Since it is not mentioned that they can or cannot change their strategy in the middle of the game, I will assume they decide a strategy at the very beginning and sticking with that until the game decided. So It is like there are two machines, and two computer guy put a code how they play and they see who wins:
First of all, we know that two random numbers are generated, so the outcome probabilities is actually known. And if a random number is below $.5$, the other number's probability to have bigger is $75\%$. below $.6$, the other number's probability to have bigger is $60\%$. Even if the random number generated between $.4$ and $.5$ is outcome, the other number's probability to have bigger than that is around $55\%$. Therefore Vizzini knows that if he gets a lower number he is supposed to change it with Inigo.
So Vizini's strategy should be
If Vizini gets bigger than $.5$ stay on that number, if he gets lower or equal to $.5$, change his number.
Inigo also knows this information, so he needs to think a way to win over this. There are some possible way to fight over this:
If he gets two higher number than $.5$, give the lower one, so Vizzini will need to stay his number to increase his chance to win.
If he gets two lower number than $.5$, give the lower one, so Vizzini will need to change this time and Inigo will win.
Other than that
If one is lower than $.5$ and the other is bigger than $.5$. Inigo has no chance if Vizzini will play the strategy that I have mentioned. Even Vizzini sees this strategy of Inigo he will not be sure if two numbers are both lower than $.5$ or higher than $.5$ or one higher one lower and he will need to stick with his strategy.
As a result of these strategies:
Their win chance becomes 50-50, and noone is in favor since getting one lower than $.5$ and the other one bigger than $.5$ is equal to both numbers less than $.5$ and/or both numbers higher than $.5$. Though Vizzini can increase his chance a bit if he stays after getting between $.4$ to $.5$, or change after getting between $.5$ and $.6$. But Inigo can also see this strategy and change his strategy accordingly, then Vizzini can go back to the original methodology, but in the long run, this will not change the actual result. But in the short run, Vizzini will have a slight higher chance to win.