Quote:WizardI've seen "Everything men know about women" about 25 years ago, which was also totally blank. In my case, I must admit, it was right.

They want a handsome, nice, smart guy, but women don't know how Venn diagrams work.

Women also want risk takers who are always available. make it look effortless and always succeed. To be fair that is exactly what men want, but they know that's why they make comic book movies.

Quote:WizardThis is by far the first time I have taken issue with Marilyn's responses. She really stirred up the pot with a bad answer to the Monty Hall question.

What is the Wizard's current position on the Monty Hall problem? She really did stir up a furor with her answer at the time but today every reference authority on the question gives her answer as the correct one. Here is the problem:

On the show Let's Make a Deal host Monty Hall gives the contestant a choice of three doors. Behind one is an automobile and behind two are goats. She gets to keep whatever is behind the door she chooses. She picks a door. Monty opens one of the other doors and show a goat. Should she stay with her original selection or should she switch? Most of the write-ins said it didn't matter.

Here is my favorite solution. We assume that Monty offers the switch whether or not she has chosen correctly.

When she makes her choice the probability is 1/3 that she is right and 2/3 that she is wrong.

If she stays with her original choice she wins if her choice was right p = 1/3

If she switches she wins if her original choice was wrong p = 2/3

She should switch!

Quote:shoshone

When she makes her choice the probability is 1/3 that she is right and 2/3 that she is wrong.

If she stays with her original choice she wins if her choice was right p = 1/3

If she switches she wins if her original choice was wrong p = 2/3

She should switch!

My problem here is if she switches or not, her probability is still 1/2. She still has 2 choices. Equal probability either way.

Quote:shoshoneOn the show Let's Make a Deal host Monty Hall gives the contestant a choice of three doors. Behind one is an automobile and behind two are goats. She gets to keep whatever is behind the door she chooses. She picks a door. Monty opens one of the other doors and show a goat. Should she stay with her original selection or should she switch? Most of the write-ins said it didn't matter.

This vague wording is exactly what was wrong with Marilyn's many columns on the topic. It must be clearly stated what Monty's behavior is.

If he didn't know where the car was and opened a door at random, then the odds the player's door has the car is 1/2.

If he does know where the car is and always opens a door with a goat after the player chooses, then the odds the player's door has the car is 1/3.

While I agree with you, even with the vague wording the answer to the question is clear. They player should certainly switch doors. At worst, the player is no worse off, and at best the player just doubled his chances of winning.Quote:WizardQuote:shoshoneOn the show Let's Make a Deal host Monty Hall gives the contestant a choice of three doors. Behind one is an automobile and behind two are goats. She gets to keep whatever is behind the door she chooses. She picks a door. Monty opens one of the other doors and show a goat. Should she stay with her original selection or should she switch? Most of the write-ins said it didn't matter.

This vague wording is exactly what was wrong with Marilyn's many columns on the topic. It must be clearly stated what Monty's behavior is.

If he didn't know where the car was and opened a door at random, then the odds the player's door has the car is 1/2.

If he does know where the car is and always opens a door with a goat after the player chooses, then the odds the player's door has the car is 1/3.

WWBD? (What would Bayes do?)

Never assume.Quote:shoshone... We assume that Monty offers the switch whether or not she has chosen correctly. ...

Monty doesn’t always offer the switch, and he himself has said that he would often offer that option based upon his opinion of the contestant - and that included both the second chance to win the prize as well as the second chance to get zonked.

Quote:unJon] While I agree with you, even with the vague wording the answer to the question is clear. They player should certainly switch doors. At worst, the player is no worse off, and at best the player just doubled his chances of winning.

WWBD? (What would Bayes do?)

What if the host knew where the car was and planned to only open another door if you picked it, thus tricking Bayesians into switching.

Quote:DJTeddyBearMonty doesn’t always offer the switch, and he himself has said that he would often offer that option based upon his opinion of the contestant - and that included both the second chance to win the prize as well as the second chance to get zonked.

I've watched old shows on YouTube and he didn't offer a switch. However, as I recall, he always opened the best door last. Thus, it didn't reveal any pertinent information when he opened one of the lower value doors first. Your chances of winning the best prize were still 1/3 at that point.

Quote:WizardI've watched old shows on YouTube and he didn't offer a switch. However, as I recall, he always opened the best door last. Thus, it didn't reveal any pertinent information when he opened one of the lower value doors first. Your chances of winning the best prize were still 1/3 at that point.

It would be interesting to see the total number of times switching was offered, and how many of those were, "Contestant initially picked the big prize." I doesn't sound like it will be 1/3, so maybe the contestant's post Monty's offer action needs to based on more than the revised probability of the offer to switch. Is there a "tell" when Monty wants you to win?

The "Big Deal of the Day" was where the two contestants who won the most and were willing to trade it all away each picked one of the three doors/curtains. Once the contestant selected their doors, the doors were always revealed from lowest value to highest value, regardless of who picked what. The contestants were not allowed to switch their picks.