockets, and they do not gamble an infinite period of time. The edge that a casino hasthe 5.26 percent on roulette, for exampleis only the amount of money they would take if a gambler bet an infinite number of times. This infinite gambler would be up for a while, down for a while, and at any given time, on average, would be down 5.26 percent from her starting bankroll.
What happens in real life, though, is that most players stop playing sometime, usually when they are out of chips. Most players keep betting when they have money and stop betting when they don't. Some players, of course, walk away when they are ahead. No player, though, keeps playing when they have no money (and no credit).
Imagine that Table 4-1 represents 1,000 players of any casino game. All players started with $100 and planned to spend an evening (four hours) playing the games. We'll assume a house edge of 5.26 percent, as roulette has, though other games have higher or lower edges.
In this examplewhich uses made-up but, I bet, conservative dataafter four hours, the players still have $56,844, the casino has $43,156, and from the total amount of money available, the casino took 43.16 percent. That's somewhat more than the official 5.26 percent house edge.
It is human behaviorthe tendency of players to keep playingnot the probabilities associated with a particular game, that makes gambling so profitable for casinos. Because the house rules are published and reported, statisticians can figure the house edge for any particular game.
Casinos are not required to report the actual money they take in from table games, however. Based on the depth of the shag carpet at Lum's Travel Inn of Laughlin, Nevada (my favorite casino), though, I'm guessing casinos do okay. The general gambler's hack here is to walk away after a certain period of time, whether you are ahead or behind. If you are lucky enough to get far ahead before your time runs out, consider running out of the casino.
There are several general betting systems based on money management and changing the amount of your standard wager. The typical system suggests increasing your bet after a loss, though some systems suggest increasing your bet after a win. As all these systems assume that a streak, hot or cold, is always more likely to end than continue, they are somewhat based on the gambler's fallacy. Even when such systems make sense mathematically, though, anytime wagers must increase until the player wins, the law of finite pocket size sabotages the system in the long run.
Here's a true story. On my first visit to a legal gambling establishment as a young adult, I was eager to use a system of my own devising. I noticed that if I bet on a column of 12 numbers at roulette, I would be paid 2 to 1. That is, if I bet $10 and won, I would get my $10 back, plus another $20. Of course, the odds were against any of my 12 numbers coming up, but if I bet on two sets of 12 numbers, then the odds were with me. I had a 24 out of 36 (okay, really 38) chance of winningbetter than 50 percent!
I understood, of course, that I wouldn't triple my money by betting on two sets of numbers. After all, I would lose half my wager on the set of 12 that didn't come up. I saw that if I wagered $20, about two-thirds of the time I would win back $30. That would be a $10 profit. Furthermore, if I didn't win on the first spin of the wheel, I would bet on the same numbers again, but this time I would double my bets! (I am a super genius, you agree?) If by some slim chance I lost on that spin as well, I would double my bet one more time, and then win all my money back, plus make that 50 percent profit. To make a long story short, I did just as I planned, lost on all three spins and had no money left for the rest of the long weekend and the 22-hour drive home.
The simplest form of this sort of system is to double your bet after each loss, and then whenever you do win (which you are bound to do), you are back up a little bit. The problem is that it is typical for a long series of losses to happen in a row; these are the normal fluctuations of chance. During those losing streaks, the constant doubling quickly eats up your bankroll.
Table 4-2 shows the results of doubling after just six losses in a row, which can happen frequently in blackjack, roulette, craps, video poker, and so on.
Six losses in a row, even under an almost 50/50 game such as betting on a color in roulette, is very likely to happen to you if you play for more than just a couple of hours. The actual chance of a loss on this bet for one trial is 52.6 percent (20 losing outcomes divided by 38 possible outcomes). For any six spins in a row, a player will lose all spins 2.11 percent of the time (.526x.526x.526x.526x.526x.526).
Imagine 100 spins in two hours of play. A player can expect six losses in a row to occur twice during that time. Commonly, then, under this system, a player is forced to wager 32 times the original bet, just to win an amount equal to that original bet. Of course, most of the time (52.6 percent), when there have been six losses in a row, there is then a seventh loss in a row!
Systems do exist for gambling games in which players can make informed strategic decisions, such as blackjack (with card counting) and poker (reading your opponent), but in games of pure chance, statisticians have learned to expect the expected.