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Alice and Bob are going to play a game, with the following rules: 1st Alice picks a probability p, 0 <= p < 0.5 2nd Bob takes any finite number of counters B. 3rd Alice takes any finite number of counters A. These happen in sequence, so Bob chooses B knowing p, and Alice chooses A knowing p and B. A series of rounds are then played. Each round, either Bob gives Alice a counter (probability p) or Alice gives Bob a counter (probability 1-p). The game terminates when one player is out of counters, and that player is the loser. Whom does this game favor?

I am helping a friend in introductory real analysis, someone please help me finish, I am stuck. Want to show that f(x)/g(x) is continuous as x goes to c given that g© is not 0. |f(x)/g(x) - f©/g©| = |1/(g(x)g©)||f(x)g©-f©g(x)| = |1/(g(x)g©)||f(x)g©-f©g(x)-f(x)g(x) + f(x)g(x)| <= |1/(g(x)g©)||f(x)||g(x)-g©| + |g(x)||f(x)- f©| Then I draw a Blank.