MitD XIII: Learning is happening

[Peelee]

Sure, but that's only because the host will never remove the right answer.

To be fair, that's like the main requirement for a Monty Hall problem.

[Fyraltari]

To be fair, that's like the main requirement for a Monty Hall problem.

Well, I'd put "there is a right answer" and "the contestant doesn't know the right answer" ahead, but that's just me.

[lio45]

To be fair, that's like the main requirement for a Monty Hall problem.

Yep, and for what seems the millionth time, it's the reason what's happening in the comic is not one - the doors that are taken off the table by MitD are chosen randomly. Statistically, the remaining doors are all just as good / just as bad as any other, regardless of the number of doors left in the pool of remaining available doors.

[Ruck]

I re-looked into this and you are half right. Yes in the classic set-up you go from 1/3 to 2/3 because as

Spoiler: this tree

Show

shows there are actually three starting points for the second choice and in two of them changing automatically means getting the right door.
Which is a 33.3333...% increase in chances to be right


However with four doors, in addition to now having four starting points, changing your answer only gives you 1/2 chance to get the right answer, as beyond the door you first chose and the door the host eliminated there remains two doors. This means that of the four starting points, one leads to a wrong anwser whatever you choose when changing (you had the right answer to begin with) and three leads to either the right or aone wrong answer when choosing (you had one of the wrong answers originally). So your chances are actually 3/8.
This is still better odds than sticking with your first answer but only by: 3/8-1/4 = 1/8 = 12.5%


With five doors, switching give you 4/15 chances of getting the right answer against 1/5 if you stick that is a 1/15 = 6.666...% increase.

The formulae are, with N the number of door:
-chance of success by sticking: 1/N
-Chance of success by switching: (N-1)/(N²-2N)
-Increase of odds by switching: (N-1)/(N²-2N) - 1/N = 1/(N²-2N)

That's if the host only opens one door. My answer was if he opened all the doors except one.

[Grey_Wolf_c]

The formulae are, with N the number of door:
-chance of success by sticking: 1/N
-Chance of success by switching: (N-1)/(N²-2N)
-Increase of odds by switching: (N-1)/(N²-2N) - 1/N = 1/(N²-2N)

You seem to be assuming that the host only opens one door. I’d like a citation for that, since the standard math description states the opposite: that the host open all doors except two (the one picked and one other), and behind all the doors he opens there is a goat. The general formula thus is that your chance of finding the prize is 1/N if you stick, and (N-1)/N if you switch, where N is the number of doors.

I’m also increasingly confused as to what this has to do with MitD.

Grey Wolf

[lio45]

I’m also increasingly confused as to what this has to do with MitD.

Grey Wolf

It's not entirely unrelated; this discussion serves the purpose of finishing off the idea that MitD's random removal of doors from the door pool may have a statistical benefit for TE ("speeding up their search").

(You're of course correct that it's unrelated to the species of MitD.)

[Fyraltari]

You seem to be assuming that the host only opens one door. I’d like a citation for that, since the standard math description states the opposite: that the host open all doors except two (the one picked and one other), and behind all the doors he opens there is a goat.

The only version I know has only three doors in which case opening "one door" and "opening all but one door" are the exact same thing. I extrapolated with what happens when there is more doors and the host opens only one because that was a funny math problem. I don't know, nor care, wether there is a "standard" extrapolation of that problem.

I’m also increasingly confused as to what this has to do with MitD.

Grey Wolf

Nothing, I was just partaking in the madness.

[Peelee]

I’m also increasingly confused as to what this has to do with MitD.

Grey Wolf

lNothing, I was just partaking in the madness.

Same, but for the sake of being even partially relevant, I sunlit that the MitD is a math problem. It fits in with Xykon believing it should be scary, and all the powers can be accounted for by variables.

Id also like to think this is the dumbest proposal so far.

[Jasdoif]

Same, but for the sake of being even partially relevant, I sunlit that the MitD is a math problem. It fits in with Xykon believing it should be scary, and all the powers can be accounted for by variables.

Id also like to think this is the dumbest proposal so far.

