There are many things that I love about Daniel Kahneman’s work, but here’s one that is often overlooked: even though the psychological domain Kahneman studied is called bounded rationality, and even though we most often talk about the biases and fallacies that litter human decision making, sometimes, those biases are not biases at all. There are situations where bounded rationality becomes quite rational and what seemed like a fallacy turns out to be not altogether fallacious. After all, the decision short cuts we employ evolved for a reason. At one point or another in the evolutionary history of humanity, they must have been useful.
Last week, I wrote about prospect theory and our irrational switch from being risk averse in the domain of gains to risk seeking in the domain of losses. This week, I’d like to discuss why that switch may, at times, be completely rational—that is, why we may be absolutely correct to bank the sure outcome and avoid the gamble.
Imagine for a moment that the tournament I was playing in Barcelona was a €27,000 or a €270,000 buy-in event instead of a €2,700 one, and that the bubble I was facing was for a payment of €42,000 or €420,000 instead of the actual €4,200 min-cash. Would my EV-pushing approach still be the correct one, payouts be damned?
First, there’s the mathematical, by-the-numbers answer, the answer supplied by pure rationality: the extra zeroes do not matter. I should act the same way no matter what, if it’s the EV-maximizing approach. I should favor risk over safety if the choice comes with a higher bottom line—in the hundreds of thousands or even millions of dollars.
Indeed, when I spoke with my poker mentor, Erik Seidel, about the differences in playing high roller events versus events with more attainable buy-ins, he told me that there was none. To him, it was always the same event: a poker tournament. This was multiple years ago, when I was researching The Biggest Bluff and watching him play in the $25ks, the $50ks, the $100ks and the $250ks—all buy-in levels that my brain could not even begin to comprehend. They are just chips, he told me. You absolutely cannot think of them in monetary terms. You just need to make the best decision and play the best poker you can. In fact, if I’m even considering the difference, that means I’m playing the wrong stakes. Too high. Too precious. Too much for my bankroll. If I can’t abstract myself, I’m doing something wrong.
And yet.
First, let’s talk in poker terms. There’s a concept in poker known as shot-taking. It’s exactly what it sounds like: you take a shot. This is how people move up in stakes. If they play cash, they might take a shot at a higher table, moving, say, from $2-$5 to $5-$10, to see if they can do well in a bigger game. And if they play tournaments, like I do, they might take a shot at a buy-in they would never normally play.
I still remember my first ever $100 buy-in—well, technically $125, the Aria daily. That might not sound like much, but for someone who had been playing micros online and $30 buy-ins live, it was massive. I also remember (very, very well) my first ever $1k—a $1200 event at the Wynn, as part of one of its tournament series. That one, I couldn’t even afford on my own, even though I’d been doing well in the smaller buy-in events. I sold 50% of my action – and even with that, I could only play one single bullet, no re-entries.
I still remember every moment of that day, from feeling the gravity of carrying all of that cash with me (Would people know? Would I get robbed? Who has ever heard of having so much money in one place!), to the thrill of buying in to this insane high buy-in tournament ($1200!!!!!), to how nervous I felt playing, to a bluff I made with ace-jack despite being scared (I got called; I was sad!), to my bustout long before the bubble was even on the horizon. Registration was still open, in fact! That’s how early I made my exit. I also remember how I felt at not cashing—like I’d disappointed all of the people who’d believed in me enough to give me money to play. It was a terrible feeling, much worse than I’d ever felt busting a tournament on my own dime.
Would I have sweated the bubble in either of those tournaments? You’d better believe it. I would have folded, meekly, and tried to do my absolute best to just make that cash and make it count, especially in the latter case when there were backers involved. Was I playing above my bankroll? Yup. Can you move up in stakes without making those leaps once in a while? Absolutely not.
So, would it have been rational for me to exercise caution on the bubble, for any number of reasons, psychological and economic? Actually, yes, it would have been. Because a cash would have made me more confident. It would have made me bolder, more likely to play better poker going forward. And it would have given me a bigger bankroll for the future. You move up by taking shots. Every time you take a shot, there will be an uncomfortable transition. And if you always go for broke, well…you’ll probably end up broke.
