The method of simulation, alternatively known as the Monte Carlo method, to which Sidney Benjamin drew our attention is a lazy way of solving problems that could be solved accurately but for the large number of different logical situations that have to be considered. The method traces out what actually happens if the conditions of a problem are observed and if certain unknown events are presumed to occur at random. The solution is taken to be the average of the results of all the experiments. Inevitably, however, this method gives rise to random error. Now certain actuarial problems depend on making assumptions on such things as the mortality to be expected to be experienced by a life or set of lives. It is of little consequence if random error is imposed on top of such assumptions. On the other hand the shape of the probability distributions that the random variables in the problem are to follow may be known exactly. For such a problem the introduction of random error is a blemish that should be made as small as possible. In this note one such problem will be considered. The argument will introduce the subject of balanced incomplete block designs, which, as far as the writer knows, have only once been touched on by an actuary and that over one hundred years ago. The problem is the chance that a Jackpot may be opened at the game of Poker, discussed by Redish and Ross.