Comments for machine-envy http://www.machine-envy.com/blog Thu, 20 Nov 2008 14:15:21 +0000 http://wordpress.org/?v=2.6.1 Comment on Deal Or No Deal vs Monty Hall by Jose http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54794 Jose Sun, 02 Nov 2008 06:51:32 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54794 What if in the MH situation, you were given an opportunity of choosing up one of 10 cases. Then Monty eliminated the other choices for you one at a time, knowing that he only eliminates the wrong case. Between each elimination, you are given the option of changing cases. He keeps doing this until there are only 2 cases left, should you switch? He keeps doing this until there are only 2 cases left, should you switch?]]> Comment on Deal Or No Deal vs Monty Hall by Tim http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54728 Tim Fri, 31 Oct 2008 21:36:51 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54728 Chris I will very simply show you why that logic is wrong and swapping makes no difference. You are left with two cases, one wins $1m and the other $1. Now apply all the logic you and some other have done but every time you use the words "winner" or "$1m box" exchange that with "$1 box" and you will see the error. The EXACT same logic can be applied for the path of the 1$ box. If you are in the land of backwards where $1 was actually more money than $1m then according to your logic then you should swap boxes in order to win the $1 case. They can't both be right hence the paradox. Your 2nd paragraph is also wrong. The host knowing where the winning box is is precisely what makes it different. If you have 3 boxes and only 1 wins and you pick a random box, the host will remove one of the losing boxes from play but he will never remove the winning box from play and that is where you gain the equity in swapping.
You are left with two cases, one wins $1m and the other $1. Now apply all the logic you and some other have done but every time you use the words “winner” or “$1m box” exchange that with “$1 box” and you will see the error. The EXACT same logic can be applied for the path of the 1$ box. If you are in the land of backwards where $1 was actually more money than $1m then according to your logic then you should swap boxes in order to win the $1 case. They can’t both be right hence the paradox.

Your 2nd paragraph is also wrong. The host knowing where the winning box is is precisely what makes it different.
If you have 3 boxes and only 1 wins and you pick a random box, the host will remove one of the losing boxes from play but he will never remove the winning box from play and that is where you gain the equity in swapping.]]> Comment on Deal Or No Deal vs Monty Hall by Chris Smith http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54719 Chris Smith Fri, 31 Oct 2008 18:38:48 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54719 You can't change your probability of choosing the winning box based solely on the knowledge you have obtained through the game, as your sample set doesn't change as you go, you are just seeing it. From the beginning, if there are 26 boxes from which to choose and only one winner, you have a 1/26 chance of winning. So if you are so fortunate as to have seen all of the others but one, you need to swap boxes. Even when you get to the end, you are still looking at the same initial conditions and the same sample set (the money didn't change boxes during the game), but it just happens that you have seen 24 other boxes. This idea of a non-changing sample set is why the Monty Hall problem works out as it does. It has nothing to do with the host or the fact that the host knows where the winning box is. If Howie and "The Banker" both know where the winning box is, as long as Howie can bluff it and "The Banker" makes his side offers in a standard way, the game is still "fair."
This idea of a non-changing sample set is why the Monty Hall problem works out as it does. It has nothing to do with the host or the fact that the host knows where the winning box is. If Howie and “The Banker” both know where the winning box is, as long as Howie can bluff it and “The Banker” makes his side offers in a standard way, the game is still “fair.”]]> Comment on Deal Or No Deal vs Monty Hall by Dalton http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54120 Dalton Sun, 19 Oct 2008 08:05:39 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-54120 Suppose you pick your case, and then you pick the last remaining case. Both of these have the same probability of being the top prize (1/26; US version). Do you agree? Yes, okay, then, you go on and open 24 cases. If you're lucky to never reveal the top prize, what are the probabilities of the two remaining cases? You've already agreed they're the same. What makes this different from MH is that in MH you always reach the opportunity to swap. In DoND, it's highly unlikely to get to two final cases and still have the top prize left. This could also be simulated with a Python program; you'll have to throw out a bunch of scenarios until you get to a scenario where one of the last two has the top prize. About 500 times out of 1000, you will have picked the top prize initially. import random iters = 1000 random.seed() million = 1000000 count = 0 picked = 0 while (count < iters): cases = [0.01,1,5,10,25,50,75,100,200,300,400,500,750,\ 1000,5000,10000,25000,75000,100000,200000,300000,\ 400000,500000,750000,million] random.shuffle(cases) yours = random.choice(cases) del cases[cases.index(yours)] for i in range(len(cases)-1): pick = random.choice(cases) del cases[cases.index(pick)] if yours == million or million in cases: count = count + 1 if yours == million: picked = picked + 1 print "out of %s times, your initial pick was top %s times" % (count,picked)
Yes, okay, then, you go on and open 24 cases. If you’re lucky to never reveal the top prize, what are the probabilities of the two remaining cases? You’ve already agreed they’re the same.

