In the most recent play in which they will eventually be dead, Hamlet’s pals Rosencrantz and Guildenstern flip a coin. A lot. It comes up heads, always heads. This surprises them. Eventually, it should come up tails. It does not. This requires Guildenstern — or maybe it’s Rosencrantz — to reexamine his faith in the law of probability. Surely they must be outside the bounds of nature if so many heads come up in a row. Only the arrival of a flip of tails could restore his faith. Yet it never comes. They are vexed.

Then again, these guys are idiots. Which brings us to the president of the United States. The Trump “administration” has been aswirl in a vortex of allegations and investigations about his campaign’s collusion with Russia. The administration’s strategy in dealing with these issues can charitably be described as “unlikely to produce positive gains.” Consider the following:

These are likely the actions of a man who believes he is guilty of a crime. But they are also incredibly stupid. If you believe you are guilty of a crime, the one thing you don’t want to do is bolster the belief that you are guilty. Yet over and over, this is what Trump does. There can be only one explanation for this: The president believes that this is a winning strategy, despite all evidence that each step so far has been a loss. And if this is true, he is like millions who believe in the gambler’s fallacy.

The gambler’s fallacy, reduced to its essence, is that if something happens a lot more or less than it should, the opposite will happen soon. This is a hopeful belief, a suggestion that the universe will balance itself out over time. But if the events are random, as in the aforementioned coin flips, they won’t necessarily balance out now. If you get 78 heads in a row, it is no more likely that you will get tails next than you will get heads.

Now, the events of the Trump team’s collusion with Russia are not random. Proof erupts on a daily basis that something did go down. But I’m not talking about the collusive events themselves here. I’m talking about the administration’s expectations of responses to its actions. Those can be treated as binary: either they do something that makes prosecution less likely or makes prosecution more likely. They keep choosing “more.”

This is because Trump believes he is due for a win. A gambler who believes in the fallacy is very likely to follow a betting strategy called the martingale. It was invented in the 1800s, and like such 19th century glitter-traps as recapitulation theory and canals on Mars, it’s complete nonsense. But it sounds good, and that’s all some people need to make very bad life choices.

When you pursue a martingale, after every loss you double your bet. That way, the theory goes, when you win you will wipe out all previous losses. Thus if you lose $100, then $200, then $400, your next bet of $800 will get you slightly ahead of the game if you win, and back to zero when you bet $100 again. At minimum, you think, you at least will never lose money.

The poorhouses are filled with people who pursue this strategy, because of two interfering problems. One is obvious: There is a house, and the house takes a cut. So your expected value (your average outcome) is to come in within the house’s cut of breaking even. That is called losing.

The other is less obvious: If you keep doubling your bet when you lose, you will eventually run out of money before you win. This is called stopping time, and it will kill you. Because you can’t win what you can’t bet. You must have unbounded wealth to win in a martingale.

Herein lies the trap for the president: He believes he has unbounded wealth. He’s sure he has the uncontested ability to pardon himself and everyone he knows, so each loss is meaningless. Only the eventual win matters. So he doubles down on a losing strategy over and over, and each step seems twice as disastrous to his case as the one before. He will keep doing things that play into the investigators’ hands—ash-canning his attorney general, pardoning his relatives, lying even when the truth is unthinkably apparent—because changing strategies is fatal to the martingale gambler.

It’s kind of odd that a casino owner like Trump acts like a gambler on tilt. But it’s going to fail him. Because the House—and the Senate—takes a cut, floating legislation that restricts his ability to veto sanctions and stops him from firing the special prosecutor and eventually doing his job at all. Each loss makes more likely the outcome that the martingale gambler fears most: he won’t be able to return to the table. That’s Trump’s daily dread. If he’s a loser when he runs out of chips to cash, then he’s a loser forever. This president doesn’t like being called a loser. Not one bit.

Of course, there’s another road available to the president. There’s a paradox related to the martingale that deals with a game of infinite expected value. Even when you have losses, your resources mean that you will eventually have a moderate positive outcome, and all will be well.

“Lazy boy”, Newsweek.

Now, you and I don’t get to deal with infinite expected value much; our lives are filled with situations where even the most positive outcomes are capped. But imagine you were president and had the near-limitless resources of the executive branch at your disposal. You could keep playing for years if you liked the game. But if you were bored and tired—if, for example, you were like a certain Lazy Boy on the cover of Newsweek—you’d walk away from the game, since the expected value of all this work isn’t interesting enough to you. Even with an infinite expected value, you’d give it up after a series of predictable and survivable downturns. Paradoxically, you’d just resign.

The president might like this theory. It’s called the St. Petersburg Paradox, and it was invented in Russia. Just like his presidency.

This was the second of a series of posts about politics and game theory. For the first post on Trump’s impeachment, go here. For the next post on Trump and white supremacy, go here. These essays are in my book Game Theory in the Age of Chaos, which you can order by clicking the link.