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This is off topic, but when the next president takes office, all of current whitehouse.gov content will be gone and replaced, no?
I'm guessing they will do something similar to when Obama took office: http://georgewbush-whitehouse.archives.gov/
Spoiler: Bob always chooses the same as his flip, Alice always chooses the opposite of her flip. B A H H - Bob chooses heads, Win H T - Alice chooses heads, Win T H - Alice chooses tails, Win T T - Bob chooses tails, Win
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 ?
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
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.
It seems too simple to be right, but can Bob just say heads all the time, and Alice say tails all the time?
Spoiler: Bob always chooses the same as his flip, Alice always chooses the opposite of her flip. B A H H - Bob chooses heads, Win H T - Alice chooses heads, Win T H - Alice chooses tails, Win T T - Bob chooses tails, Win
Some discrete mathematicians are interested in this sort of problem, which they call "simultaneous hat guessing". There are quite a few papers, in case anyone is interested and unfamiliar with this sort of thing. Another fun problem, probably better known, is sequential hat guessing: take 100 people in a line, arranged so that each person can see everyone in front of them, but no-one can see any of the people behind…
Usually problems on "countable" structures need only finite memory (to process infinite streaming input), so this problem is rather misleading.
Earlier quoted context omitted.
I'm guessing they will do something similar to when Obama took office: http://georgewbush-whitehouse.archives.gov/
Very clever. So I'm assuming they just don't write any links that involve using the full domain. (i.e. /somepage instead of http://www.whitehouse.gov/somepage )