  We give explicit formulas for ruin probabilities in a multidimensional
Generalized Gambler's ruin problem. The generalization is best interpreted as a
game of one player against $d$ other players, allowing arbitrary winning and
losing probabilities (including ties) depending on the current fortune with
particular player. It includes many previous other generalizations as special
cases. Instead of usually utilized first-step-like analysis we involve
dualities between Markov chains. We give general procedure for solving
ruin-like problems utilizing Siegmund duality in Markov chains for partially
ordered state spaces studied recently in context of M\"obius monotonicity.
