Let we have N integer slots initially containing 0's and an infinite sequence of similar independent negative binomial variables wi ~ NB(l, q). Each next value from the sequence is added to the slot containing the minimal value. The question is: what is the distribution of the step number at which any of the slots exceeds given limit k?
If you ask, it's a simplified model of attack on vulnerable ("one unit lost means all die") stack of units in Freeciv game.