The next labor of Hercules was the live capture of the Erymanthean Boar. This is the sort of thing that Hercules excels at. The more interesting part of the story, in some tellings, is that he got drunk with a centaur buddy, the other centaurs got angry at him for drinking their sacred wine, and he shot them with poisoned arrows. And shot Chiron, a kindly and immortal centaur, who was so tormented by the poison that he voluntarily gave up his immortality. So, Hercules kinda screwed the pooch on this one, but he did get around to capturing the boar by driving it into deep snow, and brought it back to his cousin the king, who was terrified of it. (Presumably they ate the boar)
Hercule Poirot's Erymanthean Boar is the French murderer Marrascaud, a dangerous and desperate criminal. He receives word of the criminal's planned rendezvous at the same remote Swiss chalet at which Poirot is staying, but fortunately there is a policeman already on the scene. (The person who passed the note would have recognized Poirot's mustaches anywhere!)
There are very few people staying at the chalet: an over-friendly American, a woman who visits every year, a trio of horse-racing enthusiasts (apparently at this time these people are seedy or dangerous and not hopelessly quaint), and a famous Austrian doctor. Poirot is sure that one of these is the killer Marrascaud -- but who?
The waiter reveals himself as the police officer mentioned to Poirot, and the two consult. He took the place of the old waiter, who the chalet owners were happy to get rid of as a complete incompetent. During the night, the train up to the chalet had broken down -- a suspicious accident. They are trapped with the killer, and those horse enthusiasts are surely his gang! But who is Marrascaud? And why did he choose to rendezvous here?
The investigations are cut short, however. The "waiter" is assaulted in the night, and his face cut up very badly. Poirot is also attacked, but fortunately the American, like all Americans, is carrying a pistol and rescues him from those knife-wielding Frenchmen. (... yeah...) They search the chalet, and find the body of the old waiter, stabbed and with a note on him indicating that this was Marrascaud, and this is what happens to people who cross his gang! But Poirot knows exactly who Marrascaud really is, and why he was there.
So how do you tell an effective thriller in *estimates* 5,000 words? Christie gets a bit of savings out of the fact that chasing a killer is always prime Poirot provender: no need to explain! She jumps into the action relatively quickly. She takes a mere thousand words to set the scene, including the lengthy letter from the Swiss police (pro tip: apparently learning about your case in a letter removes the need for lengthy dialog!) and introduce most of the characters. Another short section introduces the scene, the little hotel in which Poirot is staying, posing briefly as a silk merchant.
These scenes still managed to be fairly slow, but coming after the information about the killer on the loose, I think that serves the story rather than detracts: it adds a little to the tension. If the letter had come later, say after Poirot arrived at the hotel, then the long discussion of his fellow passengers on the funicular train would take on a much different cast. He would be merely people-watching (as he does in many of the novels) and the short scene would be more difficult to take, I'd have been much more likely to skim.
There is very little madness in Poirot stories. The violence is rarely senseless. Christie's killers may be passionate, but they do not kill or wound indiscriminately. When the policeman shows up with his face bandaged, I've been trained to wonder: why was he not killed? What imbecile thugs merely leave a threat cut up and not put out of the way for good? And once you think of them as rational, then why on earth would they leave a note on Marrascaud. Really, the only point of the note was to say, "Hey, the guy you're chasing is dead, stop looking!" ... and nobody really believes that.
That brings me, I think, to my real take-home lesson from the Erymanthean Boar: crazy villains are a cheat. The villains might be reckless or desperate, but they're not killers just for the sake of killing, nor can they be beyond rational acting. I am sure that there are authors out there who understand mental illness well enough to be able to actually write an insane villain, but for most of us "insane" just means "I'm going to have this guy do this, and I don't have to think up a reason because he's craaaaaaazy!"
To put it another way, in a fair mystery, whenever the reader starts to think, "That was really dumb of the killer" the reader should always be able to conclude, "I'm not getting a clear picture of what's really going on." Confusion should be an excuse for re-examination. The point of seeing the policeman's bandaged face should for the trained reader be the first point of saying that, and the point of finding the body should be the second.
And Christie does something else interesting: there's almost no time to breathe between those two points. The reader could stop and think, I suppose, but there's just a few more pages... I think that once the main clues start coming in like that in a short story, pauses are fatal. Only after it is all in place, and she's had a little opportunity to sow some doubt, does the story slow down again. And there is a somewhat satisfying length of time before the twist, which I also appreciate.
Had I been in Christie's editor's shoes, though, I'd have advised against the bit with the American and the gun. There's no reason for it, and it's such a Deus Ex Machina -- especially when Poirot boasts about having been so careful in another matter and of knowing all along certain identities. Maybe she felt bad about having gently mocked the character , but if she feels the need to have Poirot pre-emptively complain that it might have well been "a drama upon the stage" then it could have stood a rewrite. (Of course, she also disliked Poirot, so maybe she enjoyed the opportunity of having him slip up in a potentially fatal way)
Anyway, it's getting late. Next time, the Augean Stables.
Edit: I had forgotten to point out a subtle way that Christie has been fitting these stories to the originals. While the dangerous killer is very much like a wild boar, it's true, there's also an interesting parallel between Hercules catching the boar by driving it into deep snow, and Marrascaud being caught while trapped in a snow-bound Swiss hotel.
 Among other things she called him a "bore" which I had hoped was a pun and the American would turn out to be Marrascaud, but no. I would not be at all surprised to learn that in a previous draft, the American had been the villain, though.