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[ashersky]

Crap, sorry, still on my mind.

Can’t you just say “switching doubles your chances of winning because it’s like choosing two doors instead of one.”?

Each door has the same chance of winning.  You choose A.  C is eliminated.  Now, your choice can be visualized as either keeping A or taking B and C together, with one wrong door removed.  Switching is like choosing BOTH doors you didn’t choose (and Monty nicely removed the wrong one for you).

If you had the choice of one door or two doors at the beginning, you’d always take two, right?  That seems like a way to explain it with no confusing math or percentages.

[silverspawn]

It is just frequentism vs Bayesianism and it doesn't have anyhing to do with the Monty Hall Problem.

I know/knew nothing about any of this.  Super neat!

https://en.m.wikipedia.org/wiki/Frequentist_probability

Thanks for introducing some cool philosophy stuff.

Ok, now that we are clear on what the topic is, I don't want to make it sound like I'm neutral on this. I think probability is subjective uncertainty and the idea that it could be anything else immediately falls apart in any real life situation.

The basic idea of frequentism is fine – in an abstract experiment, probability is the limit of the relative frequency. No Bayesianian would dispute that. My subjective uncertainty of a die falling on 6 is 1/6 because that's the relative frequency of an abstract die roll and I can't distinuguish my die from an abstract die.

But some then say that you can't assign a probability to things that like "the car is behind door A" because it is either 100% or 0%... and that frustrates me to no end. In real life, EVERYTHING is already determined. if I let my computer randomiize a number, it is already determined because it's pseudo-randomness; I'd know in advance what the random number will be if I could look at the system state (or in case of RANDOM.org, look at the exact level of atmospheric noise, because that's how they generate their random numbers). And in the same way, nothing about me throwing a die is more random than the position of the car in MC. What the die will land on is already determined by phyics, I just don't know it. Because I'm ignorant... I have subjective uncertainty.

Probability is subjective uncertainty. Arguing that it's something different is idiotic.

[silverspawn]

Crap, sorry, still on my mind.

Can’t you just say “switching doubles your chances of winning because it’s like choosing two doors instead of one.”?

Each door has the same chance of winning.  You choose A.  C is eliminated.  Now, your choice can be visualized as either keeping A or taking B and C together, with one wrong door removed.  Switching is like choosing BOTH doors you didn’t choose (and Monty nicely removed the wrong one for you).

Yes, I think that is a great way of putting it! That's how I eventually looked at it too when I first encountered the problem.

[silverspawn]

I'm also working on my RMM... it's on the more complicated side... pretty excited to run it. I just hope it'll fill.

I don't know if it's actually simpler than Space Alert, but I think I can make it sound simpler 

[SpaceAnemone]

I'm also working on my RMM... it's on the more complicated side... pretty excited to run it. I just hope it'll fill.

I don't know if it's actually simpler than Space Alert, but I think I can make it sound simpler 

Space Alert lost another player today :-(

I think I need to re-balance it for fewer people, or give up on it altogether. You still willing to help with balance stuff?

[silverspawn]

I would.

... but I think you might want to try changing the OP rather than the setup. We have run games with this level of complexity before. Try to make it understandable for normal people

[Kuildeous]

Holy shit, guys. It actually happened. Some guy on the internet changed his mind.

I mean, it happens fairly often; there are actually many rational people on the internet, and they are capable of changing their mind when presented with facts. This guy wasn't one of them. He was stubborn as hell, and I eventually had to give up on him, but I argued with him far longer than any sane person should.

We gave him everything to convince him of the Monty Hall problem: Actual conditional probability equations, the million-door hyperbole, and a verifiable simulator that runs the puzzle 10k times. Someone even framed the hyperbole in an easier-to-grasp method: Suppose I ask you to guess the city I'm from, you guess Paris, and I tell you I'm either from Paris or some podunk town outside Boston. Is Paris going to be right 50% of the time? And they guy still said it was 50%!

I stopped being kind to him at that point. I wasn't overly mean, but I called his ability to rationalize into question. I gave up.

But he finally admitted that he was wrong and that it was about conditional probability, and he reversed his stance. I had to make sure I wasn't being trolled somehow. I was shocked.

[Seprix]

But he finally admitted that he was wrong and that it was about conditional probability, and he reversed his stance. I had to make sure I wasn't being trolled somehow. I was shocked.

What are the odds of that?

[silverspawn]

They definitely are either 93% or not 93%.

[Kuildeous]

So if Bob picks one of three doors and then is shown one door he didn't pick is a loser, he still has a 1/3 chance of winning the prize.

But when Carol walks in at this point, she's assigned to the other door, and she has a 1/2 chance of winning the prize.

