Wow. Old terminator. New terminator. > On Aug 10, 2023, at 12:15 PM, Stephen Guerin <stephen.gue...@simtable.com> > wrote: > > I think this might be a more concise explanation: > > Switching wins if you initially pick a goat (2/3 chance) and loses if you > pick the car (1/3 chance), so the win probability with switching is 2/3. > > _______________________________________________________________________ > stephen.gue...@simtable.com <mailto:stephen.gue...@simtable.com> > CEO, https://www.simtable.com > <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fwww.simtable.com%2f&c=E,1,EsOTR0svd8urRz5ROf6HKYh8u3AJWE1DPX-AHM04z8tjWnvzxk7BLik8UaB3B6GqmFXw7SYiwogIre-MNLFJQqlsQNRGlDbQiUTS-dUT5UuMY9tnOAkNzKE,&typo=1> > 1600 Lena St #D1, Santa Fe, NM 87505 > office: (505)995-0206 mobile: (505)577-5828 > > > On Wed, Aug 9, 2023 at 8:46 PM Nicholas Thompson <thompnicks...@gmail.com > <mailto:thompnicks...@gmail.com>> wrote: > In a moment of supreme indolence [and no small amount of arrogance] I took > on the rhetorical challenge of explaining the correct solution of the Monty > Hall problem (switch). I worked at it for several days and now I think it > is perfect. > > The Best Explanation of the Solution of the Monty Hall Problem > > Here is the standard version of the Monty Hall Problem, as laid out in > Wikipedia: > > Suppose you're on a game show, and you're given the choice of three doors: > Behind one door is a car; behind the others, goats. You pick a door, say No. > 1, and the host, who knows what's behind the doors, opens another door, say > No. 3, which has a goat. He then says to you, "Do you want to pick door No. > 2?" Is it to your advantage to switch your choice? > > This standard presentation of the problem contains some sly “intuition > traps”,[1] <x-msg://41/#m_3313630866437708646__ftn1> so put aside goats and > cars for a moment. Let’s talk about thimbles and peas. I ask you to close > your eyes, and then I put before you three thimbles, one of which hides a > pea. If you choose the one hiding a pea, you get all the gold in China. > Call the three thimbles, 1, 2, and 3. > > 1. I ask you to choose one of the thimbles. You choose 1. What is > the probability that you choose the pea. ANS: 1/3. > 2. Now, I group the thimbles as follows. I slide thimble 2 a bit > closer to thimble 3 (in a matter that would not dislodge a pea) and I declare > that thimble 1 forms one group, A, and thimble 2 and 3 another group, B. > 3. I ask you to choose whether to choose from Group A or Group B: i.e, > I am asking you to make your choice of thimble in two stages, first deciding > on a group, and then deciding which member of the group to pick. Which group > should you choose from? ANS: It doesn’t matter. If the pea is in Group A > and you choose from it, you have only one option to choose, so the > probability is 1 x 1/3. If the pea is in Group B and you choose from it, the > pea has 2/3 chance of being in the group, but you must choose only one of the > two members of the group, so your chance is again, 1/3: 2/3 x ½ = 1/3. > 4. Now, I offer to guarantee you that, if the pea is in group B, and > you choose from group B, you will choose the thimble with the pea. (Perhaps I > promise to slide the pea under whichever Group B thimble you choose, if you > pick from Group B.) Should you choose from Group A or Group B? ANS: > Group B. If you chose from Group A, and the pea is there, only one choice is > possible, so the probability is still 1 x 1/3=1/3. Now, however, if you > chose from group B, and the pea is there, since you are guaranteed to make > the right choice, the probability of getting the pea is 1 x 2/3=2/3. > 5. The effect of Monty Hall’s statement of the problem is to sort the > doors into two groups, the Selected Group containing one door and the > Unselected Group, containing two doors. When he then shows you which door > in the unselected group does not contain the car, your choice now boils down > to choosing between Group A and Group B, which, as we have known all along, > is a choice between a 1/3 and a 2/3 chance of choosing the group that > contains the pea. > > > [1] <x-msg://41/#m_3313630866437708646__ftnref1> The intuition trap has > something to do with the fact that doors, goats, and cars are difficult to > group. So, it’s harder to see that by asking you to select one door at the > beginning of the procedure, Monty has gotten you the group the doors and take > the problem in two steps. This doesn’t change the outcome, but it does > require us to keep the conditional probabilities firmly in mind. “IF the car > is in the unselected group, AND I choose from the unselected group, and I > have been guaranteed to get the car if I choose from the unselected group, > THEN, choosing from the unselected group is the better option.” > -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,7u1Fz-ktHYwOTB7KBmrJ5Qu4DoP9yFd15AP3SIkVrzNT3MGsfO1vewsJXGViOs0rHIxPWR4-BQXgAXbIq2GuTeZlZr1mMzIePX9c4RaWatdNgw,,&typo=1> > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,CPxAhk22w1RYMuDwZffZ0F5cJW9U1YPF207djtw2kK2jOVBjiCCkxIU4hoClT7g9X2_yFVQxCWf4lWspQYbYMOujmGL1u8MVSZdN1YMuFzoRnGZXhW6lq4AbeVE,&typo=1> > FRIAM-COMIC http://friam-comic.blogspot.com/ > <https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,3QD_iMFDwq3knLhXiM-tl8P4j26c-_VwTq9ZcN2ajhOevKSVJQD4_0TBv_-SGWwJ9g8X45hfVIFXIyJXbs_EH5eBfy5IeQ1nO9X46zVl0vJagU-obtnMozAx&typo=1> > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > <https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,XPJqLjYB36fSb7INuacsBElyrLzPuMlMc2I56tmNOTLvvoawr7ibWw4Vjis7SuWMnTZRgeNKlrfHnDrrvX5wzxTZYorzTspFqnNN0xkJ1OtV8C39&typo=1> > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ > <http://friam.383.s1.nabble.com/> > -. --- - / ...- .- .-.. .. -.. / -- --- .-. ... . / -.-. --- -.. . > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,02YhHjHPcGgI0prxovdSdYfyyLR2mD5RrSSyNuixpHytpRZ9fZowMYR_p1R2ylQFTiZrP2sxs4lNoh97Cq7iGeqmwE6RNTcYKc1Ux-j3lRroMw,,&typo=1 > to (un)subscribe > https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,_yUfGlNIHjwoxjj3mj9t9BgGWDHPLa_J9sojC0rrkYetrNhOduNICARp6BmHe_oLmnyUHCQQCfL0Zhu-N2Y1BWOiacMC45eEfaMn2LHqdCGdD8fZcf-AhyKr&typo=1 > FRIAM-COMIC > https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,vGKvAFpn4DeUewGXdK0MztVjUmPYNCFVOVcYMlOv-9ZdO_tjxBn2pn70sGHeC0V9w1cltjExJMsXu--KBEBpSyheyuDTKFNvqrcgx6Lw1vnh&typo=1 > archives: 5/2017 thru present > https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,A0ttM-QssVeaO6jtkMwNjNAcCB7wXtbVmA5-C6cKp4F4ysknLkSeov_LBOJTimMlMQF3muRU2mmIlBumkebxPpzWi9SsAy7BADK0K9e5cZQ9drJE2Q,,&typo=1 > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
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