HELLSTAR_trek
12-10-2006, 03:34 PM
There's an entry fee and it may be very high. There are two equally likely events and only one occurs. If event #1A occurs then you get a ten dollar prize and the game ends. If event #1A doesn't occur, then there are another two equally likely events (#2A and #2B), independent of the first two, and only one of them occurs. If event #2A occurs then you get a twenty dollar prize and the game ends. The prize keeps doubling until it is won.
The paradox is associated with the calculation of the so-called "expected value" of the game. "Expected value" is a simple, but technical concept. For example, if you buy a lottery ticket then you actually expect to lose what you paid and win nothing. However, the "expected value" of a lottery ticket is calculated by multiplying each prize by the probability of winning it and then adding those values. Thus, if a lottery did not produce any profits for the organization conducting it and if the organization had some source of money other than money paid by ticket purchasers and if the organization used that money to pay all costs other than the prize money (e.g. costs: advertising, producing tickets, drawing winning numbers, office space, wages of employees, etc.), then the expected value of a lottery ticket would be the price of the ticket (excluding any retail sales taxes).
Of course, you are guaranteed to win at least ten dollars. How much would you be willing to pay to play the game?
The paradox is associated with the calculation of the so-called "expected value" of the game. "Expected value" is a simple, but technical concept. For example, if you buy a lottery ticket then you actually expect to lose what you paid and win nothing. However, the "expected value" of a lottery ticket is calculated by multiplying each prize by the probability of winning it and then adding those values. Thus, if a lottery did not produce any profits for the organization conducting it and if the organization had some source of money other than money paid by ticket purchasers and if the organization used that money to pay all costs other than the prize money (e.g. costs: advertising, producing tickets, drawing winning numbers, office space, wages of employees, etc.), then the expected value of a lottery ticket would be the price of the ticket (excluding any retail sales taxes).
Of course, you are guaranteed to win at least ten dollars. How much would you be willing to pay to play the game?