In a gambling game, a gambler wins 0.5 for each 1.0 of the bet if a coin toss is "heads," and loses 0.4 if the coin toss is "tails." So if he bets five Australian dollars, then he wins 2.5 if the coin is heads, and loses 2.0 if it is tails. Now, suppose someone plays this game repeatedly with the following strategy. He begins with a gamble of one Australian dollar. Whatever he has after this gamble (1.5 or 0.6), he bets the entire amount on a second coin toss. After this, he can have 2.25, 0.9, or 0.36, but he then bets the full amount on a third coin toss. And he does this repeatedly until N coin tosses are complete.(adsbygoogle = window.adsbygoogle || []).push({});

What is his average winning (including the one Australian dollar he began with) after N coin tosses? As N goes to infinity, what is his average winning?

What is his median winning (including the one Australian dollar he began with) after N coin tosses? As N goes to infinity, what is his median winning?

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# Can you solve this?

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