Both of these men think they are very smart, and the other isn’t.

Over the last year, I’ve chronicled why a large number of Donald Trump’s maneuvers are logically flawed. On a game theory level, they are, to use a scientific term, dumb. I’m particularly impressed with how dumb last week’s strongman attack on the Clinton Foundation is. It’s probably the dumbest.

And to be clear, I don’t mean dumb on the merits of the case. I don’t know whether there was a pay-for-play operation in the State Department or not. (I’m lying, of course. I’m sure there wasn’t, just as I’m sure Trump is just doing it because he can’t let his popular-vote loss to a woman go. But work with me.) Attorney General Jeff Sessions should abandon the probe for one obvious reason: Secretary Clinton can’t be prosecuted for anything that happened while she was at State. The statute of limitations on federal non-capital felonies is five years. She left office on February 1, 2013. Unless they can prosecute Clinton in the next 23 days for something she did specifically in January 2013, this dog won’t hunt. (I assume that’s an expression Sessions uses. I have no particular knowledge of which dogs would or would not hunt.)

But let’s charitably presume that Sessions knows that dog won’t hunt—he said it wasn’t a good idea as recently as November—and is only doing this because his boss insists on it. Sessions wants to keep his job, because it allows him to imprison and deport darker-hued people, which makes him giggle at night. So no matter whether he knows that it’s not worth it, he’s probably gotta do what Trump demands he do. So should Trump demand he do it?

Game theory unequivocally says the answer is no. Whatever the merits, the administration would be wise to “let this go,” if it wants to live out the year. But the administration doesn’t have any game theorists in it, so they’re probably not reading this article. Thus, I’m not too worried they’ll listen to me and make the smart decision to drop the case. But here’s why they should.

Many problems in game theory are built around coalitions. For each game, there’s one big group called the grand coalition, which includes all the individuals who are playing and have agreed to play by the rules. Inside that grand coalition are several smaller coalitions, called factions, each of which has its own agenda and strategies against the others. In coalition theory, it doesn’t matter much what individuals in factions do; it only matters how each faction acts as a group, and if that group has an incentive to stay together.

To achieve their goals, factions pay costs in terms of labor, political capital, and so on. Work is hard, so factions often look to merge with other factions on specific issues to reduce those costs. This assumes that the factions’ payoffs are superadditive; that is, if two factions align, their total payoff is higher than the sum of their personal payoffs. tl;dr: People have reasons to act in groups and unite their groups into bigger groups if they can agree on outcomes.

The endgame of the Mueller investigation is the potential impeachment of Donald Trump. The only way to assess the likelihood of that outcome is to look at what those factions that can affect it want. It’s a small set of factions. No matter what the voters want, no matter what the White House wants, no matter what the media wants, none of those groups have any say in whether the president gets impeached. There are only three factions, shown below, that have a say; they are the grand coalition of will-there-be-impeachment. Currently, they don’t have a strong reason to work together, so there are lots of ways the Trump regime can go through and around them.

Lots of gaps through which the Trumps can escape justice here.

Faction 1 is the evidentiary faction, formed of the FBI and the Special Prosecutor. They provide the external basis for criminal charges against the Trump family and its cronies, and for a Congressional impeachment hearing. (The Congress has an internal basis for those, which I’ll get to in a second.) What Mueller’s team and the FBI want to do is discharge their obligations to investigate. With the Trump-Russia investigation, they have a clear mandate from their supervisors, Deputy Attorney General Rod Rosenstein and FBI Director Christopher Wray, to leave no stone unturned. This is good work, and law enforcement people like to be perceived as being on the side of good.

