Simulating a "Coin Tossing" Game

Question

i was wondering if i could simulate the following Coin-tossing-game in Mathematica:

Two Persons are playing "Coin-tossing" against each other. If one wins, he gives one Dollar to the other. Game continues until one Person has no money left.

Would appreciate your help :)

Answer 1

Let's say that both players start with 10 dollars. We can represent the game state with a list:

start = {10, 10};

Create a function which plays one round of the game. There are only two possible outcomes, we can use RandomChoice to pick randomly between them:

oneRound[{x_, y_}] := RandomChoice[{{x + 1, y - 1}, {x - 1, y + 1}}]

For example oneRound[start] will give either {9, 11} or {11, 9} with equal probability. By repeatedly applying the oneRound function to the list we can simulate the game. But we also need to stop the game when one player runs out of money. So we create another function which returns True if the game can continue and False otherwise. The condition for the game to continue is that both players have more than zero dollars:

gameContinues[{x_, y_}] := x > 0 && y > 0

To simulate a full game we need some code which starts with the list start and repeatedly applies the function oneRound as long as gameContinues returns True. As Andre suggested, we can use NestWhileList for this:

result = NestWhileList[oneRound, start, gameContinues]

{{10, 10}, {11, 9}, {12, 8}, {11, 9}, ..., {18, 2}, {19, 1}, {20, 0}}

To visualise the game:

ListLinePlot[Transpose[result], PlotLegends -> {"Player 1", "Player 2"}]