I have a homework project. I need to analyse a gambler's ruin where there are 6 possible outcomes of every wager with corresponding probabilities and payoffs and the gambler may vary the wager (say only 4 values). Am I correct in thinking the gambler's wealth (say 0 to 200 starting at 100) is a 2D random walk with unequal steps. The state space having bankroll on one axis and wager value on the other with bankroll increment determined by outcome, payoff and wager. I can easily simulate this in Excel (or Mathematica) but that won't provide the necessary ruin insight. I could do repeated simulations in Excel stopping at ruin and then derive an empirical PDF of ruin. Mathematica seems to have only 1D RW with equal steps
Here you have a boilerplate for coding the simulation. I've filled each function with a "reasonable random" behavior for a betting game that follows your experiment description. You should customize them to fit better your simulation needs.
I can't infer from your question what are the random vars for your PDF, but the outcome from the function lets you get (I think) any statistic you may want:
The "states space" random walk you mentioned in the question:
The same, viewed as a time-evolution process:
The evolution of the bank roll: