OOTS #1041 - The Discussion Thread

[DaggerPen]

And herein lies the best paladin class ability of all: summon conscience.

That'll do, Monster-san. That'll do.

[Trillium]

I hope Giant got some experience for killing the speculuation what those boots do. Kidding-kidding.


On a serious note, we now know that whatever MitD is, he leaves no footprints (even though he can stomp, somehow).

[blunk]

Here's the way I see it.

Here's a concrete example with 100 doors.

With no interference, it will take on average 50.5 picks to pick the right door.

If the MitD painted a door at random before they started (assume that nobody notices and that in the future nobody will remember which one he painted):

Painted wrong one (99% chance): average of 50 picks.
Painted right one (1% chance): 99 picks (to get all the wrong doors) + 50.5 picks to start over and get the right one

The average number of picks would be .99 * 50 + .01 * (99 + 50.5), or 50.995 picks, obviously greater than 50.5.


Edit to add: also, as I think Kish is saying, if painting random doors on average helped find the right door, it would be a great strategy for improving odds, yet we've pretty much established (in your thread) that "linear search" is the most efficient method and can't be improved upon.

[Jetstream]

Did anyone else notice that the MiTD has at least three limbs of different levels across its body?

And I swear we just saw him grow taller than Medium in the latter panels...

It might not have any limbs at all. Maybe it's a telekinetic creature. Are there any darkness shrouded telekinetic hover things? :P

[mantisshrimp]

It might not have any limbs at all. Maybe it's a telekinetic creature. Are there any darkness shrouded telekinetic hover things? :P

Yeah I think telekinesis is likley

[ti'esar]

Huh, so people were correct: the MitD is sabotaging Team Evil. I wonder how many doors they've actually tried?

I wonder how Xykon found magic boots in a dungeon populated entirely by monsters.

[Kish]

Think so?

Here's the way I see it.

Again, does that lead to "Xykon and Redcloak should randomly paint over 3 doors they haven't been in every day," and is that a conclusion you're willing to support?

And if not, why not?

[Sybarith]

: We should be trying to devise a logical search pattern, rather than just picking at random every night.

And Zykon gets hoisted by his own petard!
#RedcloakWasRight

[aurilee]

I wonder how Xykon found magic boots in a dungeon populated entirely by monsters.

Dead adventurers?

[mneme]

I wonder how Xykon found magic boots in a dungeon populated entirely by monsters.

Some monsters wear shoes. Hell, in this case the monsters are the ones doing the adventuring! And some of these monsters are Epic (or at least in the high teens), thus possibly shapeshifting.

The other plot point, though, is that Xycon now has boots of Free Movement. So maneuvers like picking him up and throwing him into a gate won't work again--because that's a grapple.

[Sybarith]

I wonder how Xykon found magic boots in a dungeon populated entirely by monsters.

In this setting? Not at all surprising.

[Great Dane]

Someone has predicted that the lessons MitD learned while playing Go might be helping him here, right?

[Taffimai]

So no footprints to the other painted doors — MitD either has long arms or flight?

I came here just to join the crowd of "ooohh, no footprints!"

With regards to the question of the MitD: if he picks three doors a day where Xykon picks one, and he does so each time after already knowing one wrong pick, the MitD has a much higher chance of painting over the correct door than Xykon has of ever finding it.

[enh]

The value of an independent variable, indeed! Nice layered meaning there.

O-chul would be proud to see the fruits of all their conversation.

[pendell]

Again, does that lead to "Xykon and Redcloak should randomly paint over 3 doors they haven't been in every day," and is that a conclusion you're willing to support?

And if not, why not?

It might be a good idea to mark them in some other color so that you know you're temporarily skipping over them. But the probability of restart , no matter how low, would be enough to preclude any search team from doing this deliberately. Nonetheless, I stand by my conclusion that the MITD may wind up inadvertently helping them by eliminating false choices.

I will, however, acknowledge that there is probably a breaking point in the search where painting over additional doors will hinder xykon and company and greatly increase the possibility of restart -- I'm guessing after they've covered at least half of the space.

Respectfully,

Brian P.

[ericgrau]

So the other X's didn't appear on the other doors by magic? They look like they might be mirror images of the original X but I'm not sure.

Btw, their selection is random except that they don't go to the same door twice. That will continue to be the case and the extra X's will have no effect at all on probability until they run out of doors. Once they run out of doors, assuming they haven't found the gate by then, then their chance of finding the gate is hurt because they might be forced to guess the same door twice. So could have no effect, could reduce chance of finding gate, on average those combined reduce chances of finding gate and delay the search. Sure by luck they could find the gate tomorrow or they could have terrible luck, but I mean on average.