I liked Aspheric's "The MitD is actually Monty Hall".

Because then the next steps are obvious: He asks if anyone has a hard-boiled egg, which of course Elan does from his potato salad...which should really be spoiled after so much time, but that doesn't bother MitD. And then it turns out Elan accidentally produced a century egg, which of course(?) is a material component for a spell that keeps things from spoiling for a hundred years. Things like rifts.

[lio45]

I submit that the hypothesis "MitD is a Glabrezu" leads to "then what we see happening in the comic is actually very likely a Monty Hall Problem situation".

If MitD is an Embodiment of Evil, then he's not sabotaging to help O-Chul and the Good Guys; therefore, he must be doing something else. What he's doing only makes sense if he's in touch with someone with good knowledge (a "higher up" ("lower down") with access to divination powers, etc.) who's able to relay to him the info that some doors (after expending divination resources on those dungeons and determining the Gate isn't in them) are "bad doors", and Monty Hall Glabrezu therefore takes them away in order to increase the odds of Team Evil of finding the Gate ASAP.

[Aspheric]

Aspheric, you're wrong about the number of doors bring "crucial", it's absolutely not. The basic problem is, there are choices, one is right, you pick blindly, then incorrect options are removed by an omniscient entity, then you're asked if you want to change your pick, and the right answer statistically is yes.

The fact that it's doors, that the prize is a car, that there are three doors, etc. are all irrelevant.

Also, if you wish to disagree with anything I said on probabilities, please point it out more precisely so I can show you it's correct.

I said it changes the chances, and that's correct, for the reasons Fyraltari pointed out. I don't know how to be any more precise than I already have been, but to be clear: my actual points don't concern the Monty Hall Problem, because that isn't what's going on. MitD is not "an omniscient entity." No one is giving TE the choice to switch, along with revealing any incorrect choices. Removing choices from the pool helps if they're incorrect choices, that's true; but MitD isn't selecting between the two. It's pretty clear that he's trying to mark the door with the Gate so that TE doesn't find it. There's no way they benefit from MitD doing this, because on the off chance that he does mark the door with the Gate, they have to start over, but won't know that until all the other doors are marked.

Again, my point isn't that MitD's actions are necessarily effective, but that they're a hindrance.

[Wizard_Lizard]

I submit that the hypothesis "MitD is a Glabrezu" leads to "then what we see happening in the comic is actually very likely a Monty Hall Problem situation".

If MitD is an Embodiment of Evil, then he's not sabotaging to help O-Chul and the Good Guys; therefore, he must be doing something else. What he's doing only makes sense if he's in touch with someone with good knowledge (a "higher up" ("lower down") with access to divination powers, etc.) who's able to relay to him the info that some doors (after expending divination resources on those dungeons and determining the Gate isn't in them) are "bad doors", and Monty Hall Glabrezu therefore takes them away in order to increase the odds of Team Evil of finding the Gate ASAP.

I think an embodiement of chaos makes more sense.

[lio45]

I said it changes the chances, and that's correct, for the reasons Fyraltari pointed out. I don't know how to be any more precise than I already have been, but to be clear: my actual points don't concern the Monty Hall Problem, because that isn't what's going on. MitD is not "an omniscient entity." No one is giving TE the choice to switch, along with revealing any incorrect choices. Removing choices from the pool helps if they're incorrect choices, that's true; but MitD isn't selecting between the two. It's pretty clear that he's trying to mark the door with the Gate so that TE doesn't find it. There's no way they benefit from MitD doing this, because on the off chance that he does mark the door with the Gate, they have to start over, but won't know that until all the other doors are marked.

Again, my point isn't that MitD's actions are necessarily effective, but that they're a hindrance.

Looks like you didn't read my posts, because you're just agreeing with everything I said (minus details like when you argue that the number of doors is crucial, etc.)

[woweedd]

I submit that the hypothesis "MitD is a Glabrezu" leads to "then what we see happening in the comic is actually very likely a Monty Hall Problem situation".

