Gambler's ruin probability - a general formula
Guy Katriel
TL;DR
This paper derives a comprehensive formula for calculating the probability of ruin in gambler's ruin scenarios involving arbitrary integer-valued payoff distributions against an infinitely-rich opponent.
Contribution
It provides a general explicit formula for gambler's ruin probability applicable to a wide range of payoff distributions, extending classical results.
Findings
Derived a universal formula for ruin probability
Applicable to any integer-valued payoff distribution
Enhances understanding of gambler's ruin dynamics
Abstract
We derive an explicit formula for the probability of ruin of a gambler playing against an infinitely-rich adversary, when the games have payoff given by a general integer-valued probability distribution.
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