Two friends, David and Hamish, were discussing on the telephone whether they should play a forthcoming croquet match at David's club or at Hamish's. Hamish said that he would toss a coin and David could call. David pointed out that this required a substantial degree of mutual trust, so Hamish suggested how they might use the published results of the following night's National Lottery draw. Hamish's proposal was, in fact, unfair and this article shows why and proposes a satisfactory alternative. There is no suggestion that the alternative proposed is a sensible way to solve David and Hamish's problem, but it does take us on a route that reinforces some important lessons. In particular it illustrates some of the advantages and disadvantages of the use of simulation, a technique widely used in more difficult problems. It also emphasises once more the importance in probability of not taking claims at face value.
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