Which makes sense to me. Having said that, I Prefer to scratch my balls and watch tv.Originally Posted by Gramazeka
After careful consideration I have decided to revert to team switch.
A baccarat wager of $100, which is close to 50/50 has two possible results, you can either end up with $200 or you can end up with $0. Switching is like making this same wager, except instead of the possibility of ending up with $0 the worst case scenario is ending up with $50. Switching is definitely +EV.
If anyone wants to deal this switching game to me, I will gladly put up $101 every round to play.
This way of looking at it is like Schrodinger's cat. The second box either contains X or 2X (while the first either contains 2X or X). You can't know until you open the second box. The EV of opening a case at random and has two possible values for X. X = $50, or X=$100. The EV is always 1.5X for both envelopes but once you break the symmetry X either has a value of $50 or $100 depending on whether the envelope you opened has X or 2X in it. So the EV of the average two envelopes, 1.5X, are either $75 (if the envelope opened was contained 2X so X =$50) or $150 (if the $100 envelope contained X).
The paradox is you could have opened either envelope first. So why would always switching to the unopened envelope always be a better choice? Like I said the key to improving your chances over randomly picking one envelope is understanding the symmetry of the problem that creates the paradox is broken once you open one. Several proven solutions to improving your results over random selection are based on application of understanding that knowing what is in one envelope breaks the symmetry between the two envelopes and using that fact to increase the EV of repeated trials to more than 1.5X.
Today the solution to this problem to obtain better results than 1.5X has been proven. The key to finding a solution is to realize opening an envelope breaks the symmetry of the problem. It is ironic to the mathematician that these strategies that improve your chances over random selection in repeated trials are based on the idea that the probability you chose the smaller or larger envelope isn't 50%-50%. That opening one envelope broke the symmetry of the two envelopes and using a strategy based on what that envelope contained to decide whether that envelope has a likelihood of having the greater amount that is higher or lower than 50% would increase you expectation over randomly selecting an envelope, when a randomly selected amount was made for the smaller amount and an envelope was chosen at random. But repeated trials have shown it does. And there is more than one way to use the broken symmetry to gain an advantage.
https://phys.org/news/2009-08-strate...e-paradox.html
So, I got it wrong but so did everyone else. You might want to give me partial credit for understanding that breaking the symmetry between the envelopes gave you an advantage if you used that information right. Unfortunately I didn't use the information to an advantage and should have an EV of 1.5X using my strategy just like never switching. But if this were a casino game I spotted its weakness. In time I might have figured out an advantage strategy to beat it.
The key to making the right choice is explained by one of the guys that came up with a strategy that performs better than random in the link in my previous post:
“The apparent paradox arose before because it didn't seem to make sense that opening an envelope and seeing $10 actually tells you anything, and therefore it seemed strange that your expected value of winning is $12.50 by switching,” Abbott told PhysOrg.com. “But we resolve this by explaining it in terms of symmetry breaking. Before the envelopes are opened, the situation is symmetrical, so it doesn't matter if you switch envelopes or not. However, once you open an envelope and use Cover's strategy, you break that symmetry, and then switching envelopes helps you in the long run (with multiple plays of the game).”
https://www.researchgate.net/publica...blem_revisited
Read part #3 of this link. The applications could be of interest.
Partial credit? Who the fuck cares. What's interesting is that Mr. Perfect admits that he got it wrong. What's not Interesting is that you're justifying it by saying everyone else was wrong also.
What's annoying as hell is
1. You've broken the truce with excessive verbosity.
2. Pages and pages of useless long winded redundant commentary on a point of minutiae.
3. Nobody gives a fuck.
4. You haven't got any sense of anykind whatsoever on when to let something go. You do this time after time after time.
What truce. You badgered me to death with some imagined feud to the point that I put you on ignore a long time ago and only opened a handful of your posts when I was curious as to what you said about something. I always regretted opening your post on those occasions. By pissing me off you made me not care what you thought or read what you thought. This post is no exception. I showed the problem was beaten with an AP strategy based on the breaking of symmetry. I also showed a link that might have AP applications to those smart enough to figure out how to use it.
You see this defines exactly the way I feel about your posts. I simply put you on ignore. The who gives a fuck about this is those that are trying to spot the weakness in a game. Something as simple as breaking the symmetry of a no win game allowed you to get winning results with the right strategy.
Isn't this exactly what many posters have told you about many of your repetitive and overly long posts. When I put you on ignore you weren't even trying to post anything helpful anymore. You were just trolling for your own amusement. I really tried hard not to put you on ignore because there was a time when you made a lot of helpful posts. That time has long since past. You can bet that this exception to your being ignored is just that an exception. You can go back to your imagined feud and continue disrupting the forum.
PS: I would still use my strategy of always switching unless there was a lot of money in the envelope. It turned out that was the winning strategy. So I had the right solution but got there without the right work. That means I got the right answer but used the logic that was flawed. I don't call that being right even though it is.
I agree. Except I would say damn the paradox and trust the math as applied to what you know at each switching decision. That would say switch once only and keep what was in the unknown envelope. That is the same as your course of action.
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