“Drawings since hit tables in lotteries” and a new multivariate geometric distribution

In number lotteries people choose r numbers out of s. Weekly published “drawings since hit tables” indicate how many drawings have taken place since each of the s numbers was last selected as a winning number. Among many lotto players, they enhance the widespread belief that numbers should be “due” if they have not come up for a long time. Under the assumptions of independence of the drawings and equiprobability of all possible combinations, the random s-vectors Y_n, n 1, of entries in a drawings since hit table after n drawings form a Markov chain. The limit distribution of Y_n as n → ∞ is a new multivariate generalization of the geometric distribution. The determination of the distribution of the maximum entry in a drawings since hit table within the first n draws of a lottery seems to be an open problem.