[JoshTriplett]

And to show how to logically work out this answer (same spoiler warning applies):

I started with a truth table as well. It's pretty easy to show that if Alice (or without loss of generality Bob) uses a fixed "always guess H" or "always guess T" strategy, that wins in two cases, but in the other two cases Bob has no way to reliably win. For instance, if Alice always guesses H, then two cases become wins:

    A B
    H H W
    H T ?
    T H W
    T T ?

But in the other two cases, Bob has the same T each time, so he doesn't have enough information to distinguish those cases, and thus he can't reliably guess correctly.

So Alice needs to use a strategy that depends on her flip. There are only two such strategies that don't trivially reduce to a constant guess: guess what you flip or guess the opposite of what you flip. Going with the former, where Alice guesses what she flips:

    A B
    H H W
    H T ?
    T H ?
    T T W

From this, clearly if Bob guesses the opposite of what he flips, someone wins in all four cases.

The only other solution is to reverse the two: Alice guesses the opposite of what she flips, and Bob guesses what he flips.

This seems like a nice warm-up for other protocols that depend on agreed-upon strategy but not a secure channel for direct communication, such as Diffie Hellman or the Socialist Millionare Problem.