DM's who want you to Roleplay but can only say "No."

[Mr Beer]

Actually, you misunderstand it as well. It's never guaranteed.

The thing is - choosing the first door has a 33% chance of getting you the item. Choosing the second door gives you a 50% chance of getting the item. It's easier to visualize if you have 100 or more doors, and they open all but one other door.

I wasn't aware of this Monty Hall problem until they ran it on Mythbusters, I was (loudly) sure at the start of the trial that switching doors couldn't possibly increase your odds of picking the prize. Even now it's something I have to think though again in order to understand because it seems crazy on the face of it that changing your choice from door x to door y increases your chances of being correct.

The '100 doors' thing does help.

[Susano-wo]

alright then, you guys are going to have to math me. (or inform me of a circumstance I am unaware of)
You pick 1 out of 1,2, or 3. Your chance is 33% They open door 3. Prize is not there. You have a choice: door 1 or 2. Either is 50%. The probability is not different at this point, whether you pick door 1 or door 2. 50% either way.

There is no way, barring some other data that I might be unaware of, that the probability changes if you do not "change" choices

[Mr Beer]

You pick a door, 33% it's the right choice. Dealer shows you a different door which is the wrong choice. If you decide to switch to the third door (which you didn't pick and dealer didn't show), you have a 50% chance of being right. So you improve your chances by switching doors.

[Hiro Protagonest]

You pick a door, 33% it's the right choice. Dealer shows you a different door which is the wrong choice. If you decide to switch to the third door (which you didn't pick and dealer didn't show), you have a 50% chance of being right. So you improve your chances by switching doors.

But... on the second choice, don't you also have a 50% chance of having the right door if you don't switch?

[Susano-wo]

But... on the second choice, don't you also have a 50% chance of having the right door if you don't switch?

exactly. you are re-evaluating the situation based on new data. That's why I quoted "changing." You are not changing or keeping, but making a new choice between the remaining 2 doors.

[Sith_Happens]

alright then, you guys are going to have to math me. (or inform me of a circumstance I am unaware of)
You pick 1 out of 1,2, or 3. Your chance is 33% They open door 3. Prize is not there. You have a choice: door 1 or 2. Either is 50%. The probability is not different at this point, whether you pick door 1 or door 2. 50% either way.

There is no way, barring some other data that I might be unaware of, that the probability changes if you do not "change" choices

The trick is to chart all the ways the situation can play out.

[jaydubs]

Think about the Monty Haul problem this way. What are your odds of picking the prize door using each of the methods? Consider the entire process from start to finish, rather than the individual choices.

If you stick with the door you pick at the beginning, you only get it right if you pick the prize door immediately. Your chance of picking the prize door out of 3, is 1/3.

If you switch doors, you end up with the prize door whenever you don't pick the prize door at first. If you start with the prize door, you'll switch to a false door. If you start with a false door, the second false door gets eliminated, and you end up on the prize door. So your chance of ending up on the prize door is equal to your chance of initially picking a false door - i.e., 2/3.

[Sartharina]

But... on the second choice, don't you also have a 50% chance of having the right door if you don't switch?

No. You still have the original 33% chance, because your initial decision is unchanged.

Again - replace three doors with 1,000,000,000 doors, and the dealer opens all but one of them.

[Knaight]

Actually, you misunderstand it as well. It's never guaranteed.

The thing is - choosing the first door has a 33% chance of getting you the item. Choosing the second door gives you a 50% chance of getting the item. It's easier to visualize if you have 100 or more doors, and they open all but one other door.

I said "you are guaranteed to pick correctly within that set if the wanted object is in that set*". If it's within the door you picked the first time, then switching obviously doesn't produce it. Moreover, that 50% chance is incorrect, the chances are 1/3 and 2/3 between the first door and the second door (representing both of the other two doors). At no point did I, or anyone else, claim that there was any way that one was guaranteed to get the wanted object if it was anywhere in the initial problem space. Though I will say that the odds of getting it asymptotically approach 1 as the number of doors approach infinity.

*Another way to put this would be that if you switch you won't accidentally pick one of the doors that you already know to be wrong.

[goto124]

I've been in situations where players essentially say 'Bow before me, for I am High Lord of Something, and kiss my feet. Else you suffer', and keep true to their promise. It is realistic, but...

Has any one encountered this kind of DM?

[Jay R]

alright then, you guys are going to have to math me. (or inform me of a circumstance I am unaware of)
You pick 1 out of 1,2, or 3. Your chance is 33% They open door 3. Prize is not there. You have a choice: door 1 or 2. Either is 50%. The probability is not different at this point, whether you pick door 1 or door 2. 50% either way.

There is no way, barring some other data that I might be unaware of, that the probability changes if you do not "change" choices

The data you are unaware of is given to you by the rule which states that Monty will always open a door after you first choose, and that door will never be the one with the prize. Therefore Monty gave you some information based on the fact that he knows where the prize is. You can exploit that fact.

Specifically, if you chose wrong originally (2/3 probability), Monty will show you the second wrong choice. That leaves only the right choice, if you switch.

Assume you originally choose door A. One of three scenarios plays out, with equal probability.
1. The prize is behind door A. Monty opens either B or C (it doesn't matter). If you switch, you lose.
2. The prize is behind door B. Monty is required by the rules to open C. If you switch, you win.
3. The prize is behind door C. Monty is required by the rules to open B. If you switch, you win.

That's two chances out of three to win by switching - because Monty's action gave you new information.

[Susano-wo]

The data you are unaware of is given to you by the rule which states that Monty will always open a door after you first choose, and that door will never be the one with the prize. Therefore Monty gave you some information based on the fact that he knows where the prize is. You can exploit that fact.

