Comments on: Riddle #2 http://www.philsteinmeyer.com/88/riddle-2/ Phil Steinmeyer's rumblings on the game biz, programming, and life Sat, 05 Jul 2008 16:11:50 +0000 http://wordpress.org/?v=2.5.1 By: Jeff http://www.philsteinmeyer.com/88/riddle-2/#comment-844 Jeff Wed, 03 May 2006 19:59:53 +0000 http://www.philsteinmeyer.com/88/riddle-2/#comment-844 My wallet is always empty, or filled with a single dollar. I'll take that bet :) My wallet is always empty, or filled with a single dollar. I’ll take that bet :)

]]> By: PhilSteinmeyer.com » Blog Archive » Riddle Answers http://www.philsteinmeyer.com/88/riddle-2/#comment-652 PhilSteinmeyer.com » Blog Archive » Riddle Answers Fri, 14 Apr 2006 22:15:27 +0000 http://www.philsteinmeyer.com/88/riddle-2/#comment-652 [...] Phil Steinmeyer’s rumblings on the game biz, programming, and life « Riddle #2 [...] [...] Phil Steinmeyer’s rumblings on the game biz, programming, and life « Riddle #2 [...]

]]> By: Phil Steinmeyer http://www.philsteinmeyer.com/88/riddle-2/#comment-647 Phil Steinmeyer Fri, 14 Apr 2006 04:42:33 +0000 http://www.philsteinmeyer.com/88/riddle-2/#comment-647 Certainly, in real life, for 2-A, you'd have to be much more aware of the situation (i.e. if somebody else proposed it to you, he's almost certainly got an empty or near-empty wallet). That's why I also did the 2-B variant, which gets around that objection. But it makes the paradox more clear. Assume you swap, sight unseen. Then, before opening the envelopes, you're offered the swap again (A for B this time instead of B for A). Theoretically, you'd have to take it again, and you'd be in an infinite loop (Rinse, repeat). 2-B is worded almost exactly as this wikipedia <a href="http://en.wikipedia.org/wiki/Two_envelopes_problem">entry </a>describes. Intuitively, it makes no sense to swap in 2-B, but it's tough to explain away the expected value argument (and the wiki article doesn't clear a lot up for me either). Certainly, in real life, for 2-A, you’d have to be much more aware of the situation (i.e. if somebody else proposed it to you, he’s almost certainly got an empty or near-empty wallet).

That’s why I also did the 2-B variant, which gets around that objection. But it makes the paradox more clear. Assume you swap, sight unseen. Then, before opening the envelopes, you’re offered the swap again (A for B this time instead of B for A). Theoretically, you’d have to take it again, and you’d be in an infinite loop (Rinse, repeat). 2-B is worded almost exactly as this wikipedia entry describes.

Intuitively, it makes no sense to swap in 2-B, but it’s tough to explain away the expected value argument (and the wiki article doesn’t clear a lot up for me either).

]]> By: Esteban http://www.philsteinmeyer.com/88/riddle-2/#comment-646 Esteban Fri, 14 Apr 2006 03:51:05 +0000 http://www.philsteinmeyer.com/88/riddle-2/#comment-646 Intuitively, I'd say the game has symmetrical opportunities, and being a zero-sum game it can't be fundamentally good or bad for both players. So it must be neutral; either decision is equally rational. I would decide purely on risk lust or risk aversion. In this game, you have all reasons to want a rather empty wallet yourself: bigger chance to win, no less reward, and lower penalty if you lose. Therefore, if the other guy is proposing the game you can assume his wallet is starved and the game is not worth it for you. The other guy should think the same of you. I know this doesn't debunk the expected value optimization argument. In this case, I feel this argument is more fallacious than in Riddle 1, but I can't explain why.. Intuitively, I’d say the game has symmetrical opportunities, and being a zero-sum game it can’t be fundamentally good or bad for both players. So it must be neutral; either decision is equally rational. I would decide purely on risk lust or risk aversion.

In this game, you have all reasons to want a rather empty wallet yourself: bigger chance to win, no less reward, and lower penalty if you lose. Therefore, if the other guy is proposing the game you can assume his wallet is starved and the game is not worth it for you. The other guy should think the same of you.

I know this doesn’t debunk the expected value optimization argument. In this case, I feel this argument is more fallacious than in Riddle 1, but I can’t explain why..

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