The American Statistician, February 1st, 1999
Using the electric network approach, we give a closed-form formula for the solution of the ruin problem in the case that the probabilities of winning a particular game depend on the amount of the current fortune.
KEY WORDS: Effective resistance: Ruin problem.
1. INTRODUCTION
The ruin problem is a classic problem of probability theory usually included in elementary textbooks (see, for instance, Feller [1967], the inspiration for many such textbooks) in the following guise: player I with an initial capital of x dollars plays a series of games against player II with a capital of n - x dollars ...
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