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Guessing Game (Posted on 2014-05-16) Difficulty: 3 of 5
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.

No Solution Yet Submitted by tomarken    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: different part b solution (VB program) | Comment 8 of 18 |
(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 2014-05-17 16:43:29
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