Tilted Forum Project Discussion Community - View Single Post - Another of those crazy paradoxes (similar to Monty Hall problem)

rsl12 · 12-22-2003, 05:08 AM

Knifemissile: Sorry if I wasn't clear. Let me start by explaining the most important point I was trying to make: There are two games to consider:

Game 1: The original game, as stated in the 1st post. You are allowed to look under one of the cups.

Game 2: You are given a certain amount of money, and told that under a box, there is either 1/2 or double that amount (50/50 chance), and you can keep the amount you have already, or switch for what's in the box.

You have stated that the two games are identical, but I believe that they are completely different, because in Game 1, it makes no difference if you switch after looking, but in Game 2, you should always switch. I will prove it via a thought experiment: let's suppose there are two dummies, dummy X and dummy Y, who play Game 1 100 times. The amounts under the cups are always the same (cup A = $1 and cup B = $2, respectively, but because X and Y are dummies, they don't know any better). Dummy X plays game 1 always switching (but randomly looking at cup A or B) and dummy Y plays game 1 never switching (but randomly picking cup A or B). Who gets more money? Near as I can tell, they should both end up with about $150. So switching makes no difference in this game.

Now let's say that dummies X and Y play game 2. They are both shown $1 dollar, and the box contains either $0.50 or $2. Dummy X always switches to the money in the box and Dummy Y always keeps the $1. If both dummies play the game 100 times, dummy X should end up with about $125, while dummy Y ends up with $100. So switching makes a difference in this game.

That's why the two games are not the same, and why the logic in my original post is not correct!

telekinetic: the experiment is repeatable, as shown here.

lordbejeesus: i thought that was the answer originally too--that it has to do with the fact that the amount can't go up to infinity, but after thinking about it more, I figured the logic I used above is more satisfying an answer...

12-22-2003, 05:08 AM	#16 (permalink)
rsl12 On the lam Location: northern va	Knifemissile: Sorry if I wasn't clear. Let me start by explaining the most important point I was trying to make: There are two games to consider: Game 1: The original game, as stated in the 1st post. You are allowed to look under one of the cups. Game 2: You are given a certain amount of money, and told that under a box, there is either 1/2 or double that amount (50/50 chance), and you can keep the amount you have already, or switch for what's in the box. You have stated that the two games are identical, but I believe that they are completely different, because in Game 1, it makes no difference if you switch after looking, but in Game 2, you should always switch. I will prove it via a thought experiment: let's suppose there are two dummies, dummy X and dummy Y, who play Game 1 100 times. The amounts under the cups are always the same (cup A = $1 and cup B = $2, respectively, but because X and Y are dummies, they don't know any better). Dummy X plays game 1 always switching (but randomly looking at cup A or B) and dummy Y plays game 1 never switching (but randomly picking cup A or B). Who gets more money? Near as I can tell, they should both end up with about $150. So switching makes no difference in this game. Now let's say that dummies X and Y play game 2. They are both shown $1 dollar, and the box contains either $0.50 or $2. Dummy X always switches to the money in the box and Dummy Y always keeps the $1. If both dummies play the game 100 times, dummy X should end up with about $125, while dummy Y ends up with $100. So switching makes a difference in this game. That's why the two games are not the same, and why the logic in my original post is not correct! telekinetic: the experiment is repeatable, as shown here. lordbejeesus: i thought that was the answer originally too--that it has to do with the fact that the amount can't go up to infinity, but after thinking about it more, I figured the logic I used above is more satisfying an answer... __________________ oh baby oh baby, i like gravy. Last edited by rsl12; 12-22-2003 at 05:18 AM..