Ah, yes, he committed the Third Classic Blunder: “When death is on the line, never enter into a contest your enemy designed and prepared.”
But, he could still let her body be found at any point on the way to the frontier; it will just look like the Guilderite agents’ evil abduction-plan went south somehow and they callously disposed of her as dead weight (which would happen to be the truth, except for the names of the perpetrators). Works just as well for Florintine war-propaganda.
So why are you complaining that Vizzini doesn’t kill her at that point? Why, if you’re right about it working just as well, doesn’t he kill her after Fezzik scales the cliff?
Because that wouldn’t have been clever. Vizzini needed to have his cunning plan unfold in a way that would allow him to sit back and watch as nations danced to his tune, just killing her and abandoning the body would lack that panache that allows him to charge top rates as a manipulator. He also is very, very bad at improvising.
That still does not solve the problem of the armed & dangerous masked man who has just (Vizzini believes) killed a master swordsman and a giant wrestler, who is obviously trying either to rescue or abduct Blossom, and who will probably be angry if Vizzini frustrates him. Vizzini has to do something to give the man in black a reason not to kill him right away.
I disagree. He apparently came up, on the fly, with a plan that admittedly wasn’t very sportsmanlike but would’ve worked perfectly; Fezzik explicitly points out that he didn’t have to miss, that he did so on purpose, and that he could still kill The Man In Black now. (Heck, he likewise came up on the fly with a plan that as far as I can tell would’ve worked just fine for Inigo: “if he falls, fine; if not, the sword.” Is it really Vizzini’s fault that Inigo wasn’t on board with the “if he falls, fine” part, or that Fezzik ditched the improvised plan to instead face the other guy as God intended?)
Well, a good leader probably wouldn’t propose plans that he couldn’t get his subordinates to follow. If he worked around Inigo’s and Fezzik’s ethical liabilities as given, could he have stopped the Man in Black?
Maybe by using all three strengths against him at once, instead of one at a time. 
Vizzini’s fatal flaw is his arrogance. He did not understand what motivated his minions, and could easily have leveraged their concepts of “fair play” to convince them that the Man in Black was trying to cheat. But he could not empathize with them, nor imagine that his clever plan could possible fail.
AFAICT, yes: if he’d sent the other two ahead with her and stuck around to handle the “if he falls, fine; if not, the sword” part, it all comes down to whether the guy falls…
Actually, Vizzini is very good at understanding the thought processes of others-- That’s his whole schtick. In the book, he’s presented as being indistinguishable from telepathic. He probably figured that the other two would in fact fight fair, but incorrectly assumed that they’d win even in a fair fight. Which wasn’t unreasonable: Very, very few men could outfence Inigo, or outwrestle Fezzik.
He likewise would have won the battle of wits, if it had been the contest he thought it was. The whole “therefore I cannot choose the wine in front of me” patter wasn’t his thought process; it was his method. He was watching the Man in Black’s reactions whenever he “chose” one goblet or the other, and seeing when he was more nervous. From there, it was a trivial (for Vizzini) matter of figuring out whether the Man in Black was bluffing or not (or more precisely, whether he was running an even-order or odd-order bluff). He’s the best in the world at that game, except of course that wasn’t the game he was actually playing.
My guess is that by the time The Man in Black catches up with Vezzini, Vezzini is prepared to turn over his captive in exchange for his life and escape. He also probably wants to know TMiB’s motivation, and possibly enter into a partnership depending. When presented with the duel of wits, he accepts because it solves his problem.
The problem I have with this analysis is that Vizzini doesn’t meta-analyze the situation at all. He jumps to the conclusion that the poison is just in one goblet, despite the fact that the Man in Black never even says so and that the point of a game like this is to present a box that it’s hard to think outside of.
And he uses a “Look over there!” diversion, which most 10-year-olds would recognize as an obvious tell, and somehow thinks that he got one over on the Man in Black?
It’s very hard to get that kind of meta-analysis across in a purely visual format. It’s the kind of thing you need writing for, to show clues and details that might be lost on screen.
Even so, they make a point of showing the Man in Black becoming visibly nervous and accusing Vizzini of stalling. That’s not him sweating; that’s him appearing to sweat and give off the wrong tells. Vizzini thought he was wholly in control because the Man in Black was very good at looking like he wasn’t in control. Because Vizzini thought he was reading MiB like a book, he wasn’t being as cautious as he might otherwise have been.
Well, Vizzini does rather goad Westley into challenging him to the battle.
Also, he (Vizzini) may have faced some retribution from Prince Humperdinck if he failed to carry out the kidnapping and murder as planned. He may have figured he had more to fear from a displeased prince (soon to be king) and his army than from one man in a mask.
There are plot holes in The Princess Bride, but I don’t think this is one of them.
That’s not how I interpret the scene at all. The Man in Black is cool as a cucumber the whole way through. He keeps the same very slight smile in every shot and playfully taunting tone of voice in almost every phrase. He moves his hand around slightly, but it doesn’t look like much of a tell. He never raises his voice, and the only emotion he seems to let out is startled confusion when playing the fool against Vizzini’s lame misdirection.
Here’s the scene on Youtube for reference.
Buttercup, not Blossom.
Sure, the Man in Black is trying to look cool and collect. He’s also giving away small tells, primarily through his hand, and there are cracks in his composure when he tells Vizzini he’s stalling at 2:28 and that he’s trying to trick MiB into giving away something at 2:55.
If MiB really were cool and collect, he’d just be staring Vizzini down until asking if he was ready to choose. But by responding the way he does, he ‘shows’ nervousness under his cool facade; it’s supposed to come off as bluff and bravado. It’s all meant to lull Vizzini into thinking he has MiB by the short hairs despite MiB trying to pretend otherwise.
In other words, what you have there is a good actor playing a good actor playing a bad actor who’s trying to be a good actor and failing. 
Thank you though I think I had the movie character confused with the PowerPuff Girls.
“Have you ever heard of Plato, Aristotle, Socrates … ?”
“Yes.”
“Morons.”
I suspect some of the confusion might also be caused by a reading of the book, wherein it describes a fair bit of increasing agitation on the part of the Man in Black. Cary Elwes’ portrayal in the filmed scene is quite a bit more calm, cool, and collected than what Goldman wrote in the novel, IMO.