I'm faced with this problem which is a slight variation on the classic Gamblers Ruin problem:
Adam always starts with £$2$ and Bella with £$14$. At each point of the game, Adam can bet any integer amount of money £k, up to the amount of money he currently has; he then wins £$k$ with probability $0.4$ or loses £$k$ with probability $0.6$. Adam takes on a strategy where he bets £$2$ at each round – so each round he wins £$2$ with probability $0.4$ or loses £$2$ with probability $0.6$. What is Adam's probability of winning the entire game?
Anyone got any idea how one would answer something like this? I can understand how to find the probability of ruin in the classic problem through conditioning on the first step, but this added twist of being able to bet £k to double your money throws me off. Thanks in advance.
That phenomenon can't happen. Adam always bets £2, which means this is the ordinary gambler's ruin question with jumps of size 2 instead of 1.