tag:blogger.com,1999:blog-1920088135580776574.post1862447276949011185..comments2013-10-28T08:30:20.487-07:00Comments on Ask Doctor Math: Let's Make a Deal or No Dealdrmathhttp://www.blogger.com/profile/17936175968300765200noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-1920088135580776574.post-82221411242622400742011-08-21T08:16:45.926-07:002011-08-21T08:16:45.926-07:00I don't think it matters how you get to the fi...I don't think it matters how you get to the final 2 figures, the question is out of a pool of 20 boxes, or however many it is, what are the chances that I picked the 250k box. The odds are 1 in 20, and that doesn't change. If it's 1 in 20 that I hold the main prize, and it's certainly in 1 of the boxes, then the other box has to have a 19/20 chance of being the top prize (as the chance of it being in one of them is 1/1).<br /><br />Think of it like this - if it were a 50/50 chance at 2 boxes, you would need to be able to guarantee selection of that box 50% of the time out of 20 boxes - impossible. In 19 out of 20 scenarios, either me picking 1, 2, 3 etc, I only won the 250k prize if I swap, random or with host knowledge is irrelevant.<br /><br />Something else occurred to me as well - The object of the game is not necessarily to win the 250k, but the highest amount possible. If after the game is played out, I am left with 1p and £2000, I can assume that the original pool I was selecting contains everything between those 2 figures and none of the greater amounts, and adjust the odds accordingly. If there is a 1p, a 50p, £1, £5, £10, £50, £100, £500, £1000 and £2000, and I know with 2 boxes at the end of the game that a 1p and a £2000 are left, then it must still hold that out of those 10 boxes, 9 times in 10 I will pick something other than the £2000 box. The fact that I picked the 1p isn't important – it could have been any amount that isn't equal to or below the £2000. In 9 out of 10 cases the £2k is in the other box and I only win the LARGEST AMOUNT I CAN if I swap (given the choice).<br /><br />Am I totally wrong?larchiehttp://www.blogger.com/profile/08070168281807391794noreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-51591564624843565682010-12-01T13:08:23.602-08:002010-12-01T13:08:23.602-08:00This is the best i have ever heard it explained. ...This is the best i have ever heard it explained. Ive always had a pretty good understanding of the MHP, but as I'm sure you know, it can be very difficult to explain the logic to others...I agree with anonymous that The hosts knowledge is often a fact that is left out of the set or explanation...great work, you made my day...stumbled across this while taking a break from studying for law school exams and its refreshing to think about a little math and probability instead...something that can at least appear.to make sensekevinchttp://www.blogger.com/profile/12132978833613199753noreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-7078640443535296362010-04-05T20:00:37.305-07:002010-04-05T20:00:37.305-07:00Here I thought it was just an expected value probl...Here I thought it was just an expected value problem (EV being the average value of total$/case#) and any decision made being how much variance you're willing to accept.Justinhttp://www.blogger.com/profile/12358425439025868731noreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-62564931971684897932009-03-06T15:49:00.000-08:002009-03-06T15:49:00.000-08:00I agree, Anonymous, and it's part of the reason I ...I agree, Anonymous, and it's part of the reason I wanted to write this. Probability works so well when we can deal in abstractions like "fair coin" or "balls in urns," but when you start involving people and their intentions, as usual, things get complicated. If you're interested in the philosophy, I'd recommend David Hume's <I>Enquiry concerning Human Understanding</I>.<BR/><BR/>Thanks for reading!drmathhttp://www.blogger.com/profile/17936175968300765200noreply@blogger.comtag:blogger.com,1999:blog-1920088135580776574.post-75274457147620943132009-03-06T13:40:00.000-08:002009-03-06T13:40:00.000-08:00I am not math expert, heck, i could not even pass ...I am not math expert, heck, i could not even pass advanced algebra or pre calculus. But, the reason there IS some much controversy over the MHP, is that in most of the explanations and scenarios I've seen, they don't tell you or make it clear that, "...we have the assumption that Hall knows which door has the car behind it...he has added information to the set of things we know about the game... This is why there has been controversy.Anonymousnoreply@blogger.com