We play a game as follows:
I place one dollar on the table. I repeatedly flip a coin. Each time the coin comes up heads, I double the money on the table. The first time the coin comes up tails, you take the money and the game is over.
What's a fair admission price for the game?
Would you play the game with me for $100?
(In reply to
something missing by Cheradenine)
alright, basically what im missing here is a
construct to represent convergence. expectancy does
not cover the whole of the "behaviour" of the game.
whats missing is how fast your earnings converge
towards the calculated expectancy. i would say the
expectancy is infinite (as calculated previously) and
the convergence is controlled by the cost of entry.
in this way, the answer to the first question is
"it depends how much money you have" as mentioned
by fl. you may not have enough cash to play until
convergence sets in.
the answer to the second question is no, for all practical purposes. however, perhaps more precise
answers are possible.
re: something missing
