Billy Pang
tuxedo_man at hotmail.com
Thu Aug 25 22:27:29 CDT 2005
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 :-) >> >> >> >> >> >> >> >> >No virus found in this outgoing message. >Checked by AVG Anti-Virus. >Version: 7.0.344 / Virus Database: 267.10.15/81 - Release Date: 8/24/2005 >_______________________________________________ >dba-Tech mailing list >dba-Tech at databaseadvisors.com >http://databaseadvisors.com/mailman/listinfo/dba-tech >Website: http://www.databaseadvisors.com