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
different part b solution (VB program) by Charlie)
BTW I've added the best initial guess to the table of values for K:
K exp. val. best
init
guess
4.00 29.72277 57
5.00 25.54455 61
6.00 21.72277 67
7.00 18.15842 69
8.00 14.63366 72
9.00 11.32673 71
10.00 8.26733 69
11.00 5.45545 76
12.00 2.89109 76
13.00 0.57426 80
14.00 1.49505 85
15.00 3.46535 85
16.00 5.43564 85
17.00 7.40594 85
18.00 9.34653 85
19.00 11.13861 85
20.00 12.77228 87

Posted by Charlie
on 20140517 16:43:29 