[aurilee]

It might be a good idea to mark them in some other color so that you know you're temporarily skipping over them. But the probability of restart , no matter how low, would be enough to preclude any search team from doing this deliberately. Nonetheless, I stand by my conclusion that the MITD may wind up inadvertently helping them by eliminating false choices.

I will, however, acknowledge that there is probably a breaking point in the search where painting over additional doors will hinder xykon and company and greatly increase the possibility of restart -- I'm guessing after they've covered at least half of the space.

Respectfully,

Brian P.

But...by just choosing to not choose those doors, isn't that the same effect in the end of just not choosing the doors during your random selection? Especially if you intend to start over. That's basically the same as if those doors were by-chance chosen last.

The way I see it, Xykon/RC and MitD are both doing the same thing: randomly selecting doors in the hopes that one holds the gate. The only difference is that Xykon/RC are doing one (maybe two?) per day, but MitD is doing at least three per day. That gives MitD a greater chance of picking the right door than Xykon/RC.

[busterswd]

Huh. Those last few panels gave me goosebumps (the good kind).

[Shining Wrath]

1. MitD is sabotaging Team Evil
2. MitD leaves no footprints
3. MitD can quickly reach 2nd story doors
4. Xykon enjoys killing things just a little too much. It may be his weakness.
5. Boots of Free Motion are, in fact, sweet. Even without the toe bones benefit.
6. Redcloak is the limiting factor on the progress of Team Evil. I wonder how difficult it would be for Xykon to replace him?

[Toper]

Nonetheless, I stand by my conclusion that the MITD may wind up inadvertently helping them by eliminating false choices.

That doesn't make sense. The only way to help Team Evil would be to increase the probability that they select the correct door on any given day. I'm not going to do the math, but it should be intuitively obvious that painting random X's leaves that probability unchanged -- sure, there's a chance that the MITD redirects the search from a wrong door that they would have chosen to the correct door, but it's exactly balanced by the chance of redirecting from the correct door to a wrong one, because Team Evil is still choosing totally at random even if the MITD randomly eliminates some options.

[Roland Itiative]

It's narrowing the overall search space, but not improving any chances at all. Yeah, tomorrow Team Evil will have three less doors to choose from, but this doesn't really improve their chances, because these three doors are just as likely to be the right one as any door they choose.

Basically, if we assume that TE explores one door, and MitD paints three extra doors every single day (unlikely, as that would be easily spotted on the first days), the MitD has odds that are 3 times better to "win". Not a guaranteed win, but higher odds nonetheless.

If the logic of "explore one door, paint four" increased the odds of finding the right door, it would become an optimal strategy, which it very clearly isn't.

[Kish]

It might be a good idea to mark them in some other color so that you know you're temporarily skipping over them.

Okay, this is what I thought you'd realized didn't work in the thread you started.

There is no functional difference, as long as they don't have the ability to go straight to the correct door, between "open the one to the right" and "open the one four places to the right." None. If you mark a door in some other color as "temporarily skipped," that color means exactly the same thing as no color at all--it means that it's a random door which you haven't been in. You seem oddly convinced that a door that they skip, whether deliberately or accidentally, is less likely to hold the Gate than a door that they don't skip. If they happen to go to the correct door tomorrow, you can arbitrarily say that if the creature hadn't falsely marked three doors they would have picked one of those doors, but that's what it is--arbitrary. There is no logic to the argument that skipping three randomly chosen doors helps them when the creature in the darkness chooses the doors and they do so unknowingly but wouldn't help them if they chose the doors and did so knowingly; if you see why it wouldn't help them to skip random doors you should apply that to the current situation.

[ChillerInstinct]

...You sneaky blighter. I'm proud of you, MitD. Let's just hope that this doesn't accidentally accelerate Team Evil's progress, though... it's entirely possible that all of those falsely X-offed doors were the wrong ones...

[Jasdoif]

Question for the math types: I suspect there's a curve of diminishing returns as X decreases over time where marking off additional doors makes it more likely we will eliminate the correct door -- that being directly tied to the probability we will find the correct door in the first place. But I should think this wouldn't make sense until you'd already covered most of the search space.

You're more likely to mark off the correct door as more doors get marked off, yes. However, at any point in time, the odds are exactly the same for a door being examined by Team Evil to be the correct door as they are for a door being superficially marked by MitD to be the correct door. If the goal is to prevent Team Evil from finding the correct door, there's no sense in delaying the mark off process to increase the odds of Team Evil finding the correct door before the process is ever started.

