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.
I came back to (finally) resolve this and post an official solution. I recall thinking that part (a) had been solved and that part (b) was still maybe up in the air.
But after rereading the comments and giving it more thought, I don't believe that Charlie & Steve's solution for part (a) is correct. That is, there is a price greater than $8.61 for which I'd be willing to play the first variant of this game.
EDIT: Not surprisingly, I now think they were right and I was wrong. I made a silly arithmetic error in one of my different approaches which led me to believe their solution could be improved.
Still TBD whether the solution to part (b) has been resolved, I'll have to work through where we left it and will hopefully get an official solution soon.
Edited on April 29, 2021, 1:31 pm
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Posted by tomarken
on 2021-04-29 11:36:45 |
Still Unsolved!