It would be a while before I tried a $1k event again – and a while still after that that I moved beyond min-cashing to actually making runs. To date, the highest buy-in event I’ve ever entered is a $25,000. I’ve done that four times—twice, by winning my entry in smaller events, and twice, by selling a hell of a lot of action. I’ve never cashed. Will I go for it if I ever find myself on the stone bubble of a $25k? Hard to know, but if I’m being honest, it’s unlikely. It will simply mean too much to me to get that first cash. Those events are well above my bankroll. Those are my shots. And I want to make them count.1
Now, let’s move away from poker. Because here’s the thing about poker: it’s a game that we choose to play. In life, you will face gambles, moments of decision between the sure thing and the higher EV thing, that you did not choose and that absolutely are not a game. Maybe they are within your so-called bankroll and maybe they aren’t. And maybe they would be life-changing—both in a positive sense, if the gamble goes your way, and in a negative sense, if it doesn’t. Real life cannot be reduced to out-of-context numbers or a multiple-choice problem in a lab study: the weightings of the choices absolutely must change to account for the circumstances at play.
Consider this. You’re faced with a choice of a sure win of $20,000—or a gamble where you’re 25% to gain $200,000 and 75% to gain nothing. The rational option is the second one, just like in classic prospect theory (except I’ve juiced up the EV of the gamble even higher; now the gamble is more than twice as attractive as the sure thing). But what if $20,000 was life-changing for you? It would get you out of debt, pay your mortgage, help your kids or what have you. Sure, it would be amazing to get $200,000. But would you really risk foregoing the life-changing amount for a risky prospect?
Now, consider this. You’re faced with a choice of a certain loss of $500—or a gamble where you’re 25% to lose $2,000 and 75% to lose nothing? You’ll notice that here, too, I’ve messed with the classic payout structure of prospect theory—in those examples, the chance of losing nothing is 25%. I’ve made the “nothing” option even more probable. But now imagine that your monthly rent is $2,000 and that a loss of $2,000 would with certainty make you unable to pay the bills—and you’ll get served with an eviction notice. Even though it’s far likelier you’d lose nothing, you absolutely can’t afford to take that risk. Is it still rational to gamble?
Of course, there are people who will say the numbers are the numbers are the numbers and everything else is just an emotional excuse. But life is not a game. Emotions are life—and while, yes, they absolutely must be taken out of decision equations when they are incidental to the decision, they can and should be incorporated when they are integral to the decision.
In the famous Iowa Gambling Task, a card game first designed to test decision making in individuals with brain damage,2 people with lesions to the ventromedial prefrontal cortex (VMF) (and, later, those with damage to the amygdala, the brain’s emotional processing center) were unable to think through the long-term consequences of gambles and ended up going broke. They did not experience fear or loss aversion at the prospect of huge losses, instead focusing only on immediate gains, and as a result, they couldn’t correctly weight the risks associated with their actions. Sure, they made more money in the immediate turn—but the huge losses soon offset those gains. Had they switched to the safer decks of cards, they never would have had the upswings they did—but they would have emerged with cash at the end of the study. Not experiencing loss aversion, not feeling the emotions of risk and uncertainty in this particular case made them less rational.
Emotions, it turns out, can be rational, viable signals that are trying to tell us something important about the decision process. Sometimes, the numbers are the numbers. And sometimes, especially when real life is in play instead of a deck of cards, the numbers become more than they are on paper, weighted with emotion that is trying to communicate vital information about a choice. They key is to figure out which emotions are essential—and which, noise that are simply excuses for irrationality. And making that determination, figuring out when to dismiss emotion and use cold hard calculus and when to take it into account, well, that’s something we can spend a lifetime figuring out.
Read Part I of this series on prospect theory here. There may be a part III…but the likelihood is uncertain ;).
I have stone bubbled $10k buy-ins in style, though. It’s never fun, but I do go for it. That’s my highest pain threshold as of now!
Thank you for writing this.
I’m an amateur player trying to improve and while I have I hit a huge downswing this summer. So recently at a small tournament I opted for some technically incorrect plays- going the min cash vs the win. I needed a cash. My brain and confidence would have suffered without and that could have had negative impacts on future play. Interestingly, I did get the min cash, yet also went on to place 4th for my biggest career cash (tiny compared to your stakes but still). In my case there was an emotionally positive +ev play and that’s what I did. Sometimes real life has to differ from gto- thanks for acknowledging that
What you described are basically boundary conditions in physics. While something may be true mathematically, ie the EV approach is correct, you don't live in a pure mathematics world. You live in a physical world, math just helps describe it. And in Physics, boundary conditions are "constraints that must be met by a quantity that varies across a space or enclosure at every point on its boundary." Clearly these situations can arise in the larger context of your life and your bank account. So the "rational" move is not always the correct move, if it can affect you in a larger sense (you go broke, etc...) Nothing irrational there, you have to place the bet inside the larger context of your life.