If you want good odds that the correct door is superficially marked off, that's easy: mark off over half of the remaining doors in one session. That's likely to cause problems outside the search procedure though (ie Redcloak or Xykon are bound to notice).

[Tvtyrant]

"Bitter fruit of eternal despair"
"Also certain berries!"



Love it! Who's up for a spinoff comic of just these two? It's like Abbot and Costello, only with fangs.

Still...

I get what the MITD is doing. He's painting over additional doors in order to prevent the monsters inside from getting killed by Xykon and crew. He's very compassionate.

But in this case that compassion may prove to be his undoing. Unless he happens to paint over the correct door, he's narrowing the search space by eliminating additional false doors, hastening Team Evil's eventual discovery of the gate.

Strong, compassionate ... but not yet wise. A child, maybe.

Respectfully,

Brian P.

The Monster is right here. As far as his experience goes, nothing is capable of fighting Xykon. Since no one is going to be able to stop them, speeding up the search is a meaningless variable as they will inevitably reach the right one. Given a small chance that they finish all of the doors and then decide this was a bust, the Monster is taking the only possible route where Xykon is foiled.

[Bucky]

Painting a door with an X without searching it doesn't affect the probability that the gate is behind any specific unpainted door. This should be obvious.

So the MitD's gambit has no effect whatsoever on the search's progress until they run out of unpainted doors.

[Euclidodese]

"I love this arc so muuu-uuuch!"

Sabotaging by painting multiple gates doors... someone is getting tricky.

But took me a bit of "I must be missing something" until I realized what he did.

Aaaaaaah. Now I get it... I would have noticed eventually, but thanks. A winner is you. (Originally I thought it was some weird joke about something mundane being overly hyped up by getting loads of panels.)

And we now know what Xykon's boots do. Not terribly useful against the OotS.

They would have been good for when Tsukiko was alive, in case she went in for an unwanted hug.

[Euclidodese]

Painting a door with an X without searching it doesn't affect the probability that the gate is behind any specific unpainted door. This should be obvious.

So the MitD's gambit has no effect whatsoever on the search's progress until they run out of unpainted doors.

But at least there's a chance, that the gate will be under one of those wrongly-ticked doors, and then they won't know that they haven't checked all the tunnels, they'll think they have, so they may think Serini tricked them, that the gate isn't here at all... They might leave, search the world for clues of the 'true' gate location.

[Adaon Nightwind]

I love me some Monster in the Darkness. :)

I wonder how Xykon found magic boots in a dungeon populated entirely by monsters.

If i may refer you here, to the last panel :

http://www.giantitp.com/comics/oots1029.html

[Shining Wrath]

"Bitter fruit of eternal despair"
"Also certain berries!"



Love it! Who's up for a spinoff comic of just these two? It's like Abbot and Costello, only with fangs.

Still...

I get what the MITD is doing. He's painting over additional doors in order to prevent the monsters inside from getting killed by Xykon and crew. He's very compassionate.

But in this case that compassion may prove to be his undoing. Unless he happens to paint over the correct door, he's narrowing the search space by eliminating additional false doors, hastening Team Evil's eventual discovery of the gate.

Strong, compassionate ... but not yet wise. A child, maybe.

Respectfully,

Brian P.

Think so?

Here's the way I see it.

Let X be the total number of doors. Let Y be the number of doors the MITD paints.

The probability that he will paint over the correct door is therefore (Y/X), where Y << X , correct?

The probability that he has painted over only false doors, by contrast, is (1-Y)/X. If Y << x, then 1-Y/ is much, much closer to X. In other words, a much higher probability.

So the probability that the MITD will mark the correct door as false is very low -- the probability that he is eliminating additional false doors is very high. Thus, absent some truly remarkable fortune, he is inadvertently helping team evil.

This assumes that MITD does not actually know where the correct door is already through his preternatural senses -- in which case the plan is perfectly sound.

Question for the math types: I suspect there's a curve of diminishing returns as X decreases over time where marking off additional doors makes it more likely we will eliminate the correct door -- that being directly tied to the probability we will find the correct door in the first place. But I should think this wouldn't make sense until you'd already covered most of the search space.

Respectfully,

Brian P.

Two observations:
First, if there are N doors, then if no false marks are made we know that in a maximum of N trials (1 per night, probably) Team Evil finds the gate. With F false marks, though, there is a change P=F/N that Team Evil will conduct (N-F) trials, realize that all the doors are marked, and then start over again (or give up and conclude the Gate is not within the dungeons at all).
In the first case, all the monsters behind every door Team Evil opens, die. In the second case, the monsters behind F doors may live. I suspect the MitD is motivated in part by sympathy for the slaughtered monsters, and that would matter to him.