The Clinton Foundation investigation is not good work. In 2016, the FBI consolidated its cases and concluded there was no there there, and it looks like only the howls from the president and his sycophants have stirred it up again. This is what dictators do, and what the FBI does not want to be doing. It can’t prosecute anyone, it doesn’t appear to have much evidence, and it hates being used as a political football. The FBI’s goal is to make this case go away, and there’s only one way to do that: make the president go away. I don’t believe anyone in the FBI would consciously do anything to push the Russia case a way it wouldn’t naturally go, but I do believe they’d want to accelerate it going that way. So by investigating Clinton’s foundation, the administration incentivizes Faction 1 to get further down the path toward impeachment.

Faction 2 is the Democrats in Congress. Pretty impressively for them, they haven’t broken ranks over opposing Trump. But they do have a major internal disagreement over whether calling for his impeachment is good for them. What they want is power, and one way to get it is to portray the Trump administration as the enemy of American democracy. Since the prosecution of political opponents is a hallmark of totalitarianism, this is what Democrats are saying Trump is doing with the FBI. Trump didn’t make his case any better by saying “I have the absolute right to do what I want to do with the Justice Department.” Hoo, that’s chilling, and it is very likely to tear down Democrats’ qualms about running Trump out of town.

Moreover, there are two types of Democrats in Congress. The larger group is “establishment” Democrats. They love Hillary Clinton and think it’s their job to defend her. The smaller group is the “progressive” Democrats. (I’m putting these words in quotes because they’re basically all liberals and just disagree on tactics.) The progressives don’t think much of Clinton, and would love to sweep some entrenched Democrative operatives away. The key here is that the establishment Democrats are the ones who oppose impeachment. Prosecuting Clinton makes them form a coalition for impeachment with their progressive allies, who overwhelmingly approve of it. So by investigating Clinton’s foundation, the administration incentivizes Faction 2 to get further down the path toward impeachment.

Faction 3 is the Republicans in Congress. They have tenuous majorities right now, but face a potential wave election which may bounce many of them back into the private sector. Their goal is to minimize the damage Trump will cause them in November. Naturally, impeaching a president from their own party isn’t something they want, as shown by their internal investigations into basically nothing of consequence. But it’s not like they’re saying nothing. In fact, a coven of GOP politicos are very mad at Sessions for recusing himself on Russia and not investigating Clinton… oh wait, now he is. To keep the Clinton investigation going, they’ll need to be in favor of Sessions staying.

As long as Sessions is there, he’ll have to stay away from the Russia thing, and his deputy Rosenstein has already made it clear he’s not firing Mueller. So by supporting the investigation of Clinton, they’re supporting Sessions, and by supporting Sessions, they’re supporting Mueller. Mueller will give Americans even more reason to turn the GOP out on the street. If they suffer a November bloodbath, they’ll likely turn on the president. The only way to avoid that bloodbath is to creep toward punishing Trump and his kin for the illegal acts they committed. So by investigating Clinton’s foundation, the administration incentivizes Faction 3 to get further down the path toward impeachment.

Now there are no exits through which the Trumps can escape justice.

This is extraordinarily poor tactics even for an extraordinarily poor tactician. It’s not going to work on any level: no one named Clinton is going to prison, and no one named Trump is helping themselves avoid going to prison. It’s just creating a true grand coalition working toward impeachment. The factions’ wildly different payoffs are superadditive; working together on impeachment reduces the personal cost each faction feels for getting it done. Not only is working toward impeachment easier for all factions, but it’s more likely to get done because the administration has united the grand coalition in support of that goal. Now they can all win if Trump goes.

My advice to Chairman Trump: Drop this Putinesque foray like it’s a toxic bomb. Oh right, you’re not reading this. You’re probably deep in your Wikileaked copy of Fire and Fury right now. I hear it’s a ripping good read.

This is the thirteenth installment of a series of posts on politics and game theory. It has covered impeachment, Russian collusion, white supremacy, abortion, guns, nuclear war, the national debt, the NFL, sexual harassment, the Mueller investigation, taxes, and Trump’s first year. These essays are in my book Game Theory in the Age of Chaos, which you can order by clicking the link.