Monday night, President Obama will visit "Late Show with David Letterman" for the eighth time and -- at the risk of redundancy here -- the final time, too. "Letterman" wraps May 20, so it will be the last time for all the final guests from here on out.

But let's talk POTUS, shall we? (And for those just tuning in, I will post one of these "Daily Daves" -- a look at a single element in this singular career over the years -- up until the final farewell.)

Even though it sometimes seems otherwise, presidential visits to late night shows are relatively rare; POTUS staffs deem them somewhat risky -- late night guys do have a habit of turning their gaffs or worse into endless monologue fodder -- while the actual visit requires an armada of security that does not merely shut down traffic but whole city blocks.

Meanwhile, political seers and political pundits and apolitical TV critics have long tended to look at such visits as a reflection of a host's political persuasion. There is evidence in support of that. For example, George W. Bush was on "Tonight" as president once, and as an ex--president once. He was never on "Late Show" as president (or as ex-president either, for that matter). Bush was indeed on the show many years ago, when he was still Texas governor.

Then this: President Clinton was on "Leno" a total of zero times. That's right ... never. Reasons are murky, although former "Tonight" staffer Dave Berg wrote in his memoir of his years there that Clinton was angered by Leno's endless Monica Lewinsky jokes. (A Center for Media and Public Affairs study in 2014, on the eve of Jay's departure, actually counted 4,607 Clinton-related jokes on "Tonight," although Bush got scorched 3,239 times, for second place; I couldn't find a joke tally for Letterman.)

However, Letterman himself probably had a few hundred Lewinsky jokes over the years -- so many, in fact, that he told Barbara Walters just before she retired that the constant Lewinsky barrage was one of his bigger regrets.

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Even so, Clinton still managed a "Late Show" visit 10 times, although only once (1997) as sitting president.

Ergo, "Late Show" has greater luck with Democrats, "Tonight Show" under Leno with Republicans? Right, or maybe statistics do not tell the whole story: Monday will mark Obama's third visit as president. The president was on Jay Leno's "Tonight Show" ...  four times.