The Authoritarian Von Savant

I'm sorry, you're right I didn't get 'what your were making up.' But I stand by the observation I offered. Based on the conversation here, it seems you are often blocking and not following the logic that is presented in the replies here.

 

ERRORS FIXED!

I got mixed up in the composition of that message, and switched 'red' and 'black' as I went on. In the quote box below, this has been fixed. Apologies for any confusion.

 

What you are saying is that the host has three possibilities, only one of which will make you a winner if you stick with your original choice. But how does this differ from the NBA scenario? The fixer has three possibilities. Memphis beats San Antonio and then Miami. San Antonio does the same. Whichever one wins loses to Miami. The partial dope the fixer gives you is the winner of the San Antonio-Memphis semifinals. So how is that winner twice as likely to beat Miami? Does he inherit the losing team's one-third chance, doubling his own? That's ridiculous, but Marilyn seems to give her door that inheritance. The fixer
too has three possibilities, only one of which will make you a winner, but it doesn't happen in real life that you should pick Miami, excluding any data that say whoever has the toughest semifinal opponent is more likely to win the finals.

"A majority of correspondents eventually agreed with Marilyn." I don't have access to the minority report, so I'm without backup, just like the Heat.

 

The logic seems to be that the host can text you the message to switch or call it to you by phone. You get the same message.

I'll have to try this on another message board, the same one with the multiplication of negatives. The difference is I had no doubt of the answer, but I wanted someone who could explain it in real-life situations.

 

Don't argue any more until you do the experiment.

 

The NBA scenario involves two distinct events - the semi-final and the final. Before you learn of the fix, Miami only has to play one more game while SA and Memphis have to play two. That means Miami has a 1/2 chance of winning overall, while the other two have a 1/2 chance of winning the semi-final then a 1/2 chance of winning the final - a 1/4 chance of winning overall.

 

The two distinct events in the game show are the contestant's original choice and then the contestant's choice of whether he wants to switch. The host has the ability to reveal two 50% possibilities (that the door he opened revealed where the winning door was) plus one 100% possibility (that it did not, automatically making the contestant's first choice the winner. So the host's total revelation amounts to the same increase of the unopened door from 1/3 to 1/2 as the contestant's increased odds.

For the NBA analogy to be more like the game show, but still be obviously 50-50, the fixer will only tell that Memphis will not win the finals and may not even play in the finals and that the bettor has to switch before the semifinals are over. The host doesn't know which door to open if he knows they will both lose. So the fixer doesn't have to know the winner of the semifinals.

"SA and Memphis have to play two"? That is impossible. Only one of them has to play in the finals. You lost me there. Your conclusion may be right even if it is based on a false premise, but it makes it hard to follow.

 

The point is that for either of those teams to win overall, they would need to play two games. Remember this is all prior to knowing about the bribe;

For SA to win overall, they must beat Memphis in the semi-final and then beat Miami in the final.
For Memphis to win overall, they must beat SA in the semi-final and then beat Miami in the final.
For Miami to win, they only need to beat the semi-final winner in the final.

This means that the odds of winning overall start at 1/4 for SA, 1/4 for Memphis and 1/2 for Miami. This is different to the 1/3 starting point for the Monty Hall game which is why the answer is different.

Have you tried the demonstration donquixote99 suggested?

 

Prometheus: have you run an experiment on the Door Game, as I suggested?

I ran the experiment, using the method I described above, for 30 trials, with the following results:

Switching Wins: 19 instances
Staying Wins: 11 instances

This is very consistent with Vos Savant's contention that one gains a 2/3 chance of winning by switching. I can't guarantee the results will always be this consistent with the predicted results with only 30 trials, but with a larger number of trials they are quite certain to be.

I again urge you to do the experiment and see for yourself.

 

It's all theory. In theory you have a 50-50 chance that your fallen piece of toast will land butter side down. You can drop that piece of toast 100 times and have every one of them drop butter side up, and the 101st is still 50-50.

But, we know the game show host is NOT going to pick a door that has the prize behind it. Thus, the odds change from one in 3 to 50-50. Switching from an unknown to an unknown changes not one little blessed thing.

 

I suggest you also do the experiment. Go from theory to reality!

Let us know if you do, and what results you see.

I predict, based on theory verified by experiment, a 2/3 to 1/3 result in favor of switching.

 

No, I would rather find out some math teacher who still disagrees with Marilyn and would explain why the experimental proofs are biased. Or conversely, someone who was convinced by those real-life proofs but still can't figure out why it wasn't 50-50. Until then, I maintain that the host can only tell the contestant two things: That there is a 50% chance that it is door B or a 50% chance that it is door C. Obviously, you can't add these two together or else it would be impossible for A to win, so they must average out and equal A's chance, which has been also raised to 50-50.

By the way, you didn't see my own error. It doesn't make any difference if the host's tone gives the answer away, because we are not talking about how many times the contestant wins, but how often he would have won if he had switched.

 

I see. Instead of doing a test that might show your logic to be faulty, you hope to find someone who will support your position.

So instead of seeking truth, you adopt a defensive stance. Can't stand the risk that you might be wrong, seems to me. But c'mon. It's OK. Everyone is wrong sometimes. Shoot, I made silly errors the first time I typed up the experiment procedure. No big thing. I posted a corrected version and life goes on.

Be brave! Be fearless! Do the experiment!

 

The Door Problem, logically:

Switching is the better strategy unless you pick the right door the first time.
Your chance of picking the right door the first time is one out of three.
Switching will be the right strategy two out of three times.

 

You aren't the only one with rights here; if you can dismiss my NBA scenario, I can at least be suspicious of your experiment being an accurate illustration of the puzzle. Besides, when somebody tells me to do something, I automatically dismiss it. Authoritarians talk the way they do because they have no way to persuade.

Suppose you roll three quarters; the one from a certain state being the winner. The contestant's first choice is the quarter on the left; the host always eliminates the quarter on the right unless it is the winner. I don't think of this as my turn to try the test; it's is my turn to tell you what to do.

 

Rights? No one questions your rights. And I certainly am claiming no "authority" here. I am telling you what to do only rhetorically; the imperative emphasizes the fact that I feel you are resisting the truth for some reason.

This is not important enough to argue over. I'm bailing from this thread; PM me if you ever decide to do the experiment. In the meantime, have a nice life.