Please help Re: Simplifying an explanation to the Monty Hall Puzzle

[kwbMitel]

I am tutoring a 12 year old that is struggling in math.

One of my first memories was finding my love for math puzzles at that age (or really a bit younger)

The Monty Hall Puzzle is my favourite for showing the counter-intuitive nature of math at times.

I wont be discussing My favourite puzzle that involves alternate solutions. If you know me, you know what that is.

I know starting with the Monty Hall Puzzle is not the ideal choice considering there are bone fide geniuses that don't agree or at least didn't agree at some point. I'm not saying I include myself as one of those geniuses but I too was amoung the nay-sayers for a short time. (Coding to the rescue)

Nevertheless here we are.

Sometimes looking at a thing from a different direction can illuminate a discrepancy (or a solution). There was a lottery odds question at some time where someone asked if there was a different probability of buying half the tickets for one draw or half the the quantity of tickets 1 ticket at a time over X draws.

Long story short, I proposed that there was little to no difference while most were saying that the odds of one at a time never changed from draw to draw for the multi-draw method. The answer was well north of 40% though, not the 50% I claimed and definitely not the >1% the others were saying, but eventually started saying Greater than 40% but less than 50%. The kicker for me was to flip the question and calculate the odds of losing and I got a number that matched the 40%+ crowd. Wins all around.

Flipping the Monty Hall question looks like this.

What if right at the beginning I offered you 2 choices instead of one.

Does that change anything?

One door can still be revealed. It will naturally be one of your 2 doors and we can ask the question again. Switch or No.

I see it as strongly emphasizing the first choice being the important one with respect to odds but I know the answer and may just be fooling myself.

 

[kwbMitel]

Chris, I have read and understand your last and I thank you for taking the time to write it as I see it as forward progress to establishing common ground.

When I speak to someone such as a 12 year old. I try to avoid words like obvious that have black and white definitions. Obvious can have negative connotations and assumes a lot about the Audience. If for example the audience does not find something obvious then you've already put them at a disadvantage cognitively speaking. I prefer to use Natural Conclusion or it can be concluded vs it must be concluded. I really mean MUST, but am using CAN, in a way to open discourse if they Can"t.

I don't presume that you as an Adult Can't, so I somewhat changed my tone with you to MUST. I believe this is what you took as moving the goal posts. It is not that. It represents the respect I have for your ability to appreciate the difference between can and must, so I chose must to be clearing in my meaning in a mathematical sense.

What I went on further to say, and was completely unnecessary and possibly insulting, was that if you could not agree that the fact is Obvious, then your analytical skills might be deficient. While I actually believe that statement, it did not need to be said, and definitely did not show respect. So if you feel you can forget that, and I will in fact stricken it from the record. Can we make more progress towards common ground?

What is your answer to the two questions. I will provide a followiup depending on your answer. I don't want to bias your answer but my bias should be OBVIOUS.

 

[kwbMitel]

Let's take a step back.

I see now that you agree with the 2 questions, common ground at last.

I also see that you appear to come to the same natural (obvious) conclusions that those two questions imply.

To make sure, and I will try for as much precision in what conclusion I would say that is.

Monty MUST reveal a door that is one of the two doors that are not your pick. Further He knows what door contains the Grand Prize. Further he will not reveal the Grand Prize. Therefore, there will ALWAYS be a choice that Monty can make with his knowledge, that does not reveal your choice or the Grand Prize within the two doors that are not your pick.

Can you improve on that wording?
Can you agree that at least the intent of that wording is more common ground?

Taking a break at this time

Please note my edit to my post 19 Feb 23 17:03 in red

 

[Chris Miller]

Right now in the midst of a psychotic break. I am seeking help but help is not immediate as I am not so far gone as to require emergency treatment.

It may come to you as a surprise that I'm in quite a similar state. Well, Id say I still am, but some therapeutic measures ended for me, others didn't evven start yet. It's clear that this causes this frustration as something that should help just leads to new frustration. I never meant to insult you, I considered my demands should have as limited reach to you as you make of them, as all of this is of course voluntary and just a discussion for tingling our brains, well, that's in short what I'd describe what such puzzles are for me. My intention was to help you focus on that part, because you had the feedback from me about that. I actually think I see a light at the end of the tunnel how your variation could help someone understand the original problem by applying what can be learned. Just like the extension to 100 doors intention is.

And on the way, I was actually delighted to hear from you, that your own implementation of the problem made things clear to you, which didn't seem clear just by thinking them through very "dry" and theoretically. We could write some code about these variations to see how they turn out to work. The "theorists" would always blame such experiments aka "Monte Carlo Simulations" as not proving something, the results always have some statistical noise. But you can clearly differentiate a 1/2 chance from a 2/3 chance, for example.

To get back to your state, I am surprised you said

Mike being the most obvious of those

I know Mike Lewis from another forum here and can assure you he's the last to attack anyone, become unfair or impolite, I think he just wanted to take out the tension that built and point out this is just a puzzle and not something world shattering.

I think this answer is lost as you don't continue reading here but in the other forum. Let me see, if I can meet you there.

Chriss

 

[karluk]

The success of the distraction was counter balanced with the unsatisfying result of not being able to make my point, yet again.

In my view you should take a lot of comfort from the fact that much of the time your inability to make your point arises, not from your failure to communicate, but from your listener's inability to hear. That was true of CajunCenturion in the Pond Prison Revisited thread, and it was true of me in the recent "So long fellas" thread. I completely missed your clear statement at the beginning of the thread that you were starting your escape with a 90 degree turn. It's a completely defensible strategy, but I wouldn't do it, so I must have seen what I expected you to write, rather than what you actually wrote. My apologies, since my mistake contributed greatly to our communication difficulties in that thread.

 

[kwbMitel]

If you followed a link of mine to get here, this is not the "last Comment" I referred to but a followup. I've also deleted that comment.

Chris, re: Mike. I did not mean to imply that I thought Mike was attacking me or that anyone else was for that matter. His response was Clever Ha Ha to me. Yours and Strongm were clever in a different directions by seemingly ignoring what I will call self evident truths in my statements. I've gotten in trouble with Self Evident Truths before. Lets say that was the mistake(s) that I made that is related to Euclid's 5th Postulate. I maintain that in 2 dimensions, the postulate is not wrong, but concede that it does not cover other dimensions. Relevant Link

@Karluk Your last moves me. Thank you, the 90 degree turn as the first move was a concession on my part to get me closer to what I see as the common ground of the math formula that to me dictates this direction and ignores the implications. I never got to talk about those implecations because the conversation, in my mind, went completely sideways. Sideways!, HA the best unintentional pun yet! My apology to you as the listener is that I also, and without mentioning my motive, stealthily took an opportunity to answer a different question at the same time. This muddied the water (pun) in ways that made my escape (pun) from communication prison (pun) all but impossible (pun?). You showed far more patience than I deserved all things considered.

 

[Mike Lewis]

I did not mean to imply that I thought Mike was attacking me or that anyone else was for that matter.

I didn't think that for one moment. On the contrary, I thought your comments were quite helpful in explaining the situation.

Mike

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Mike Lewis (Edinburgh, Scotland)

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