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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 VLM on Monday October 02 2017, @06:29PM (4 children)
Sorry sir, no.
Your first guess is 1 in 3.
Then monty releases the very important data point that one door is definitely not the right door, and you're not allowed to change to that door. There was a 2/3 chance it was one of the other two doors and by opening one that definitely is not, that means 2/3 chance collapses into one remaining door.
This relates to your final choice being 1 out of 2, not 3. You can't select the door that monty opened and showed was empty.
How bout you flip it. negative going logic instead of positive going logic... Your first choice is not 1/3 of yes but you're really saying its 2/3 of no. There's a 1/3 chance that both of the remaining doors put together are "no" and that is the same as saying a 2/3 chance that one of the other doors is yes. Monty opens one of the other doors proving its a "no". Instead of two doors sharing a 2/3 no, you've got one unopened door thats now a 1/3 no, aka a 2/3 odds of yes.
(Score: 2) by FatPhil on Tuesday October 03 2017, @07:44AM
However, sometimes the question is ambiguously worded, or leaves wiggle room for deliberate misinterpretation. The actual make a deal scenario *does* deviate from the monty hall problem, for example. The host must be disinterested, and must always offer a chance to swap (and know where the car is). Real Monty didn't always offer the swap, and was not entirely disinterested.
It's funny that the person you're responding to so nearly made the link between his premises and the correct conclusion, and in fact your entire argument:
"""
Your odds of guessing correctly are based on the number of doors you are allowed to choose for your final choice(s). But if you only get one final choice then your odds are still one in three.
"""
Because:
sticking means chosing one door for opening.
switching means chosing *every other door*, just with no surprises from the ones monty revealed.
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 0) by Anonymous Coward on Tuesday October 03 2017, @07:51AM (2 children)
How about this analysis.
At first the door you choose is 1 out of 3.
The other two doors together are 2 out of 3.
When the single door is opened, that changes nothing, the other two doors are still 2 out of 3.
If the contestant changes the selection, they are effectively choosing two doors over one door
giving the 2/3 probability.
Note that of the "other two doors", at least one is always a looser, so a looser can always be opened.
(Score: 0) by Anonymous Coward on Tuesday October 03 2017, @12:02PM
Pretty much this.
Remove the temporal element and the choice becomes "do you pick this 1 door or these 2 doors", which makes it obvious to me why switching gives 2/3 odds of winning.
(Score: 2) by VLM on Tuesday October 03 2017, @03:55PM
Thats more eloquent and brief than my explanation AC, nice job.