If MitD is an Embodiment of Evil, then he's not sabotaging to help O-Chul and the Good Guys; therefore, he must be doing something else. What he's doing only makes sense if he's in touch with someone with good knowledge (a "higher up" ("lower down") with access to divination powers, etc.) who's able to relay to him the info that some doors (after expending divination resources on those dungeons and determining the Gate isn't in them) are "bad doors", and Monty Hall Glabrezu therefore takes them away in order to increase the odds of Team Evil of finding the Gate ASAP.

That...doesn't sound plausible.

I think an embodiement of chaos makes more sense.

Frankly, I doubt MITD is an embodiment of anything. I mean, I doubt a purely-chaotic being would, say, stay in a box he hates or keep within a cloud of darkness he wants out of just because someone told him to. Especially given that they have no way to enforce it on him.

[Crusher]

Frankly, I doubt MITD is an embodiment of anything. I mean, I doubt a purely-chaotic being would, say, stay in a box he hates or keep within a cloud of darkness he wants out of just because someone told him too. Especially given that they have no way to enforce it on him.

Calling a Glabrezu an "embodiment of evil" really isn't specific enough. Its a demon, so it'd be an embodiment of *chaotic* evil. Expecting an embodiment of chaotic evil to only act when given specific orders to follow would be pretty unlikely.

That having been said, I agree that him being an embodiment of *anything* is unlikely, but not to the degree that I'd consider it disqualifying. Out of curiosity, what's an embodiment of True Neutrality? I assume there must be such a thing but I can't seem to find it. Anyone happen to know?

[hamishspence]

Out of curiosity, what's an embodiment of True Neutrality? I assume there must be such a thing but I can't seem to find it. Anyone happen to know?

They're called Rilmani and, in 3.0-3.5, are found in the Fiend Folio splatbook.

[Aspheric]

Looks like you didn't read my posts, because you're just agreeing with everything I said (minus details like when you argue that the number of doors is crucial, etc.)

If you can't understand why I wrote what I wrote, I don't know what to tell you. And when you make condescending remarks like this, I question why I bothered engaging you at all.

Frankly, I doubt MITD is an embodiment of anything. I mean, I doubt a purely-chaotic being would, say, stay in a box he hates or keep within a cloud of darkness he wants out of just because someone told him too. Especially given that they have no way to enforce it on him.

I wonder how much freedom you get, as a purely-chaotic being, to take lawful actions. Like, at what point do you fall from chaotic grace by not being chaotic enough? Is that even possible? I kind of like what the unlikelihood of going against one's alignment does in a narrative sense, though I'm not sure I would necessarily make that case for the Glabrezu, one way or the other.

[Grey_Wolf_c]

I wonder how much freedom you get, as a purely-chaotic being, to take lawful actions. Like, at what point do you fall from chaotic grace by not being chaotic enough? Is that even possible? I kind of like what the unlikelihood of going against one's alignment does in a narrative sense, though I'm not sure I would necessarily make that case for the Glabrezu, one way or the other.

I am of the opinion that in OotS it is physically impossible for an embodiment to go against their nature, anymore than a human can jump ten times their own height. But if they could, I'd imagine that a chaotic being that starts having a routine, or starts avoiding making decisions anew by simply doing what they decided to do the previous time the decision came up is slowly becoming lawful.

Grey Wolf

[Fitzclowningham]

I am of the opinion that in OotS it is physically impossible for an embodiment to go against their nature, anymore than a human can jump ten times their own height. But if they could, I'd imagine that a chaotic being that starts having a routine, or starts avoiding making decisions anew by simply doing what they decided to do the previous time the decision came up is slowly becoming lawful.

Grey Wolf

A Chaotic being can have preferences. You can have the same breakfast every day and still be Chaotic. It's the prioritizing of personal preferences over convention that makes Chaos Chaotic.

[Wizard_Lizard]

A Chaotic being can have preferences. You can have the same breakfast every day and still be Chaotic. It's the prioritizing of personal preferences over convention that makes Chaos Chaotic.

Do you not roll dice tosee whether you have toast with butter, toast with jam, cereal, etc.?

[woweedd]

A Chaotic being can have preferences. You can have the same breakfast every day and still be Chaotic. It's the prioritizing of personal preferences over convention that makes Chaos Chaotic.

