Recent content by FactChecker

Hay!!! I take that personally. ..... well, ok. :cool: If that was the FB consensus, I am surprised and impressed.

"Hedging your bets" is a legitimate technique to reduce the severity/variance/magnitude of alternative outcomes.

Suppose Monte makes his decision blindly and the game is declared invalid and restarted if he opens the prize door. Then, for valid games that continue, the probability of both remaining doors is 1/2. Depending on what rules Monte follows, there are legitimate probabilities of 1/2 and 2/3. I...

But there might be a detail missing here. If Monte opens a door blindly, and it happens to be a goat by luck, then 50% is, indeed, correct. How does that fit into this visualization? This seems to be missing any insight into how Monte's door selection is involved. ADDED: Legitimate...

It's a Rorschach test. I would reject the switch because I am a paranoid person. ;-)

Just to be clear. None of this is about "the contents changing". It is only about changing your estimate of the odds of doors having goats or the car.

The real difference is between luck versus the sure thing of a rule. If Monte blindly opens a goat door, that is luck that changes the odds of both your door and the remaining unopened door equally. On the other hand, if Monte opens a door following the rule that he can not open the prize door...

The only one I know as an example is the country song, "Walk My Walk", that recently won an award and was AI-generated. There was a big uproar about it a couple of months ago. Its lyrics seemed to me to be just a string of separate C&W sad statements.

Right. I'll leave it to anyone who knows Japanese to evaluate the lyrics.

If not AI, they might as well be. A weakness of AI songs is the lyrics, which I can not understand in these. AI lyrics seem to piece together a string of stand-alone statements with the same theme. They don't have a story or narrative quality.

In the Monte Hall game, the player only has one choice that he does before Monte opens any door. So you don't think that Rule 2 and the fact that Monte did not open that remaining door gives any sort of hint that should be used to adjust the odds but that same implication does not apply to your...

Exactly. Good point. It is the "filtering" action of the rule that makes the difference. With the rule, you know that if the remaining door(s) might have the prize, that door will not be opened. I like to use an even more extreme example to illustrate the process and why I like to call it a...

Have you done the math? Math is your friend in this. The conditional probabilities are completely different in the two situations. See Dale's post above, but you should do the complete calculation or use a probability tree.

Yes, it does make a difference. There is a difference between an accidental result of rare luck versus the intentional act of avoiding opening one door. Consider the example (again) of the game with 100 doors. In the first case of luck, the only inference that can be made from opening 98 doors...

Yes. Restarting the game is the same as making a rule that he can not open the door with the prize. Any time he violates that rule, the game is invalid and start over.