Monte Carlo Fallacy

I once had a very lucrative day at the casino. Must be some 30 years ago now when I went to the casino with a friend with no money at all, and left the place with $1,500. I thought I was being smart back then. It turns out that I was just extremely lucky.

We entered the casino at two o' clock in the afternoon. I had no money, but was there on invitation from a friend who lend me $75 (it actually was 75 Dutch guilders, the currency of The Netherlands back then, but I'll use dollars in this post to keep things simple). When the casino closed three o'clock in the morning, I had paid back the $75 and had $1,500 in my pocket; my friend, who invited me and lost almost the same amount of money was flabbergasted. "What did you do to be so lucky!?" I answered that luck had nothing to do with it: I had a system and stuck to it the entire day, evening and night.

Only years later I learned that the system I used has a name: it's called the Martingale Roulette system. It went like this: whenever the color red or black came up at least 5 times in a row, I placed a small bet on the other color (I also did this for odd or even and low or high numbers). The casino had three tables that accepted bets small enough for my modest amount of money, so I kept an eye on all three of them. The first bet had to be the smallest possible for my system to work; whenever I lost, I doubled the bet, and kept on doubling the bet until my color came up. This way I always won the initial small amount, the first bet. Halfway through the evening I had paid back the $75 to my friend and bought him a drink; we went our separate ways for the whole day because he liked playing Blackjack with larger amounts than I could afford. In fact, just before closing time I had more than $2000 in profits, but I figured I could place one last larger bet and put $500 on red... I lost that bet but left the casino a happy man. Feeling bad for my friend, who lost more than $1000, I even gave him $500 and thanked him again for loaning me the initial $75 before taking the bus home (yeah, we had public transportation all through the night back then) with the $1000.

What I've just described, my behavior and the system I used, is a result of the famous Monte Carlo fallacy or gambler's fallacy. The term "Monte Carlo fallacy" originates from the best known example of the phenomenon, which occurred in the Monte Carlo Casino on August 18th, 1913. The casino made millions of dollars that day, and gamblers lost millions of dollars, due to this fallacy. The gambler's fallacy is the idea that past behavior influences future behavior. This can be a good strategy because often it's true, like with getting to know a person's behavior or preferences. But this cognitive bias breaks down when applied to chance. On that fateful night in 1913, gamblers noticed that the roulette ball had fallen on black for quite a while, and when it just kept falling people got interested. They started betting on red, thinking that the ball had fallen on black so many times that it had to fall on red sooner rather than later; exactly my thoughts on that lucky day.

The ball landed on red eventually, but only after 26 spins of the wheel. Whoever bet on red at the 27th spin won of course, but at that time the casino had already cashed in millions. You see, the casino has the advantage here, not because they're cheating, not because they have a hidden magnet under the table, but simply because they deal with millions of spins and gamblers only with a few dozens of spins. If you were to flip a coin over and over again for a thousand times, the odds of it landing on heads is close to 50%. If you were to flip it a million times more, the odds would be even closer to 50%. But if you were to zoom in on the individual flips, you'd see some streaks of it landing on tails for many times in a row. That's the difference between the casino's perspective and the gambler's perspective. And we haven't even spoken about the built-in advantage for the casino, which is the fact that there are 37 numbers on the roulette wheel, not 36; there's the green zero also, which means that the chance for red or black, odd or even, high or low, is slightly less than 50%. So even if the chance of landing black 26 times in a row is around 1 to 66.6 million, the chance for either one resets with every spin and remains slightly less than 50%.

We fall for this fallacy all the time, not just in the casino or while betting. People who fly a lot, for example, often think that with every next flight the chances of them being involved in a crash goes up. Or when lightning strikes, we assume it'll never strike again in the same place. There are countless examples of us assuming that the past explains the future when there's no reason to. What makes the gambler's fallacy even easier to understand is the fact that it originates in us trusting the math too much, without really understanding it. We assume that flipping a coin carries 50/50 odds, whether we flip it 10 times, 10 thousand times or 10 million times. Unconsciously we assume that the coin, the roulette wheel or the die "remembers" how many times it's been flipped, spun or cast and what the results were, and then obeys the law of averages. That's not true, of course. So be aware of this fallacy and if you'd like to learn some more about it, watch the below linked video.

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