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The Gambler’s Ruin is a well-known problem that can be used to illustrate a variety of probability concepts.

Two players are playing a game against each other, betting the same amount on each turn (here, we use $1). On each turn of the game, Player A has a fixed probability p of winning $1 from Player B, where 0<p<1. The probability that Player B will win $1 from Player A is 1-p. Player A and Player B each start with some initial fortune (which may or may not be equal to each other), and the game continues until one player has all of the money.

The Gambler’s Ruin problem is useful for teaching conditional probability, Markov chains, and for simply visualizing a stochastic process. This app shows a graphical representation of one iteration of the Gambler’s Ruin, and also can simulate many runs under a variety of settings that may be manipulated, to obtain simulated estimates of the average length of a game, and the probability that Player A will win under those settings. In a mathematical statistics class, the simulated estimates from this app could be used to corroborate analytic solutions.

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