I fell down a Wikipedia rabbit hole tonight and discovered this gem:
It was a dark and stormy night! Blaise Pacal was walking home when he was accosted by an absent-minded mugger who had forgotten to bring his cudgel. Undeterred, the mugger makes Pascal an offer, "Give me your purse and tomorrow night I shall give you back twice as much money!"
Pascal, who isn't a complete idiot, replies, "No, you're not exactly the model of honesty, so I'm much more likely to loose my purse than I am to get anything back."
The mugger really wants Pascal's purse though. "Give me your purse and tomorrow night I shall give you back four times its worth!"
"No," replies Pascal, "You're even less likely to give me four times the value of my purse than you were to give me twice its value."
"Eight times it value tomorrow night!" Offers the mugger. "Sixteen times?" "Thirty-two?"
Some time passes and now our overly-persistent mugger is offering Pascal 1,152,921,504,606,846,976 times the value of his purse! Pascal, who has been doing his best to ignore the mugger for at least the last hour suddenly realizes that in the extremely unlikely event that the mugger honours his promise then the single silver denier that his purse actually holds will be returned as roughly 4.8 quadrillion gold Francs.
The mugger will continue doubling his offer indefinitely. At what point will the mugger make Pascal an offer that he can't refuse?
Bonus points:
It was a dark and stormy night! Blaise Pacal was walking home when he was accosted by an absent-minded mugger who had forgotten to bring his cudgel. Undeterred, the mugger makes Pascal an offer, "Give me your purse and tomorrow night I shall give you back twice as much money!"
Pascal, who isn't a complete idiot, replies, "No, you're not exactly the model of honesty, so I'm much more likely to loose my purse than I am to get anything back."
The mugger really wants Pascal's purse though. "Give me your purse and tomorrow night I shall give you back four times its worth!"
"No," replies Pascal, "You're even less likely to give me four times the value of my purse than you were to give me twice its value."
"Eight times it value tomorrow night!" Offers the mugger. "Sixteen times?" "Thirty-two?"
Some time passes and now our overly-persistent mugger is offering Pascal 1,152,921,504,606,846,976 times the value of his purse! Pascal, who has been doing his best to ignore the mugger for at least the last hour suddenly realizes that in the extremely unlikely event that the mugger honours his promise then the single silver denier that his purse actually holds will be returned as roughly 4.8 quadrillion gold Francs.
The mugger will continue doubling his offer indefinitely. At what point will the mugger make Pascal an offer that he can't refuse?
Bonus points:
Spoiler: