Game theory is a rather fun branch of mathematics that tries to predict the odds of having what you want happen, when stacked up against other rational agents. I've never studied it formally myself, but it's always intrigued me. The classic example (to me, anyway, and which I am not going to bother to explain) is that the contestant on Let's Make A Deal should always change their choice (of Doors Number One, Two, or Three) after the host reveals one of the prize packages, because doing so actually doubles the odds of getting the best prize package instead of the booby prize. Those are the sorts of puzzles it tries to figure out -- like what is the best amount of money to bet at the end of Jeopardy! (depending on how much you and your opponents have at the time). But both of those are examples with easily-quantifiable odds, which aren't always (in real life, outside of game shows) all that easy to accurately predict. So I'm using the term rather loosely here, not in a strict "figure the odds" mathematical way -- more of "gaming it out" than formal game theory. But the Biden conundrum has certainly been getting a lot of attention lately, so I thought I'd take a shot at playing the game too. Or, at the very least, outlining it in a rational fashion for everyone else to play too.

The problem, in a nutshell: Joe Biden says he's the best Democrat to beat Donald Trump in the 2024 presidential election. He might just be right about that, too -- he certainly is the only person who can provably make such a claim. He made the same claim back in 2020 and the "electability argument" certainly convinced a whole bunch of Democratic primary voters to test it out. Which worked out just fine, in the general election. So to give him the benefit of the doubt, let's say he is the best person Democrats could put up against Trump.

But what happens if Trump loses? What happens if he doesn't win the Republican nomination? Well, then you've got Joe Biden running against a Republican who is most likely: (1) not as unhinged and acerbic as Donald Trump, and (2) younger than either Trump or Biden. Perhaps even a lot younger. The big question: if this comes to pass, will Biden still be the best Democrat to carry the party's banner in 2024? Or will Biden's advanced age become a key factor that convinces swing voters to swing to the Republican side?

And yes, for the pedants out there, I am fully aware that game theory does require "rational agents" and that that term is highly debatable when it comes to Donald Trump, but for at least the simplest case of figuring out what the best course would be, it is rather immaterial whether Trump is rational or not -- the real question is: "Do the voters care?" They're the rational agents that are the unknown in this whole equation, not Trump himself (again, this is for the simplest case; it would get more complicated if you threw in: "Will Trump run a third-party campaign if he doesn't get the GOP nomination?" to mix it up).

But back to the basic conundrum. It's pretty easy to see that while you can posit that Biden himself would be the best candidate to beat Trump, he easily might not be the best candidate to beat, say, Ron DeSantis (or whichever other Republican manages to beat Trump in the primaries). A younger Democrat might have a much better shot at doing so. Which makes the conundrum almost insolvable, since Democrats won't know in advance what Trump's chances of winning the GOP nomination truly are.

Biden himself, of course, could solve this puzzle one way, by deciding not to run. Nobody knows the chances of this happening. He certainly sounds like he is confident he'll be running again, but even if he wasn't actually planning on running, he'd still project that image for as long as he thinks he can get away with it -- since once he does announce that he'll only be a one-term president, he'll instantly be called a "lame duck."

Biden never came out and promised he'd only serve one term, but he did hint at it in the 2020 campaign. He talked of being a "bridge" to a new generation of Democratic leaders. He positioned himself as a transitory president whose sole purpose was to defeat Donald Trump. This was because of his age, plain and simple. People knew he'd be the oldest president ever. But now the prospect of Trump being the GOP candidate again may have changed the picture. Biden may have been thinking when he said all of that that Trump would fade into the background and 2024 would be a wide-open contest on both sides of the aisle. So it's understandable if he makes the same case now as he made back then, to put all this another way.

But I read a speculative article today in The Atlantic which tried to make the case that it'd be a good thing for all concerned if at least one prominent Democrat jumped in the race, preferably before Biden makes his formal announcement. This -- like all such media speculation these days -- is based on polling which shows a healthy majority of Democratic voters would far prefer someone else being the standard-bearer in 2024. Biden isn't actually disliked by the base, mind you, but a lot of people do want someone else next time around (for all their various reasons).

Anyway, here's where the article started from:

There has to be one good Challenger X out there from the party's supposed "deep bench," right? Someone who is compelling, formidable, and younger than, say, 65. Someone who is not Marianne Williamson. Someone who would be unfailingly gracious to Biden and reverential of his career -- even while trying to end it.

The article then tosses a few names out, but they're really almost interchangeable to the main argument:

The big riddle is: Who? Let's assess an (extremely) hypothetical primary field. First, eliminate Vice President Kamala Harris, Secretary of Transportation Pete Buttigieg, and any other member of Biden's administration from consideration. Such an uprising against the boss would represent an irreparably disloyal and unseemly act and simply would not happen. Let's also eliminate Senator Bernie Sanders from consideration, because been there, done that (twice), and he's actually Biden's senior by a year.

