Let prize X in a game be a random variable with a cumulative distribution function F, E[X] [not equal to] 0, and Var(X) < [infinity]. In a Gambler's Ruin Problem we consider the probability PF(A, B) of accumulating fortune A before losing the initial fortune B. Suppose our Gambler is to choose between different strategies with the same expected values and different variances. PF(A, B) is known to depend in general on the whole cumulative distribution function F of X. In this paper we derive an approximation which implies the following rule called A Rule of Thumb (not only) for Gamblers: if E(X) < 0 then the strategy with the greater variance is superior, while in case E[X] > 0 the strategy with the smaller variance is more favorable to the Gambler. We include some examples of applications of The Rule. Moreover we derive a general solution in the...</[infinity].>

We prove that in the case of independent and identically distributed random vectors (Xi,Yi) a class of kernel type M-estimators is universally and strongly consistent for conditional M-functionals. The term universal means that the strong consistency holds for all joint probability distributions...

In the paper we derive a closed form formula for a probability of success in a roulette-type game. The player begins the game having j chips and plays one chip at a time. In each game, he either wins w chips with probability p or loses his chip with probability 1-p. The game terminates when the...