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Monty Hall, Co-Creator and Host of 'Let's Make a Deal,' Dies at 96
Monty Hall, the genial host and co-creator of "Let's Make a Deal," the game show on which contestants in outlandish costumes shriek and leap at the chance to see if they will win the big prize or the booby prize behind door No. 3, died at his home in Beverly Hills, Calif., on Saturday. He was 96.
[...] "Let's Make a Deal" became such a pop-culture phenomenon that it gave birth to a well-known brain-twister in probability, called "the Monty Hall Problem." This thought experiment involves three doors, two goats and a coveted prize and leads to a counterintuitive solution.
[...] Mr. Hall had his proud moments as well. In 1973 he received a star on the Hollywood Walk of Fame. In 1988, Mr. Hall, who was born in Canada, was named to the Order of Canada by that country's government in recognition of the millions he had raised for a host of charities. In 2013 he was presented with a lifetime achievement award at the Daytime Emmys.
The Monty Hall problem:
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?
Vos Savant's response was that the contestant should switch to the other door. Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance. [...] Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong. Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating the predicted result.
Related: Get Those Brain Cells Working: The Monty Hall Problem
(Score: 2) by theluggage on Tuesday October 03 2017, @09:55PM (1 child)
Sure, but the slippery bit (that has fooled the great and the good) is getting why that hasn't changed the odds of the car being behind your door, but has changed the odds for the remaining door. The "total probability must be 1" thing proves it, but the trouble is that proving something like that is not the same as explaining something. What explained it for me was the experience of writing code to simulate it - which forces you to "depersonalise" the whole thing and think in terms of how repeated trials might work.
(Score: 2) by VLM on Wednesday October 04 2017, @07:43PM
Hmm well flip positive and negative thinking like I alluded to in another post.
I'm not saying I think there's a 1/3 chance the car is behind my door, I'm really saying there's a 2/3 chance its behind the other doors. And that pesky Monty leaked information such that "the other doors" has collapsed down from a buncha doors, down to precisely one remaining unopened unselected door. All the 2/3 is sitting on that one remaining door.
The 2/3 chance of it being behind other doors has remained constant from the first step. Its just the set of "other doors" has collapsed thanks to Monty from a buncha doors to precisely one door. That one remaining unopened unselected door owns the whole 2/3 chance subspace now, it doesn't share with multiple doors.
Its an English Language puzzle. Instead of all this "where is the car" odds, it seems clearer if we talk about "where isn't the car" odds. I've seen attempts at artificial languages from esperanto to lojban and it would be interesting to see mathematicians write a general purpose language. Well, interesting might not be the correct word. But it would be something, thats for sure.