You play a sequence of independent games each of which you win probability p and lose...

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You play a sequence of independent games each of which you win probability p and lose with probability q = 1-p. You start with £2k and stop when you reach £2m or £0, where 0 <k <m are integers. You have a choice of two strategies. You can either stake £1 on every game (so that you win or lose £1 depending on the outcome, as usual), or you can stake £2 on every game (so that you win or lose £2). Find the ratio of the probabilities of ending with £2m under the second strategy versus under the first strategy. For which p, k, and m is the first strategy better? And the second strategy? You play a sequence of independent games each of which you win probability p and lose with probability q = 1-p. You start with £2k and stop when you reach £2m or £0, where 0 <k <m are integers. You have a choice of two strategies. You can either stake £1 on every game (so that you win or lose £1 depending on the outcome, as usual), or you can stake £2 on every game (so that you win or lose £2). Find the ratio of the probabilities of ending with £2m under the second strategy versus under the first strategy. For which p, k, and m is the first strategy better? And the second strategy?

Answer rating: 100% (QA)

To solve this problem lets denote P1P1 Probability of ending with 2m under the first strategy stakin... View the full answer