Seventeenth century philosopher and theologian Blaise Pascal is accosted by a mugger in an alleyway in his home city of Rouen, France. The mugger, however, has forgotten his weapon. Knowing that Pascal is a man of logic, he offers him a deal: the philosopher gives him his wallet, and in exchange the mugger will return twice the amount of money tomorrow.
Pascal declines, pointing out that it is unlikely the deal will be honoured. The mugger, undeterred, continues to offer higher and higher rewards, explaining that even if it is just one chance in a thousand that he will be honourable, it would make sense for Pascal to make the deal for a two thousand times’ return. Pascal responds that the probability for that high return is even lower than one in a thousand. The mugger argues back that for any low probability to pay back a large amount of money there exists a finite amount that makes it rational to take the bet—and given human fallibility and philosophical scepticism a rational person must admit there is at least some non-zero chance that such a deal would be possible. Finally, the mugger offers Pascal a thousand quadrillion happy days of life. Convinced by the argument, Pascal gives the mugger his wallet.
The next day, Blaise Pascal goes out again, having received a significant sum of money from his father, a tax collector for the city. Unfortunately, he is immediately mugged again, by the same mugger in the same location. Realising that this makes his day quite unhappy, he begins to wish he knew of some way to convince himself not to accept yesterday’s deal. He lacks the time to dwell on the matter, however, as the mugger once again presents him with an ultimatum. The mugger states that unless Pascal gives up his wallet, he will use a ticker-tape Turing machine to simulate and kill a number of people equal to six trillion times the number of stones making up the Rouen cathedral.
Pascal weighs the possibilities and comes to the conclusion that the chance of so much loss of human life (real or otherwise) far outweighs the loss of his wallet, and is about to relinquish the money, when his arm is suddenly gripped by none other than eighteenth-century statistician, philosopher, and Presbyterian minister Thomas Bayes, on vacation from his hometown and time zone in England. Bayes explains to Pascal that he has failed to factor in his own Bayesian approach to epistomology, which allows beliefs to be interpreted as subjective probabilities. They are therefore subject to the laws of probability theory and as such act upon the norms of rationality. Since Pascal believes that the chance of the consequences of not giving the mugger the wallet coming to pass are astronomically low, low enough to actually offset the literal consequences, he’s able to rationally avoid giving money to the mugger. The defeated criminal sulks off, Bayes bids Pascal goodbye, and the latter continues on to spend his father’s money at a casino, where he effortlessly escapes a series of Dutch books.