Otherwise, indulge me in a bit of mentioning. Here is a hodgepodge of possible primary nuisances: Michigan Governor Gretchen Whitmer; Senator Cory Booker of New Jersey; Senator Chris Murphy of Connecticut; Senator Amy Klobuchar of Minnesota; former Representative Tim Ryan of Ohio; Representative Alexandria Ocasio-Cortez of New York; California Governor Gavin Newsom; Maryland Governor Wes Moore. This is a noncomprehensive list.

The article then ends up with a rather rosy prediction for how it'll all work out:

Challenger X could earn goodwill by campaigning with class and expressing unrelenting gratitude to Biden. She could simply nod and shrug in response to the various admonitions. Emphasize her own credentials and the grave threat posed by Trump, Florida Governor Ron DeSantis, or any other Republican. Say repeatedly that she would do whatever was necessary to help and support the president if primary voters nominated him again.

. . .

Challenger X would almost certainly receive tons of press coverage -- probably good coverage, too, given that the media are predisposed to favor maverick-y candidates who inject unforeseen conflict into the process. When the voting starts, maybe this upstart would overperform -- grabbing 35 percent or so in the early states, say. Maybe she wouldn't surpass Biden, but could still reap the good coverage, gracefully drop out, and gain an immediate advantage for 2028. Or maybe Biden would take the hint, step away on his own, and let Democrats get on with picking their next class of national leaders. To some degree, the party has been putting this off since Obama was elected.

Quite obviously, Democrats today have a strong craving for someone other than the sitting president. (Also obvious: That someone is not the current vice president.)

It's at least a plausible scenario. I'd have to admit that I'm not sure who exactly I would lay odds on actually being bold enough to run against Biden, though. Biden has done a pretty good job of straddling the ideological divides within the Democratic Party so far, so he doesn't have anyone out there who is all that angry at the course of his administration up to this point. The progressives saw what Biden proposed in his Build Back Better plan and heartily approved -- which is understandable, because it was far more progressive than the rather-tentative agenda Biden ran on. But then Joe Manchin and Kyrsten Sinema torpedoed it, so the moderate or corporatist wing of the party was happy enough with the outcome. To put it another way, there's no real Pat Buchanan or Teddy Kennedy out there so annoyed with the current president that they're going to run no matter what (caveat: as the article says, someone "who is not Marianne Williamson," of course).

Which means it'd be seen as a totally self-serving thing to do, for any Democrat to openly challenge Biden's re-election effort. But there indeed might be a few ambitious Democratic politicians who are just as eager as the base voters seem to be to see someone who is not an octogenarian lead the party ticket.

The basic problem is a gamble. Since it is impossible for Democrats to know in advance what the Republican base voters are going to do, nobody will know if Trump is going to be the nominee or not. And having someone not named Donald Trump on the GOP ticket would change the entire flavor of the race. A whole lot of "Never-Trumper" Republicans who voted for Biden might just return to the GOP fold with a different nominee.

Joe Biden is going to try to make the case that even if Trump doesn't make it (and, to keep things simple, also doesn't make a third-party bid afterwards), the Republican Party is still now the MAGA party and Trumpy to its core, therefore he will still be the best candidate to defeat "Trumpism." And he might be right about that, just like he might be right that he's the best guy to take on Trump again.

But then again, he might not be right. If the Republicans nominate someone in their 50s (or 40s, even) who isn't a fire-breathing MAGA devotee, Democrats might have a much better chance of victory with a candidate who couldn't feasibly be the grandfather of his Republican opponent. Which nobody will know until it happens. Life is full of uncertainties. The question boils down to who Democrats think will win the Republican nomination. If more Democrats think that Trump is not going to make it, then a challenger to Biden would probably have a decent chance of beating him in the primaries. If more Democratic voters think Trump's going to skate away with the nomination, then Biden might be the safest choice.

What the games theory boils down to is a choice between the worst-case scenario on either side. Would Biden running against some non-Trump candidate have a better or worse chance of winning than a non-Biden candidate running against Trump? To tell everyone the truth, while writing this I was considering the matter but couldn't come up with a great case for taking either side of that bet. A lot would depend on who the non-Biden candidate actually was, I suppose. Would Amy Klobuchar or Gretchen Whitmer have a better chance of beating Trump than Joe Biden would have of beating Ron DeSantis or Nikki Haley?

Until Democratic voters are actually presented with such a choice, it'll all remain hypothetical. The only (nominal) Democrat I've heard yet who has even toyed with flirting with a presidential bid is Senator Joe Manchin, and I know what my answer would be in that particular case. But if an actual Democrat (one who doesn't drive a Maserati, in other words) jumped in the race, a whole lot of Democratic voters -- myself included -- will indeed be gaming out which choice would be better. From where I sit, President Joe Biden has done a much better job than I expected him to do so far, so four more years of him in command would be just fine with me. But I would also have electability and age on my mind as well -- if given an actual choice.

-- Chris Weigant

Follow Chris on Twitter: @ChrisWeigant