  This paper treats of a kind of a gambler's ruin problem, which seeks the
probability that a random walker first hits the origin at a certain time. In
addition to a usual random walk which hops either rightwards or leftwards, the
present paper introduces the `halt' that the walker does not hop with a certain
probability. The solution to the problem can be obtained exactly using a Gauss
hypergeometric function. The moment generating function of the duration is also
calculated, and a calculation technique of the moments is developed. The author
derives the long-time behavior of the ruin probability, which exhibits
power-law behavior if the walker hops to the right and left with equal
probability.
