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 Guessing Game (Posted on 2014-05-16)
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(2): different part b solution (VB program) | Comment 9 of 18 |
(In reply to re: different part b solution (VB program) by Charlie)

Charlie:

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?)?

 Posted by Steve Herman on 2014-05-17 17:08:23

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