We can think of this problem as trying to allocate correct and incorrect guesses across possible worlds. 

For a single person, their expected probability of being correct (conditional on venturing a guess) is always 0.5 - that is, every time we allocate probability mass to them making a correct guess in some world, we must allocate the same total probability mass to them making an incorrect guess in another world.

Because of the asymmetry in our win condition, we can do better than 50/50, because we can have our winning scenarios only use one correct guess while our losing scenarios can take up three (but no more) incorrect guesses. So the best we can hope for is to have a 3:1 ratio of successful outcomes to unsuccessful outcomes - i.e., 75% odds. 

If we had more than 75% probability mass on correct worlds, we'd have more than $0.75$ weighted person-correct-guesses, which we'd need to balance out with an equal number of weighted person-incorrect-guesses - but we can only fit those into possible worlds with a density of $3$, and we'd have fewer than $0.25$ measure of possible worlds in which to do that allocation.