1 Optimal Gambling Jonathan has a coin that may be biased, but he doesn't think so. You disagree with him though, and he challenges you to a bet. You start off with X0 dollars. You and Jonathan then play multiple rounds, and each round, you bet an amount of money of your choosing, and then coin is tossed. Jonathan will match your bet, no matter what, and if the coin comes up heads, you win and you take both yours and Jonathan's bet, and if it comes up tails, then you lose your bet. (a) Now suppose you actually secretly know that the bias of the coin is % 00? [Hintz Under this betting strategy, what happens if you ever lose a round?] ((1) The problem with the previous approach is that we were too concerned about expected value, so our gambling strategy was too extreme. Let's start over: again we will use a gambling strategy in which we bet a fraction q of our money at each round. Express X, in terms of n, q, X0, and W\