[PatrickHenry]

the "second-floor frog fallacy"

That's a good one, and it's in the same general area of fallacies, but not quite the same as "incorporating the continuum." Here's another example of -- ahem! -- my fallacy: you cut the cards, and then start dealing them out, one at a time. The resulting array has the awesome probability of one in 52 factorial, which is, more or less, one in 8.06581752 × 10⁶⁷. However, as to any one card's chances, the odds are nowhere near as great.

[tortoise]

That's a good one, and it's in the same general area of fallacies, but not quite the same as "incorporating the continuum." Here's another example of -- ahem! -- my fallacy: you cut the cards, and then start dealing them out, one at a time. The resulting array has the awesome probability of one in 52 factorial, which is, more or less, one in 8.06581752 × 1067. However, as to any one card's chances, the odds are nowhere near as great.

The phase space may be huge, but the odds of finding a winning hand are much, much better. Which winning hand does not matter.