For a long while, I didn’t have a television, and I truly enjoyed it; I listened to music, spent a lot of time reading, and Gordy the dog kept me occupied with keeping him occupied. Moving to Maine changed that: the house I bought basically came furnished, which was perfect for me as I was moving from the equivalent of a one-bedroom apartment, with a few hundred square feet, to a modest but still fully detached 1940 cottage, with around 1500 square feet. The prior owners, an elderly couple moving to be closer to grandkids, were making the reverse size move, so it worked out for everyone. And one of the things they left behind was a large, wall mounted television set, and thus, TV reentered my day to day life.
Since the cheapest way to get phone and internet service in the US is to bundle it with cable TV and your cellphone, that’s what I did, gaining access to 1 gigabit download speeds but also to approximately 1200 channels of television. Having lived without TV for a number of years, and before that having had only basic terrestrial service in the UK for four years and then before that living in Alberta (Canadian television is worthy of a completely different essay), but also being a proper Gen-X kid who was partially raised by a cathode ray tube, it was a bit mind-blowing, and I will admit that I lost it for awhile, surfing channels aimlessly, a bit overwhelmed for choices but also overwhelmed by how little quality was out there, and how difficult it was to find anything enjoyable to watch. My mind was being flooded with endorphins as long as the tube was on, a mechanism wired from growing up, but I wasn’t really enjoying myself – until I settled into a kind of routine, finding what I like and screening out (mostly) the rest.
I’m better at limiting myself now: evenings and weekends are all about live sports (I’ll watch pretty much any live sporting event except for fight sports), and during the morning, in the background as I get emails and work updates out of the way, I’ll watch Have Gun Will Travel, followed by a Perry Mason episode, followed by a Matlock episode, followed by In the Heat of the Night, a race-charged local police procedural from the 1980s. I don’t stream anything – I don’t subscribe to Netflix or Hulu or even HBO; the boy has Disney+ courtesy of his mother but I leave that to him – and since all of these syndicated reruns have long since stopped producing new shows, after somewhere between six and nine months, you’ve seen the entire run of each series, and you start over again. The murder mysteries are no longer at all surprising; the moral arc of Richard Boone restoring order via a high body count to the West is known in great detail.
Every now and again, though, I find something interesting. Yesterday I got up way too early – a hazard of Maine in the summer, when short nights end with sunrise just after 4am and civil twilight starting much earlier – and flipped on the television and saw an old episode of Maverick, James Garner’s first really big role and an example of what network television could do back before Norman Mailer strangled the joy out of it. Garner plays Bret Maverick, a wiseacre poker player who occasionally points a gun but rarely shoots straight, traveling across the fictional Wild West operating various levels of card sharping, each episode resulting usually in the loss and regain of his savings or the gain and subsequent loss of a small ill-deserved fortune. Maverick then leaves town at the end of the episode, and the credits roll to the playing of a jaunty western theme song – like The Littlest Hobo, but not quite as melancholy and also Maverick is James Garner and plays poker, not a German shepherd who solves mysteries.
This particular episode involved Maverick getting stuck on a jury deciding the fate of an innocent cowhand that the people of this week’s town wanted to hang, and Maverick’s sense of justice was offended. He manages to convince his fellow jurors of the injustice – and inaccuracy – of a guilty verdict, all but one. Pike, the juror in question, is convinced that the coincidences cited by the accused that he says proves his innocence are simply too outlandish, too improbable, to be simultaneously true. And Maverick then strikes upon an idea – and also figures out a way to earn back the money that had been swindled from him at the beginning of the episode to set up the whole jury thing in the first place.
Maverick says well, Pike, I think you might have too much confidence in calculating the odds of the man’s story being false. And I think I can prove to you that people shouldn’t trust their ability to calculate the odds on a linked set of events like that. Let me show you, he says, and takes out a deck of cards and gives them to Pike. Shuffle them, cut them, shuffle them again, he says; I won’t touch them, and the deck is clean, but verify that yourself.
Pike does so, and agrees the deck is clean.
Now, says Maverick, what are the odds that the first five cards I draw will be a “pat hand”, do you think? A pat hand, mind you, is five cards that do not need a draw to improve – a flush, a straight, four of a kind, and a full house.
Pike thinks a moment and says, oh, maybe 1 in 10.
And what do you think the odds of doing that again, on the next five cards?
Same again, says Pike – 1 in 10. Pike is a good businessman, his fellow jurors agree, and he’s the best with numbers in town.
So, asks Maverick, that’d be what, 1 in 100 odds that you’d do that twice in a row, right?
Pike thinks and says, yes, exactly.
So, asks Maverick, five times in a row would be, oh, 100,000 to 1, right?
Pike thinks for a moment and says he supposes so.
What do you think the odds would be to put together five pat hands out of the first 25 cards you draw? Now think, says Maverick: it’s not five in a row, just that out of those 25 cards, I can put together 5 pat hands – not in a row, but in aggregate, using all the cards?
Pike thinks for a moment; it’s not quite 100,000 to 1, he says, but I doubt you’ll be able to do it in a day’s worth of shuffling and dealing.
Great, says Maverick – that’s one way of considering the odds, a lot like you thinking about the odds of the man being innocent. But I’ll bet you that if you draw 25 cards, we’ll get those five pat hands – and if I’m right, you’ll admit that your using your odds to suppose the man into guilt (and of course a noose) are similarly wrong, and you’ll vote Not Guilty. And to make it really interesting, if you lose, I get $500. And if I lose, I’ll bow to your judgment, and we’ll all agree in the man’s guilt, and I’ll pay you $500. Deal?
Pike thinks. He asks to reshuffle the deck, worried that he’s being conned by the professional card player. But he agrees, and draws 25 cards.
