(The text of the problem is presented in its original form)
Ann and Bob are gambling at a casino. In each game the probability of winning a dollar is 48 percent, and the probability of losing a dollar is 52 percent.
Ann decided to play 20 games, but will stop after 2 games if she wins them both. Bob decide to play 20 games, but will stop after 10 games if he wins a least 9 out of the first 10.
What is larger: the amount of money Ann is expected to loose, or the amount of money Bob is expected to loose?
My difficulty is that the problem seems quite ambiguous as presented: does it mean that Ann will stop after the first two games if she wins, and if she loses she will play the whole 20 games even if a sequence of two wins appear again?
Same for Bob: is it only the first 10 games or the first "good sequence" appearance we are talking about here?
(The latter seems more realistic for the construction of a stopping time.)
Finally, is the game considered fair? e.g. if one bets a dollar, does he receives if he wins, or do we need to take into account the non-zero (negative) expectation when constructing the martingale?
But maybe there are some common rules for this kind of problem which I'm not familiar with.
Thanks for your help.