Another logic riddle, a lot tougher, builds on principles from the others

[Grumblenuts]

No, I get it. You start with 1/3 odds, now you know 1 of the 3 is not right, making your odds 2/3. If you stay with your cup, your odds are still 1/3.

You also know the position of one that definitely "is not right." Perhaps try plugging that info into your app to see if the odds improve even more..

 

[Faun]

You also know the position of one that definitely "is not right." Perhaps try plugging that info into your app to see if the odds improve even more..

That's what my app did. It replicated the OP's riddle. I also ran it where it never changed cups. One billion iterations. Took about 30 seconds to run.

Result: 33.3%

 

[Grumblenuts]

That's what my app did. It replicated the OP's riddle. I also ran it where it never changed cups. One billion iterations. Took about 30 seconds to run.

Result: 33.3%

LOL. You needed no computer for that. 1/3 to hold and 2/3 to stay was already given, so to actually apply this gain of position information to the second "choice" you'd have to add some code.

Let's just stick with your 2/3 result since we already know the carny rigs the game so as to make that result inevitable. The initial condition in terms of both winners and positions can be symbolized thus since you can really only choose Cup #1 and nothing is always revealed under Cup #3:

? X 0 : where "?" = maybe, dunno | "X" = dunno + no access | "0" = known loser

Obviously only 2 of the 3 can be winners and only 1 of the 3 if you could never switch to Cup #2. You've already stated as much w/o needing your app. However, the question remains as to whether knowing the position of one loser cup increases your odds when switching to better than 2 in 3?

Keep in mind that you can never switch to #3, only to #2. In other words, you really only have the supposed "choice" of #1 to begin with (no choice), and then only a really dumb choice between sticking with Cup #1 or switching to #2. At best, you are really only provided a choice between two, never 3, and only one informed choice.

Consider setting up your app to calculate the odds given one really had no choice to begin with and will definitely switch now, knowing that Cup #3 was never really an option.

100% (no choice) + 50% (1 in 2) yields ??? (more than 2/3?)

 

[Faun]

LOL. You needed no computer for that. 1/3 to hold and 2/3 to stay was already given, so to actually apply this gain of position information to the second "choice" you'd have to add some code.

Let's just stick with your 2/3 result since we already know the carny rigs the game so as to make that result inevitable. The initial condition in terms of both winners and positions can be symbolized thus since you can really only choose Cup #1 and nothing is always revealed under Cup #3:

? X 0 : where "?" = maybe, dunno | "X" = dunno + no access | "0" = known loser

Obviously only 2 of the 3 can be winners and only 1 of the 3 if you could never switch to Cup #2. You've already stated as much w/o needing your app. However, the question remains as to whether knowing the position of one loser cup increases your odds when switching to better than 2 in 3?

Keep in mind that you can never switch to #3, only to #2. In other words, you really only have the supposed "choice" of #1 to begin with (no choice), and then only a really dumb choice between sticking with Cup #1 or switching to #2. At best, you are really only provided a choice between two, never 3, and only one informed choice.

Consider setting up your app to calculate the odds given one really had no choice to begin with and will definitely switch now, knowing that Cup #3 was never really an option.

100% (no choice) + 50% (1 in 2) yields ??? (more than 2/3?)

You're so far off base.

First of all, this is not actually a "carney game." Even if you were right, and you're not, that the odds of winning become 1/2, no carney would ever offer such a game where they never make money over the long term. And since the odds become 2/3 for people smart enough to switch every time, carnies would lose their proverbial shirts.

The next mistake you made was assuming the player always picks cup #1 and the host always shows cup #3. By doing that, you've eliminated randomization, which is a critical factor in this riddle. You literally changed the outcome to match your conclusion the odds are 1/2 by rigging the game.

And while it's true I didn't have to write the app, I did so for fun anyway. I do stupid shit like that. It's why I'm a programmer. But unlike your rigged game, it randomly picked cups and randomly revealed cups. And there's no doubt after a billion iterations, staying with your initial cup 100% of the time results in wins 1/3 of the time; and switching cups 100% of the time results in wins 2/3 of the time.

