ECONOMIC+RIDDLES

rss url="http://data.kataweb.it/rss/quotidianilocali_homepage/trentinocorrierealpi/home?pos=1,3,4,5,6,21,22,23,70,71,72,73,74,81,82,83,90,91" link="true" description="true" number="10" enclosure="true"DUE: OCTOBER 16, 2009

 I have a game.I will flip a fair-headed coin and promise to pay anyone willing to play $10n where //n// is the number of times I flip heads in a row before I flip the first tail.I will grant the right to play this game to whoever offers me the most money for the entry fee.

 Assuming that I have the funds to make good any winnings, how much should a rational person pay me to play this game?



EV or Expected Value is the value of the winnings multiplied by the probability of winning.EV is ordinarily the amount recommended on a bet or investment.For example, if one was betting on a coin flip with a prize of $1.00, one should bet up to 50¢ because half the time you will make a $1 and the other half your will make $0.Averaging these two possibilities gives you 50¢, the maximum one should bet; any bet below 50¢ should turn a profit on average.

 This game presents a paradox, however.The EV of this game is the sum the EV for all possibilities, which equals infinity (EV = ∞).This suggests you should be willing to bet an infinite amount of money to play this game.This is not the correct answer.

 The solution is important to understanding how much one should pay now for an uncertain future benefit including how much one should pay for a stock?How much should you pay for your education?How much should you pay for a medical procedure?

If you can calculate the amount a rational person should bet to the nearest 10¢, you will receive 100 extra-credit points. If you cannot calculate the amount, but can correctly explain how you would calculate it, you will receive 20 extra-credit points.

Hint:St. Petersburg