I'm not even going to bring that up. That'll drive the deniers nuts. It even makes me feel uncomfortable.

[Awaclus]

So if Bob picks one of three doors and then is shown one door he didn't pick is a loser, he still has a 1/3 chance of winning the prize.

But when Carol walks in at this point, she's assigned to the other door, and she has a 1/2 chance of winning the prize.

I'm not even going to bring that up. That'll drive the deniers nuts. It even makes me feel uncomfortable.

Well, from Carol's perspective, Bob also has a 1/2 chance. From Bob's perspective, Carol has a 2/3 chance.

[scott_pilgrim]

It's sort of like a game of poker. If we each roll a die and cover it up and bet on whose die is higher (pretend we both lose in a tie), and I roll a 4 and you roll a 3, I will think I have a 1/2 chance of winning and you will think you have a 1/3 chance of winning. From a third person omniscient perspective, I have a 100% chance of winning. But that doesn't make either of our calculations wrong.

[Seprix]

How to break your computer

1. Go to Random Stuff Part III
2. Press All

[LaLight]

How to break your computer

1. Go to Random Stuff Part III
2. Press All

I did this with Homage...

[silverspawn]

So if Bob picks one of three doors and then is shown one door he didn't pick is a loser, he still has a 1/3 chance of winning the prize.

Only if the person revealing the door had the algorithm of "Always reveal a losing door after the first door was chosen".

But when Carol walks in at this point, she's assigned to the other door, and she has a 1/2 chance of winning the prize.

I'd say that's not true. Just because she walked in later doesn't mean she has to assume the door was randomly revealed.

What matterse is how the reveal was determined. If you don't know, you have to speculate, and then there is no clear probability.

[pingpongsam]

They definitely are either 93% or not 93%.

So, a 50% chance of being 93%?

[silverspawn]

They definitely are either 93% or not 93%.

So, a 50% chance of being 93%?

No, 50% is a stupid prior. Priors should be derived from simplicity (Occam's Razor) – 93% is a much more specific than not 93%, so 93% has a lower prior.

[Kirian]

"Stupid Prior" is the name of my Weird Al cover band.

[silverspawn]

"Stupid Prior" is the name of my Weird Al cover band.

I'd have given that a really low prior. Priors aren't everything.

[Kuildeous]

How to break your computer

1. Go to Random Stuff Part III
2. Press All

Probably time for a Random Stuff IV.

So if Bob picks one of three doors and then is shown one door he didn't pick is a loser, he still has a 1/3 chance of winning the prize.

Only if the person revealing the door had the algorithm of "Always reveal a losing door after the first door was chosen".

Which he does, per the Monty Hall puzzle.

But when Carol walks in at this point, she's assigned to the other door, and she has a 1/2 chance of winning the prize.

I'd say that's not true. Just because she walked in later doesn't mean she has to assume the door was randomly revealed.

She doesn't have to assume anything. Barring any other indication, she has a 50% shot. Now if she were told that Bob chose that door first and then had a reveal, then she has a new indication.

[scott_pilgrim]

But when Carol walks in at this point, she's assigned to the other door, and she has a 1/2 chance of winning the prize.

I'd say that's not true. Just because she walked in later doesn't mean she has to assume the door was randomly revealed.

She doesn't have to assume anything. Barring any other indication, she has a 50% shot. Now if she were told that Bob chose that door first and then had a reveal, then she has a new indication.

Your original statement makes it pretty ambiguous what information Carol has, but what the probability of winning is from her perspective is dependent entirely on what information she has. For example, if she just walks in the room with no knowledge of what's happening, and is told "you get whatever is behind that door", she definitely won't expect to have a 50% chance of winning a car, she probably doesn't even expect cars to be involved. If she is told "there is a car behind exactly one of these two doors, and you get to keep whatever is behind that one", then her complete lack of knowledge of anything else in the scenario gives her a 50% chance of winning, in the same way that if you gave me a true/false test in Korean, I would have a 50% chance at getting any particular question right. Any statement in a set of n mutually exclusive, collectively exhaustive statements that differ in name only has a 1/n chance of being true; here, Carol doesn't know anything about the two possibilities except that they are mutually exclusive and collectively exhaustive, so she assigns each a probability of 1/2.

But then if you continue explaining to her how this situation came to be, her probability goes back up to 2/3. So you seem to be making the assumption that she somehow knows that there is exactly one prize behind the two doors, but doesn't know how she got into that position. I think the apparent weirdness of her probability disagreeing with Bob's comes from the fact that it would be weird for her to have that exact amount of information in the first place.

[2.71828.....]

 random stuff part IV is #fakenews