What you need to wrap your head around, and what makes this such an interesting riddle, is there are still 3 cups even though one was revealed. So the odds are still x/3 after one cup is revealed. The odds never become 1/2 since you picked 1 cup out of 3 to begin with. There are still 3 cups in the game. So sticking with your original cup means your odds don't change. They remain 1/3. Meaning the remaining chance of winning if you do switch cups is the rest -- 2/3.

 

[Grumblenuts]

I am not off base whatsoever, have always considered you a political ally, and treated you with nothing but respect. I've just been trying to expand this conversation a bit beyond the obvious. Outside the box.. Critically.. Think about it.. or don't and just remain all superior and upset. Your prerogative. I gather now that it's not a simple matter of discussion for either you or FF, but I've been here long enough to remember previous Monty Hall threads. None of this has come as news to me.. but believe whatever floats your dinghies if you must..

 

[Faun]

I am not off base whatsoever, have always considered you a political ally, and treated you with nothing but respect. I've just been trying to expand this conversation a bit beyond the obvious. Outside the box.. Critically.. Think about it.. or don't and just remain all superior and upset. Your prerogative. I gather now that it's not a simple matter of discussion for either you or FF, but I've been here long enough to remember previous Monty Hall threads. None of this has come as news to me.. but believe whatever floats your dinghies if you must..

I'm being respectful as well. I'm not name calling or insulting. But you are off base and I explained why. Don't take that as invective, I likewise consider you an ally politically.

Think of it like this... if you were shown one of the three cups before guessing one of them and then had to pick which of the remaining 2 cups has the prize, then there would only be 2 cups involved and your odds would be 1/2.

But that's not the case. Instead, you're picking a cup before being shown one of the wrong cups, so even though you're shown a cup, there's still 3 cups involved, so your chances of winning remain 1/3. But you no longer have a 2/3 chance of losing, as you did before a cup was revealed, because you now know which of the other two cups is wrong. Your initial guess remains a 1/3 chance but that increases the odds the other cup has the prize to 2/3.

 

[Grumblenuts]

Think of it like this... if you were shown one of the three cups before guessing one of them and then had to pick which of the remaining 2 cups has the prize, then there would only be 2 cups involved and your odds would be 1/2.

But that's not the case. Instead, you're picking a cup before being shown one of the wrong cups, so even though you're shown a cup, there's still 3 cups involved, so your chances of winning remain 1/3. But you no longer have a 2/3 chance of losing, as you did before a cup was revealed, because you now know which of the other two cups is wrong. Your initial guess remains a 1/3 chance but that increases the odds the other cup has the prize to 2/3.

That's your experiment, which I fully understood. As I painstakingly explained, I was talking about the one portrayed in the OP where FF says quite plainly:

You step up to a carnival booth. The carney running the game has 3 numbered cups upside-down on the table in front of you. He tells you there is $300 under one of them, and nothing under the other two. He knows what is under each cup.

For $100, you get to choose a cup to be flipped and keep whatever is underneath.. You pay your $100 and point to Cup #1.

The carney flips over Cup #3 to reveal nothing is under the cup. He then asks you if you would like to keep your choice or change it to Cup #2.

What do you do? Does it even matter whether or not you switch your choice from Cup #1 to Cup #2?

Notice that actually nothing but the choice of switching from Cup #1 to Cup #2 is really provided as an option. Now, I was suggesting that, say, why not presume our gambler had been watching the game for a while prior (as I've always done at carnivals), so already knows that this carny always forces Cup #1 on you and uncovers Cup #3 revealing it to be of one of the two with nothing under them.. and proceed from there. Now that's not really asking too much, is it?

FF even cements having no choice about starting with Cup #1 by asking only "Should you switch your choice to Cup #2?" in his poll question.

"you're picking a cup before being shown one of the wrong cups"

Nope, you're provided no choice in the matter.

 

[Fort Fun Indiana]

Thanks again for sort of confirming that it would make no difference, just as I suspected.

You're welcome. Whenever you feel too lazy to reason stuff out, I'm your guy. Hit me up.