Of course, Maverick wins the bet. Pike wants to find a reason for being wrong, but admits he lost, duly votes not guilty, the terrified boy escapes the gallows, and Pike reluctantly pays up.
As the episode ends, Pike asks whether Maverick what the odds were to lose that bet. Maverick said, oh, I’m not sure of the exact odds, but he tries the trick for fun and has never lost. He calls it Maverick Solitaire, now a semi-official term in probability – and the 25 card draw wins almost every time (simulations done by bored stats majors pegs the odds at 98.1% of winning on any given draw from a 52 card deck). What I was actually betting, says Maverick, was that you, Pike, were an honest and honourable businessman who would settle a bet even when he lost – and the odds on that bet, for both of us and for the accused, were very good as well.
Great episode, great story, but what made it so interesting was the obvious lesson being given not just within the story, but to the viewing audience in general, in probability, and more specifically, in our intuitional failure in being able to assess probabilities in reality and apply those to our decisions. Maverick doesn’t even try to say he’s particularly good at probability; he describes his understanding to simple repeated experiences of playing a game, which indeed is how most card players get better at card games over time. He knows enough probability to be able to spot how other people miscalculate it, but makes no claims for his own immunity to being similarly dense. As he states at the end, he wasn’t taking a particular chance, or even calculating any mathematical odds: his bet was on the integrity of his opponent, and on the likelihood he would make good when he lost a fair bet. Indeed, in so doing, he really simply acts as an advocate of human justice: he doesn’t want a young man to lose his life because of a jury’s ability to stumble blindly based on bad probability, instead of focusing on the facts.
It reminded me, interestingly, of how Mark and I originally bonded, early in our working relationship at Barclays Global Investors. I was in London and we went out for lunch, and he was on a bit of a rant about exactly this topic – how human minds seem to be wired to not understand probability – and it became a long conversation about the role of probability in markets versus the role of behaviour and the psychology of market participants. Of course, that isn’t an either-or discussion, and markets don’t consist of individuals solely reliant on intuition in calculating odds: teamwork and the evolution of readily programmable simulations allow us to overcome (or at least, become aware of) the failings we have as individuals, and human psychology is not a constant. But that’s what made for a good conversation, and our willingness to play with the ideas, listen to new ideas, challenge them in the spirit of mutual improvement instead of an ambition to win, and a ready reliance on our sense of humour (however difficult to merge American and British notions of such things) proved to be a solid foundation for a friendship which has now, with fits and starts, spanned more than two decades.
What were the odds of that happening? A teacher I knew in high school used a great phrase in these sorts of situations – “odds are slim to none and slim just left town” – and of course that’s correct, but one of the particular challenges for human beings is making sense of chains of improbable events. All events are improbable, really, when viewed in isolation; but when you chain events, certain outcomes become more likely, even as they remain elusive to direct prediction. The inability to understand that “paradox” – it isn’t really a paradox but to most people it is – that is, the paradox of apparent causality really being simply the most likely outcome out of a set of still variously probable potential outcomes, and the paradox of highly unlikely outcomes being realized not invalidating the overall trend or relative likelihood of other events in the future – sits at the heart of the crisis we seem to collectively feel exists in the 2020s.
In fact, it’s at the heart of how we observe the universe and how it seems to operate. Quantum mechanics is, really, just a highly formalised way of describing the sometimes independent, sometimes chained probabilities of events occurring at subatomic scales – that is, it’s just a highly specialised way of describing the human condition. It bothers people, physicists included, that causality appears to break down, indeed that even the directionality of time seems to break down in the formalised calculus in which we express those physical events, but it’s fascinating to me that it is so bothersome when we see the same in our own interpersonal interactions. Climate modelling has the same bother for most people: why can’t we find discrete reasons for global warming, so we can do something about them? Well, simple: because the reasons are not discrete, and changing our behaviour will change the outcome but in ways which aren’t directly predictable, even if we can make a pretty good guess. So we take actions based on the pretty good guess, the biggest action of which should be humility in the face of a global physical level of complexity that nevertheless we as humans seem to have some influence (but not control) over, and we marvel at the complexity – but instead of doing that, the species-level equivalent of going to lunch and listening and reflecting and laughing, we are bothered by it.
I think I understand the why of that bother, though, even though it speaks volumes about how immature we remain. We are afraid of leaving this life, of leaving to others our works and our memories, knowing intuitively (and we’re right on this one) that the use of our works and memories after we are gone have nothing to do with us, but only to do with the needs and fears of those who come later. Just like in markets, the probabilities and the mathematical relationships are hard to intuit, but the psychology of fear, of desire, and the ongoing simple hard work of reminding ourselves to be humble and willing to admit being wrong, is at the heart of the challenge.
Perhaps that’s the most remarkable element of the Maverick episode: at the end, Pike admits he was wrong, and buys Bret a friendly “no harm no foul” drink at the town saloon. That was no more realistic today than it would have been in 1964, when the episode was produced, or in 1875, the age in which it was set. The smart money bets on human beings refusing to admit when they are wrong – election fraud conspiracy theorists and human climate change deniers being perhaps today’s laughable but all too real object examples, but that’s just today, and even those of us who can comfortably acknowledge these obvious factors of modern life are simultaneously being wilfully or even violently ignorant of other forces to which we’ve overemphasised our lousy intuition for probability and chains of interaction.
Maverick took a chance on Pike being not just an honourable loser in a bet, but on his being willing to acknowledge that the bet revealed him to be susceptible to failure, not just on a deck of cards, but on a verdict in which a man’s life hung in the balance. Because he had a good screenwriter, and because all of it was just for play, James Garner won the bet and sold the performance. Unfortunately, the odds aren’t as good for the rest of us in real life. But being humble, and being human, requires us to draw the next card, and to make our bets, no matter what.