Charlie Munger, Blaise Pascal, and the psychology of misjudgment in ‘the gambler’s fallacy’

The psychology of misjudgment and the gambler's fallacy

The New Yorker recently posted a devilishly interesting piece on the myth of the hot hand in gambling. (The author, Jay Caspian Kang, writes both for the New Yorker and ESPN.com’s Grantland). This topic has received much scrutiny in the sports world (including a spate of debunking articles, followed by a more optimistic piece—don’t be too surprised if subsequent studies take a similarly non-liner explanatory path). This study is the first of its kind I’ve seen applied to gambling. Though, I have seen more evidence than I’d care to recall of the phenomenon in practice. 

A new study on the existence of a 'hot hand' in gambling is something out of a Dostoevsky novel.

This piece is rich in what Munger calls ‘the psychology of misjudgment’—right down to the commissioning body: the ‘Responsible Gambling Trust’, an organization funded by casino companies trying to find ways to prevent problem betting. You can bet that the headlines the study will generate—‘New Report: Hot Hand Real in Gambling’—will discourage very, very few problem gamblers.

The study results were staggering. It examined more than 500,000 bets taken from an online sports-gambling site too gauge the effect that previous wins and losses had on future wins and losses. Within the study, the overall winning percentage for all bets was about forty-eight percent. Isolating only winning initial bets, the study authors found that in their next bet, the winners won at a rate of forty-nine percent. That a nice, but not amazing, improvement. What happened next, though, was jarring. Players who had won consecutive bets won their third bet fifty-seven percent of the time. Now we’re talking. Winners of three straight won forth bets sixty-seven! percent of the time, and fifth bets seventy-two percent.

Taken from a pool with an overall winning percentage of 48, those results are worth noting. 

Hot hand, indeed. 

The losers lost in just as incredible pattern; fifty-three percent of bettors who lost their initial bet lost their subsequent wager. Sixty percent of those who retained the wherewithal to make another wager lost their third. Those who kept going got down to a twenty-three percent success rate after five straight losses. 

Of course, anyone who has spent more than thirty minutes in a casino is aware of this phenomenon. It’s even got a name: the gambler’s fallacy. “If you’ve ever called heads on a coin flip, seen the coin land tails up, and then called heads again because ‘heads is due,’” Kang reminds us,  “you’ve been caught up in the gambler’s fallacy.”

If you’re a gambler, no matter what you think: you’re wrong

The study found that gamblers on streaks—good or bad—acted under the influence of the gambler’s fallacy in a way that prolonged both winning and losing streaks. “Winning bettors began placing more prudent bets because they assumed their luck would soon run out. Losers began placing bets with longer odds because they wanted to win big when their luck finally, inevitably changed.” 

The study’s findings are taken right out of the Charlie Munger playbook. Streaky gamblers who win, it found, “do so because they expect to lose, and streaky gamblers who lose do so because they expect to win. Or, more simply put, when you’re losing, you’re wrong, but when you’re winning, you’re also wrong."

Learning the very first mental model

Basic mathematics is the very first mental model Munger suggests people add to their toolkit. “Obviously, you've got to be able to handle numbers and quantities ‑ basic arithmetic.”  As an investor, of course, Munger predictably thinks the “great useful model” is compound interest. Next, is the elementary math of permutations and combinations as discovered by Pascal and Fermat. Interestingly, the pair engaged in the project at the behest of friends who needed to fairly award stakes to players in card games that needed to be suspended or interrupted in the middle of a hand. 

The insight, though, that Munger provides that’s useful is knowing basic statistical probability can guide conduct in ways that will lead to outcomes that outperform the average. Sometimes significantly so. All that’s needed is acquiring and using the system for deriving probabilities that is “dramatically consonant with the way that the world works. And it's fundamental truth.” While probability isn’t that hard to learn, Munger thinks what is difficult is to “use it routinely almost everyday of your life.” 

It turns out, Munger argues, that people mostly can’t automatically use this system. “If you understand elementary psychology, the reason they can't is really quite simple: The basic neural network of the brain is there through broad genetic and cultural evolution. And it's not Fermat/Pascal. It uses a very crude, shortcut ‑ type of approximation.” While what we have by dint of natural ability contains elements of Pascal's formulae in it, what we have is a very poor substitute.

The improvements to natural ability may be fairly minor, but the effects can be outsized. “If you don't get this elementary, but mildly unnatural, mathematics of elementary probability into your repertoire, then you go through a long life like a one‑legged man in an ass‑kicking contest. You're giving a huge advantage to everybody else.

The Exceptions: Warren Buffett & Moe Norman

One of the most interesting aspects of Munger’s argument in that famous section of his talk on worldly wisdom is the argument he uses immediately following his assertion that our brains just aren’t wired to calculate probability effectively. “So you have to learn in a very usable way this very elementary math and use it routinely in life” he said. And I completely agree. But I’m not so sure I follow his next point, “just the way if you want to become a golfer, you can't use the natural swing that broad evolution gave you. You have to learn to have a certain grip and swing in a different way to realize your full potential as a golfer.”

You don’t have to have a subscription to the Golf channel or have committed the Tiger Woods swing coaching tree to memory to know that today’s golfers have swings that don’t exactly resemble any movement our prehistoric ancestors likely made. Unlike the major movements in CrossFit—like the squat, the deadlift, the overhead press, etc—that are required by anyone who wants to sit down, stand up, put anything on a shelf or pick up anything off the ground, the golf swing doesn’t look like anything survival would have required hundreds of thousands of years ago.

I’m not completely convinced by Munger’s analogy, though. I think there may be people who do have these kinds of aptitudes naturally. Munger’s partner Warren Buffett comes to mind, actually. A dear friend, mathematician Paul Fife, who recently died had that kind of ability. I never knew him until he was more than fifty years old…but if he didn’t have those kinds of abilities at birth, he’d been so good at doing that stuff for so long it was effortless and seemingly natural. Another, more pertinent example considering the topic of gambling, is Freeman Dyson, who cracked the code on a prisoner's dilemma strategy in which "one player can enforce a unilateral claim to an unfair share of rewards." 

There’s one example in golf, too, that would seem to run counter to Munger’s point. Moe Norman. He was a legendarily strange guy, with a weird swing to match. In fact, his social awkwardness was likely one of the factors that drove—and kept—him away from the professional golf tour. But his homemade swing was dead straight.
 

One of the hot hand in gambling authors remarks that, “If there’s one idea to take away from the study, it’s this: just don’t gamble.” And don’t get into a competition of closest-to-the-centerline with Moe Norman or his disciples.