This is my favorite puzzle in the last issue of the Emissary, proposed by Peter Winkler.
Puzzle. Alice and Bob each have 100 dollars and a biased coin
that flips heads with probability 51%. At a signal, each begins
flipping his or her coin once per minute, and betting 1 dollar (at even
odds) on each flip. Alice bets on heads; poor Bob, on tails. As it
happens, however, both eventually go broke. Who is more likely to have
gone broke first?
Follow-up question: As above, but this time Alice and Bob are flipping the same coin (biased 51% toward heads). Again, assume both eventually go broke. Who is more likely to have gone broke first?