I've spent some time reading other questions about Gambler's Ruin, but couldn't find the answer I was looking for. In most questions, it is assumed the Gambler wins \$1 or loses \$1. I'm curious how one could approach the problem with a payoff or loss that is not equal.
For example, what is the probability of ruin on a gambler who starts with \$1000.00 who wins \$41.00 with probability 0.6 and loses \$43.00 with probability 0.4? Is it possible to generalize such a solution?