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I once read another formulation of this problem, a PDF by Nick Bostrom: http://www.nickbostrom.com/papers/pascal.pdf. It depicts this problem as a dialogue between the mugger and the mugged, which I found more entertaining to read than the HN link, and the PDF’s description still preserves all the important attributes of the problem. If you find the HN link boring, try the PDF.

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Thanks, I enjoyed that. I suppose the one issue with the dialogue is that as the mugger increases the payoff, it would only make sense to decrease the likelihood that he delivers on the promise.

Put differently, the expected value would be P(Keeps promise|Amount of promise)*(Amount of promise). However, both of the multiplicands in that are inversely proportional.

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