I would like to simulate the evolution of a bankroll of a 2 player game where you have the probability of winning p. If a player wins, the bankroll grows by 1 unit minus a fee that each player pays, let's say the fee is r. So, when a player wins a game the bankroll grows by 1-2*r, since each player pays the fee. If a player loses the game obviously the bankroll diminishes by 1 unit.
In the example below p=0.517 and the fee is such that the player wins 0.959 units. When I generate the plot I am surprised to see that the line decreases while I would expect that it would increase. Am I generating the NestList incorrectly? Thanks.
RandomWalk[n_] := NestList[(# + If[RandomReal >= 0.517, 0.959, -1]) &, 0, n] ListPlot[RandomWalk, Joined -> True