In the standard gambler’s ruin problem, with total stake ? and gambler’s stake ?, and the gambler’s probability of winning at each play is ?, calculate the probability of ruin in the following cases;
i)
ii)
Also find the expected duration in each case.
We are solving the standard gambler's ruin problem. --- ### Definitions: * $a$: total capital (gambler + opponent) * $k$: gambler's starting capital * $p$: probability of winning each play * $q = 1 - _______ ______ __________ _________ ____ ______ _______ ___ __________.
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In the standard gambler’s ruin problem, with total stake ? and gambler’s stake ?, and the gambler’s probability of winning at each play is ?, calculate the probability of ruin in the following cases;
i)
ii)
Also find the expected duration in each case.