But that's the thing: MITD doesn't want to stay in his box or darkness. If he were pure Chaos, i'd expect him to have stepped out by now. He only stays because of the orders he was given, certainly not a Chaotic mentality.

[Wizard_Lizard]

But that's the thing: MITD doesn't want to stay in his box or darkness. If he were pure Chaos, i'd expect him to have stepped out by now. He only stays because of the orders he was given, certainly not a Chaotic mentality.

But what if the most chaotic thing is to defy expectatiojs of how you shoud be?
In that sens mitd is past chaos and out the other side!

[Fyraltari]

Isn’t that Lawful?

[Kashem]

Re: All of the statistics:

What we are looking at is fundamentally the difference between Random with replacement and Random without replacement.

If MitD wasn't marking doors, then Team Evil would be running a Random without replacement search. Their odds would improve every single time they picked, because they would know that the gate was in the remaining doors, or they would have found it. If there were 5 doors, then their odds would be 1:5, then 1:4, then 1:3, then 1:2, then 1:1. At the end, they are guaranteed to find the gate.
With MitD marking doors, it basically becomes a Random with replacement search. If there are 5 doors, TE picks one, and MitD marks the other 4 so they can't remember which one they picked, then no matter how many rounds of that you go, Team Evil will keep having that 1:5 chance. There is no longer any guarantee, at all, that they will ever find the right door (though the odds say that eventually, they almost certainly will)

This scales up to as many doors as you want it to. After 100 doors, Team Evil will be no closer to finding the gate than it was at door 1. If they had successfully marked the doors, then they would be closer, and have better odds, no matter how many doors there are. They have basically lost the knowledge that the doors that they marked definitely don't have the gate behind them.

Re: the straw picking analogy:
The flaw in the analogy was the thought that your next pick had a 1:100 chance if you weren't interfered with. After picking 1 straw, your next pick would have a 1:99 chance. In fact, if you keep your straw, then no matter how many extras are removed, your next would still have a 1:99 chance. The magic happens when, after some number of picks, you run out of choices. At that point, instead of continuing to get better odds, your odds RESET, because we have to add ALL of the straws back, including the ones you picked.

[Hardcore]

Does MitD know about this?

[Crusher]

They're called Rilmani and, in 3.0-3.5, are found in the Fiend Folio splatbook.

Oh, that's right. Thank you. I knew about them at one point but completely forgot.

[Wizard_Lizard]

Does MitD know about this?

Yes. Mitd is actually a super genius who hdes behind the facade of a loveable murder machine who likes soup.

[Kish]

In the highly unlikely case this wasn't mentioned many times: Giant is usually pretty consistent when it comes to speech bubble color from what I can mostly tell.
Therefore, MitD is not of the Undead, or Good or Evil Outsider types. I'm not sure if the blue bubble represents Elementals, neutral Outsiders, or what though.
Sorry if I'm necroing this thread, just thought I'd throw my coins into the very full jar.

Malack begs to differ.

Also, and much more prominently as she never has a black speech bubble no matter how overtly she's being a demon, Sabine.

[woweedd]

Also, and much more prominently as she never has a black speech bubble no matter how overtly she's being a demon, Sabine.

To be fair, that might just be for the sake of consistency, as Rich had yet to establish that convention during her early appearances.

[Aspheric]

Also, and much more prominently as she never has a black speech bubble no matter how overtly she's being a demon, Sabine.

I always felt like the differently coloured speech bubbles represented the tenor/sound/other magical effects of a voice. Presumably, most mortals that a succubus would try and seduce are attracted to other mortals. Given that she also has to disguise as mortals, it makes sense that her voice is represented visually in the comic as any other human/dwarf/elf/etc., and not have any weird booming, echoing qualities that scream "I AM AN OUTSIDER."

A Chaotic being can have preferences. You can have the same breakfast every day and still be Chaotic. It's the prioritizing of personal preferences over convention that makes Chaos Chaotic.

Wouldn't a being of Pure Chaos prefer a morning routine that isn't ruled by convention?