 

[Grumblenuts]

And while it's true I didn't have to write the app, I did so for fun anyway. I do stupid shit like that. It's why I'm a programmer.

I thought that was great and immediately thanked you for sharing it. I grew bored with programming long before there was even a www, but stupidly attempted a computer engineering degree at Drexel anyway. Coding algorithms is not "stupid shit" at all to me, but I mostly tend to draw things in SolidWorks for fun instead these days.

 

[Grumblenuts]

"Inferred" means something follows from the information given.

From a reader's perspective. Being the author allows you to dictate what was actually intended or "implied." You get no say as to what any reader may or may not infer.

 

[Fort Fun Indiana]

From a reader's perspective. Being the author allows you to dictate what was actually intended or "implied." You get no say as to what any reader may or may not infer.

No, that's nonsense. Else biology students could rightfully believe the sun revolves about the earth, as the biology text didnt state otherwise.

But modifying the riddle is fun. Knock yourself out.

 

[Anomalism]

No, that's nonsense. Else biology students could rightfully believe the sun revolves about the earth, as the biology text didnt state otherwise.

But modifying the riddle is fun. Knock yourself out.

Heliocentrism is communist propaganda.

 

[Grumblenuts]

No, that's nonsense. Else biology students could rightfully believe the sun revolves about the earth, as the biology text didnt state otherwise.

But modifying the riddle is fun. Knock yourself out.

It has nothing to do with being "right", only reasonable for a given reader to conclude from their unique perspective. But laugh it up and knock yourself out modifying basic English.

 

[Fort Fun Indiana]

Heliocentrism is communist propaganda.

So you're saying the Bible is communist propaganda. I mean, you didn't say it wasn't!

 

[Fort Fun Indiana]

only reasonable for a given reader to conclude from their unique perspective.

Haha hahaha

No.

But I always enjoy your creativity. I like stories.

 

[Grumblenuts]

Haha hahaha

No.

Yes.

Example provided by Cambridge Dictionary:

It is reasonable to infer an intelligent source from complex and sophisticated mechanisms.
From CNN

It is thus also unreasonable to infer an unintelligent source from complex and sophisticated mechanisms. Actually, both assertions are BS imo, unfortunately being practically inseparable from god-of-the-gaps reductionism.

 

[Faun]

I thought that was great and immediately thanked you for sharing it. I grew bored with programming long before there was even a www, but stupidly attempted a computer engineering degree at Drexel anyway. Coding algorithms is not "stupid shit" at all to me, but I mostly tend to draw things in SolidWorks for fun instead these days.

Writing code in general is not stupid shit. Writing an app to test the odds of this 3 cup riddle is. But it was still fun to write.

 

[Grumblenuts]

Writing code in general is not stupid shit. Writing an app to test the odds of this 3 cup riddle is. But it was still fun to write.

You remind me that decided not to pursue programming for a living because I didn't want to risk spoiling the shear joy I experienced doing it for my own purposes. By literally making it my "work." The commonly shared belief that one should choose a career doing what they love has never rung quite true for me. I don't recall ever experiencing any difficulty programming. Always just read what I needed to and applied it like cooking from a recipe. Same with CAD. In engineering school I learned that engineers are vastly assholes. So I decided to quit kidding myself and cease training to become one. I've discovered since that maximum happiness comes from having just enough. The real challenges are getting rid of shit, never accumulating more, and gaining good friends.

 

[Faun]

You remind me that decided not to pursue programming for a living because I didn't want to risk spoiling the shear joy I experienced doing it for my own purposes. By literally making it my "work." The commonly shared belief that one should choose a career doing what they love has never rung quite true for me. I don't recall ever experiencing any difficulty programming. Always just read what I needed to and applied it like cooking from a recipe. Same with CAD. In engineering school I learned that engineers are vastly assholes. So I decided to quit kidding myself and cease training to become one. I've discovered since that maximum happiness comes from having just enough. The real challenges are getting rid of shit, never accumulating more, and gaining good friends.

I'm the opposite. I love what I do and I consider myself very lucky to have a job I love. I taught myself how to code early on and was fortunate enough to make a career out of it.

 

[Grumblenuts]

I love being retired