[dba-Tech] The Three Doors Problem

Billy Pang tuxedo_man at hotmail.com
Fri Aug 26 01:44:24 CDT 2005


just rereading below, maybe c) should be split into two scenarios (one for 
catfish and another for pickerel); therefore, chances of winning would be 
2/4 instead of 2/3.


>From: "Billy Pang" <tuxedo_man at hotmail.com>
>Reply-To: Discussion of Hardware and Software 
>issues<dba-tech at databaseadvisors.com>
>To: dba-tech at databaseadvisors.com
>Subject: Re: [dba-Tech] The Three Doors Problem
>Date: Fri, 26 Aug 2005 03:27:29 +0000
>
>the way it was explained to me was that if you do swap doors, you double 
>your chances (on paper) of winning the grand prize.  this is based on the 
>assumption that no matter what is behind the original door you choose, the 
>game show host WILL ALWAYS pick out a non-winning door to tempt you to 
>change your mind.  if you keep this assumption, given the fact that the 
>host will never reveal the winning door, he is telling you which door does 
>not have the prize and this knowledge is worked into your probability of 
>picking the winning door.
>
>that is, there are only three possible scenarios,
>a) if you pick pickerel, he shows you catfish, if you swap, you win
>b) if you pick catfish, he shows you pickerel, if you swap, you win
>c) if you pick winning door, he shows you catfish or pickerel, if you swap, 
>you lose
>
>given this, the "swapping doors" strategy wins 2 out of 3 times.  
>therefore, if you don't know what is behind the door you first pick, your 
>best strategy is to wait for your host to give you a hint and you pick the 
>other door.
>
>Billy
>
>>From: Peter Brawley <peter.brawley at earthlink.net>
>>Reply-To: Discussion of Hardware and Software 
>>issues<dba-tech at databaseadvisors.com>
>>To: Discussion of Hardware and Software issues 
>><dba-tech at databaseadvisors.com>
>>Subject: Re: [dba-Tech] The Three Doors Problem
>>Date: Thu, 25 Aug 2005 22:03:18 -0500
>>
>>John
>>
>> >And Arthur, while your door just increased from 1 in 3 to 1 in 2, so did 
>>the
>> >other door. It matters not whether you switch or whether you stay, you 
>>have
>> >a 50/50 chance of winning. There is no particular reason to switch, but 
>>you
>> >don't affect your odds in the slightest by switching. Pick a door (of 
>>the
>> >two remaining), any door, and you have a 50/50 chance.
>>
>>You can test your theory empirically. Visit 
>>http://people.hofstra.edu/staff/steven_r_costenoble/MontyHall/MontyHall.html. 
>>Do a dozen trials of holding your choice, and a dozen of switching it. Kep 
>>a count of the number of wins with each strategy. That gives you a 2x2 
>>table. Now visit http://www.unc.edu/~preacher/fisher/fisher.htm, plug in 
>>your numbers in the little table near the bottom, and click 'Calculate'. 
>>The 'this tail' number is the probability that your numbers could have 
>>come about by chance from a scenario where the probabilities were 50-50.
>>
>>Or if you prefer, you can keep your theory :-) .
>>
>>PB
>>
>>-----
>>
>>John W. Colby wrote:
>>
>>>LOL, but the answer is screwy.  Now take the example where TWO people are
>>>choosing doors simultaneously.  The third door is shown to NOT contain 
>>>the
>>>prize.  Both people should swap by the logic of the puzzle, but one of 
>>>them
>>>is still going to lose and the other win.  Each person (door) has a 50%
>>>probability of winning.  Which one will win?  There is no way to predict 
>>>the
>>>answer, each person has a 50% probability of winning the prize.
>>>
>>>The logic SOUNDS good but is screwy.  Each door has a 1 in 3 chance of 
>>>being
>>>a winner.  Eliminate one door and each door has a 1 in 2 chance of being 
>>>a
>>>winner.  It matters not whether the third door is eliminated during the 
>>>game
>>>or before the game starts.
>>>
>>>And Arthur, while your door just increased from 1 in 3 to 1 in 2, so did 
>>>the
>>>other door.  It matters not whether you switch or whether you stay, you 
>>>have
>>>a 50/50 chance of winning.  There is no particular reason to switch, but 
>>>you
>>>don't affect your odds in the slightest by switching.  Pick a door (of 
>>>the
>>>two remaining), any door, and you have a 50/50 chance.
>>>
>>>John W. Colby
>>>www.ColbyConsulting.com
>>>
>>>Contribute your unused CPU cycles to a good cause:
>>>http://folding.stanford.edu/
>>>
>>>-----Original Message-----
>>>From: dba-tech-bounces at databaseadvisors.com
>>>[mailto:dba-tech-bounces at databaseadvisors.com] On Behalf Of Stuart 
>>>McLachlan
>>>Sent: Thursday, August 25, 2005 10:20 PM
>>>To: Discussion of Hardware and Software issues
>>>Subject: Re: [dba-Tech] The Three Doors Problem
>>>
>>>
>>>On 25 Aug 2005 at 20:04, Arthur Fuller wrote:
>>>
>>>
>>>
>>>>I am the host of a TV program and you are the guest. This is the deal: 
>>>>there are 3 doors. Behind one of them is $100 million. Behind the other 
>>>>two are a dead catfish and a dead pickerel respectively. I invite you to 
>>>>select a door. You choose any one of the three: call it x I open another 
>>>>door, and say, Had you selected door y, you would have won a dead 
>>>>catfish. Now, would you like to stick with your original choice or 
>>>>switch to the other door? Does it matter? If not, why not? If so, why 
>>>>so? There is a clear answer to this problem. Who is going to be the 
>>>>first to come up with it? Arthur
>>>>
>>>>
>>>>
>>>>
>>>
>>>Ah, the good old Monty Hall puzzle.
>>>
>>>Strictly speaking, you need to qualify it by saying "I open another door 
>>>which I know contains a dead fish and show you the contents"  If you 
>>>could open the money door by accident, it is a different situation.
>>>
>>>Anyhoo, the answers is:
>>>Yes it matters, you should swap.
>>>
>>>I won't give the reason now  'cause it's a spoiler.   I know some peole 
>>>will not agree with me and will go to great lengths to explain why I am 
>>>wrong :-)
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>
>
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>
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