# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

Author Message
test78
Daedalian Member

Rollercoaster
Daedalian Member

 Posted: Thu Mar 07, 2002 7:34 pm    Post subject: 2 Well, 'answering' a paradox usually raises more questions than it answers, but I'll chime in and risk the verbal beatings. In part II, I have a problem with the statement that there is a 50% chance of winning once you learn the amount in your envelope. It reminds me of the statement, "I have a 50% chance of winning the lottery this week - either I WILL or I WON'T."
tigg
Daedalian Member

 Posted: Thu Mar 07, 2002 9:14 pm    Post subject: 3 For part 1: As I understand utility theory, they draw a distinction between the value of money and the utility of money. The value of a \$10 bill is always \$10, but depending on your circumstances, that \$10 may mean a lot to you or not. In other words, if you give \$10 to Bill Gates you are wasting his time. If you give \$10 to a pauper, he can buy dinner. The same \$10 increase in wealth will have a high utility for the pauper and a low utility for Bill Gates. A utility function maps the value of money to the utility of money for a given person. The standard assumption of utility theory is that utility is a non-linear function of value. (Actuaries will tell you that this assumption is the basis for insurance companies.) In a very simple case, your utility function may be: U(v) = sqrt(v), where v is the money's value and U is utility. For example, the value of \$4 has utility 2. The value of \$16 is 4. etc. Anyway, in the question at hand we have a bet to consider. It is one thing to compute the expected value of the outcome and another to compute the expected utility. Presumably, we want to optimize the expected utility. I'll use U(v) = sqrt(v). If you don't take the bet, your expected utility is: U1 = (sqrt(X)+sqrt(Y))/2. If you do take the bet, U2 = (sqrt(X+Y)+sqrt(0))/2 Since U1 is always bigger than U2. I think you don't want the bet.
Lepton
1:41+ Arse Scratcher

 Posted: Thu Mar 07, 2002 10:59 pm    Post subject: 4 The communists are out to get me. I never take risks.
Chuck
Daedalian Member

 Posted: Thu Mar 07, 2002 11:03 pm    Post subject: 5 I think this puzzle assume that utility equals money. After seeing what I have, can I still assume that I have a 50% chance of having the larger amount?
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year by All usersChuckLeptonRollercoastertest78tigg Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum Puzzles and Games----------------Grey Labyrinth PuzzlesVisitor Submitted PuzzlesVisitor GamesMafia Games Miscellaneous----------------Off-TopicVisitor Submitted NewsScience, Art, and CulturePoll Tournaments Administration----------------Grey Labyrinth NewsFeature Requests / Site Problems
You cannot post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum