17th 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 1000 that he will be honourable, it would make sense for Pascal to make the deal for a 2000 times return.
Pascal responds that the probability for that high return is even lower than one in 1000. 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 1000 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, it occurs to him that the mugger's argument must have been somehow fallacious. He lacks the time to ponder exactly why, however, as the mugger once again presents him with an ultimatum. The mugger states that unless Pascal gives up his wallet, he will use his magic powers from outside the Matrix to run a Turing machine that simulates and kills 3 ↑↑↑↑ 3 people (using Knuth's up-arrow notation; describing a number that would require significantly more writing material to express in base-10 notation than there are atoms in the universe).
Pascal weighs the possibilities and comes to the conclusion that the chance of so much loss of human life far outweighs the loss of his wallet, and is about to relinquish the money, when his arm is suddenly gripped by none other than 18th-century statistician, philosopher, and Presbyterian minister Thomas Bayes, on vacation from his hometown in England. Bayes explains to Pascal that he has failed to factor in something important: the Bayesian approach to epistomology, that states that beliefs can be interpreted as subjective probabilities. Thus, they are subject to the laws of probability theory and therefore 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, that belief can actually be factored into his decision.
Pascal, convinced by Bayes, keeps his money. The mugger goes home, defeated. Bayes bids Pascal goodbye, and the latter moves on to a casino, where he escapes a series of Dutch books by remembering the lesson taught to him.