We decide to play the following game: An integer N will be randomly selected from the interval 0 - 100, inclusive. You try to guess N. After each guess, I tell you whether N is higher or lower than your guess.
If you successfully guess the integer, you win N dollars. Each guess costs you K dollars.
For each of the variants (a) and (b) below, what is the maximum value of K for which you'd be willing to play this game? Which strategy would you use to try to maximize your winnings in the long run?
(a) Once you start a round, you must continue until you guess N exactly.
(b) You may stop playing a round if you determine that N is too small to keep paying more money to guess N exactly. The money you've already spent on guesses is lost, but you may then start a new round with a new N.
(In reply to re: different part b solution (VB program)
Color me skeptical. Maybe you've hit on a better strategy, but I am not clear what it is. Could you flesh it out a little?
If K = 13.26, what is your initial guess? 81? 82?
What is your 2nd guess if N is higher? What is your 2nd guess if N is lower (or do you just stop playing if N is lower?)?