What makes this different from MH is that in MH you always reach the opportunity to swap. In DoND, it’s highly unlikely to get to two final cases and still have the top prize left.

This could also be simulated with a Python program; you’ll have to throw out a bunch of scenarios until you get to a scenario where one of the last two has the top prize. About 500 times out of 1000, you will have picked the top prize initially.

import random

iters = 1000
random.seed()
million = 1000000

count = 0
picked = 0

while (count < iters):
cases = [0.01,1,5,10,25,50,75,100,200,300,400,500,750,\
1000,5000,10000,25000,75000,100000,200000,300000,\
400000,500000,750000,million]
random.shuffle(cases)

yours = random.choice(cases)
del cases[cases.index(yours)]

for i in range(len(cases)-1):
pick = random.choice(cases)
del cases[cases.index(pick)]

if yours == million or million in cases:
count = count + 1
if yours == million:
picked = picked + 1

print “out of %s times, your initial pick was top %s times” % (count,picked)
]]> Comment on Automated python testing with nose and eclipse by Chaim Krause http://www.machine-envy.com/blog/2006/07/29/automated-python-testing-with-nose-and-eclipse/#comment-53843 Chaim Krause Fri, 10 Oct 2008 17:30:20 +0000 http://www.machine-envy.com/blog/?p=45#comment-53843 This is a great idea. I do all my Python development in Eclipse with Pydev and just started using nose. This will save me some time. Thanks for posting it. Comment on Deal Or No Deal vs Monty Hall by Ben Stilwell http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53499 Ben Stilwell Mon, 15 Sep 2008 16:57:53 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53499 Its a problem I began thinking about last night after watching the movie '21' which included the MH problem. In the end I wasn't sure, on the one hand the losing doors are opened on purpose and on the other they are opened randomly and luckily. Does this change probability? I basically went back and forth with my reasoning thinking it could be 50/50 or maybe 25/26(US version of the game). I had settled on that it was advantageous to switch. When you pick a case you have 1/26 chance of hitting the million and the odds of not selecting the million being 25/26. Which means that the odds of the million being in what of the ladies cases is 25/26. As cases are eliminated these odds shouldn't change. I do however understand Johns last point about the Goat having similar odds, so by tomorrow I may change my mind :p. But if you look at it as 1 car vs 25 goats, does the goat really have similar odds?
In the end I wasn’t sure, on the one hand the losing doors are opened on purpose and on the other they are opened randomly and luckily. Does this change probability? I basically went back and forth with my reasoning thinking it could be 50/50 or maybe 25/26(US version of the game).

I had settled on that it was advantageous to switch. When you pick a case you have 1/26 chance of hitting the million and the odds of not selecting the million being 25/26. Which means that the odds of the million being in what of the ladies cases is 25/26. As cases are eliminated these odds shouldn’t change.

I do however understand Johns last point about the Goat having similar odds, so by tomorrow I may change my mind :p. But if you look at it as 1 car vs 25 goats, does the goat really have similar odds?]]> Comment on Deal Or No Deal vs Monty Hall by John Langley http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53087 John Langley Thu, 28 Aug 2008 20:39:12 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53087 Thank you James Casbon. Now I'm the idiot because I thought I knew what I was talking about. I apologize for my abrasive language. I'm back to believeing it's a 50/50 split when we get down to the final two cases. In my scenario I assumed the $1 million took the path down to the final two cases. But, just as easily, the goat could have taken that path too. In the end, I am left with two cases that took a path. I don't know which scenario happened. Monty Hall knows which scenario happens. He eliminated the goat for you. So, in 21 of the examples, you are going to be presented with an ending scenario that involves $1 million and a goat. But, you really don't desirve this because on DNOD, you would have arleady eliminated the $1 million earlier. You woudl never get to a Monty Hall scenario at the end. The only time you do get to the end of having $1 million in a case and a goat int he other case is the 50/50 case. I'm not an Einstein. But, Einstein proved all of his theories through logic and reasoning. I don't like numbers because I work with them as part of my job. I know how they can get manipulated. I value companies. OMG. You just wouldn't believe the things that people do with numbers when it comes to valuing a company.... If I could delete my comment sent yesterday, I would. Not becuase I was wrong. But, because I called all of you nice people idiots.
I’m back to believeing it’s a 50/50 split when we get down to the final two cases. In my scenario I assumed the $1 million took the path down to the final two cases. But, just as easily, the goat could have taken that path too. In the end, I am left with two cases that took a path. I don’t know which scenario happened.

Monty Hall knows which scenario happens. He eliminated the goat for you. So, in 21 of the examples, you are going to be presented with an ending scenario that involves $1 million and a goat. But, you really don’t desirve this because on DNOD, you would have arleady eliminated the $1 million earlier. You woudl never get to a Monty Hall scenario at the end. The only time you do get to the end of having $1 million in a case and a goat int he other case is the 50/50 case.

