On 12/29/2012 11:41 PM, Dan Asimov wrote:
(Sorry about my careless typing.)
OK, is the St. Petersburg paradox essentially that:
If in a coin-matching game, I use the strategy of playing until my first win, where my bet on any given play is 2^N dollars, where N is the largest integer such that I've just lost the last N matches, (with my first bet being 2^0 = 1 dollar), so that upon each win I'm guaranteed a net profit of $1 . . .
. . . then how come this doesn't guarantee me a net profit of at least $1, with probability 1, even though coin-matching would seem to be symmetrical, i.e., favoring neither player?
Because you only have a finite number of dollars to start with and to guarantee your $1 profit the expected amount you need to bet is infinite. Brent Meeker