I’m not an Einstein. But, Einstein proved all of his theories through logic and reasoning. I don’t like numbers because I work with them as part of my job. I know how they can get manipulated. I value companies. OMG. You just wouldn’t believe the things that people do with numbers when it comes to valuing a company….

If I could delete my comment sent yesterday, I would. Not becuase I was wrong. But, because I called all of you nice people idiots.]]> Comment on Deal Or No Deal vs Monty Hall by James Casbon http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53026 James Casbon Tue, 26 Aug 2008 10:58:30 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53026 <p>Thanks, John for your analysis, and for the show Cops ;)</p> <p>That 'pretentious' 'stupid probability math' is backed up by a simulation that requires no probability maths at all.  Have you found a flaw in that as well?</p> Thanks, John for your analysis, and for the show Cops ;)

That ‘pretentious’ ’stupid probability math’ is backed up by a simulation that requires no probability maths at all.  Have you found a flaw in that as well?

]]> Comment on Deal Or No Deal vs Monty Hall by John Langley http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53020 John Langley Tue, 26 Aug 2008 08:24:41 +0000 http://www.machine-envy.com/blog/2006/12/26/deal-or-no-deal-vs-monty-hall/#comment-53020 Hey idiots. Swap the case. Monty Hall DOES apply because you are given knowledge throughout the game - just as if Monty Hall was telling you a goat was inside of each case eliminated. It doesn't matter if Monty Hall tells you this, or if you just get lucky on DOND. The fact remains that after your choice is made, you are given knowledge that $1 million still remains. This is new knowledge. By the time you get down to the end with only two cases remaining, you KNOW that one of the cases has $1 million, and the other case does not. This knowledge could have been given to you by Monty Hall, Helen Keller, Jack Benny, or by your stupid luck. Nonetheless, you are left with two cases and one has $1 million. You know that one of them has $1 million. If the total number of cases is 22, then the odds that your case has $1 million is 1 in 22 (these are the original odds when you picked your case). The odds that the remaining case has $1 million is 21 in 22. Switch cases. The Monty Hall principle does apply. It is a completely different story if Howie did not tell you that you were left with two cases, one with $1 million and the other with something else. Pretend that you started with 22 cases and just randomly eliminated 20 cases. The big information board isn’t working, and hot chicks holding the cases never open the cases. They just sit there looking stupid and so damn hot, and they forget to open the cases to show you what you just eliminated. So, you have just eliminated 20 cases. You don’t know what you eliminated. Your thumb is up your ass and you are now left with two cases. Should you switch? You should switch only if it gives you the opportunity to walk up to the hot model holding the case. It does nothing for your odds of winning. But, hopefully you were able to get a little sniff of her perfume. Odds are you already lost the $1 million with one of your earlier eliminations anyway. You don’t know anything about the last two remaining cases. If you switch or not, the odds are still 1 in 22 that you picked $1 million. Take that stupid probability math and stick it where the sun doesn't shine. It's so pretentious. Dont' let someone confuse you with flawed logic even if they use fancy numbers. Switch cases. The Monty Hall principle does apply.
It is a completely different story if Howie did not tell you that you were left with two cases, one with $1 million and the other with something else. Pretend that you started with 22 cases and just randomly eliminated 20 cases. The big information board isn’t working, and hot chicks holding the cases never open the cases. They just sit there looking stupid and so damn hot, and they forget to open the cases to show you what you just eliminated. So, you have just eliminated 20 cases. You don’t know what you eliminated. Your thumb is up your ass and you are now left with two cases. Should you switch? You should switch only if it gives you the opportunity to walk up to the hot model holding the case. It does nothing for your odds of winning. But, hopefully you were able to get a little sniff of her perfume. Odds are you already lost the $1 million with one of your earlier eliminations anyway. You don’t know anything about the last two remaining cases. If you switch or not, the odds are still 1 in 22 that you picked $1 million.

Take that stupid probability math and stick it where the sun doesn’t shine. It’s so pretentious. Dont’ let someone confuse you with flawed logic even if they use fancy numbers.]]> Comment on Automated python testing with nose and eclipse by James Casbon http://www.machine-envy.com/blog/2006/07/29/automated-python-testing-with-nose-and-eclipse/#comment-52905 James Casbon Thu, 21 Aug 2008 08:52:42 +0000 http://www.machine-envy.com/blog/?p=45#comment-52905 Bruno: I don't think you can get the PYTHONPATH from eclipse using an external tool. But I just posted a recipe to nose-users that will allow you to use the python you configured there: ttp://groups.google.com/group/nose-users/browse_thread/thread/910b1d61933520d7 ttp://groups.google.com/group/nose-users/browse_thread/thread/910b1d61933520d7]]>