Specifically, if you chose wrong originally (2/3 probability), Monty will show you the second wrong choice. That leaves only the right choice, if you switch.

Assume you originally choose door A. One of three scenarios plays out, with equal probability.
1. The prize is behind door A. Monty opens either B or C (it doesn't matter). If you switch, you lose.
2. The prize is behind door B. Monty is required by the rules to open C. If you switch, you win.
3. The prize is behind door C. Monty is required by the rules to open B. If you switch, you win.

That's two chances out of three to win by switching - because Monty's action gave you new information.

Thank you for the detailed explanation. But its still wrong. :P (I know, I know, it's widely accepted but I am still arguing. sorry >.<)

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The choice is between door number 1 and door number 2. was it unlikely that you picked right initially? yes. does that change the probability that you are choosing between 2 equally possible choices now? no. Each choice is independent.

Its like the difference between what your chances are to roll nat 20 twice in a row, vs your chance on either or 2 rolls. Your chance to roll 20 is always 5%, no matter how many 20s were rolled before that, but the aggregate probability that the overall occurrence could happen is much lower.

In the Hall problem, you have already made the first choice, in which you either conformed to probability (picked wrong door) or did not (picked right door.) that part is done, and now you have a new choice, with a 50 50 chance. The second door is not 2/3, because 3 is no longer really a choice, only 1 and 2 are.
Sorry if I appear belligerent, but I just cant see the logic in the proposed probabilities.

[Hiro Protagonest]

The data you are unaware of is given to you by the rule which states that Monty will always open a door after you first choose, and that door will never be the one with the prize. Therefore Monty gave you some information based on the fact that he knows where the prize is. You can exploit that fact.

Specifically, if you chose wrong originally (2/3 probability), Monty will show you the second wrong choice. That leaves only the right choice, if you switch.

Assume you originally choose door A. One of three scenarios plays out, with equal probability.
1. The prize is behind door A. Monty opens either B or C (it doesn't matter). If you switch, you lose.
2. The prize is behind door B. Monty is required by the rules to open C. If you switch, you win.
3. The prize is behind door C. Monty is required by the rules to open B. If you switch, you win.

That's two chances out of three to win by switching - because Monty's action gave you new information.

Actually, 1 is 1 and 2, then 2 and 3 are 3 and 4.

1. The prize is behind door A. Monty opens door B. Switch, you lose.
2. The prize is behind door 1. Monty opens door C. Switch, you lose.

[BRC]

Thank you for the detailed explanation. But its still wrong. :P (I know, I know, it's widely accepted but I am still arguing. sorry >.<)

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The choice is between door number 1 and door number 2. was it unlikely that you picked right initially? yes. does that change the probability that you are choosing between 2 equally possible choices now? no. Each choice is independent.

Its like the difference between what your chances are to roll nat 20 twice in a row, vs your chance on either or 2 rolls. Your chance to roll 20 is always 5%, no matter how many 20s were rolled before that, but the aggregate probability that the overall occurrence could happen is much lower.

In the Hall problem, you have already made the first choice, in which you either conformed to probability (picked wrong door) or did not (picked right door.) that part is done, and now you have a new choice, with a 50 50 chance. The second door is not 2/3, because 3 is no longer really a choice, only 1 and 2 are.
Sorry if I appear belligerent, but I just cant see the logic in the proposed probabilities.

I think Part of it is that Monty always opens
1) A door with a goat
2) A door that you did not choose.

This means that if you didn't pick the right door, Monty does not get to choose which door to open. He only gets to choose which door to open if you picked the door with the car.

So, there is door one, Two, and Three.

You pick door One.

If Door one has the car behind it (1/3rd), Monty gets his choice between opening doors Two or Three.
If Door Three has the car behind it, Monty MUST open Door Two.

So, in the second choice, it makes more sense to switch because there is a 2/3rds chance you were wrong the first time, which means there is a 2/3rds chance that the prize is behind door 3.

You're looking at the probabilities at the wrong time.

The logic goes like this.
Doors A, B, And C, where Door A is always the door that you pick first.
Doors X, Y, and Z. Where X and Y have goats, and Z has the prize.
Monty opens Door M.

Given the following:
M!= A and M !=Z

If A=Z, then M= B or C

Therefore
If A= X, M=Y. Z!=M and Z !=A
If A=Y, M=X, Z!=M And Z!=A
If A=Z, then M= X or Y=B or C

There is a two-thirds chance that you forced Monty to select the only door that was neither A nor Z. Once you're there, you know which door is door Z.

[Jay R]

Actually, 1 is 1 and 2, then 2 and 3 are 3 and 4.

1. The prize is behind door A. Monty opens door B. Switch, you lose.
2. The prize is behind door 1. Monty opens door C. Switch, you lose.

Those two combined have a probability of one third - the probability that you picked the right door initially. You've split it into four possibilities, but not four possibilities of equal probability.

Thank you for the detailed explanation. But its still wrong. :P (I know, I know, it's widely accepted but I am still arguing. sorry >.<)

Spoiler

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[/url]

The choice is between door number 1 and door number 2. was it unlikely that you picked right initially? yes. does that change the probability that you are choosing between 2 equally possible choices now? no. Each choice is independent.

Its like the difference between what your chances are to roll nat 20 twice in a row, vs your chance on either or 2 rolls. Your chance to roll 20 is always 5%, no matter how many 20s were rolled before that, but the aggregate probability that the overall occurrence could happen is much lower.

In the Hall problem, you have already made the first choice, in which you either conformed to probability (picked wrong door) or did not (picked right door.) that part is done, and now you have a new choice, with a 50 50 chance. The second door is not 2/3, because 3 is no longer really a choice, only 1 and 2 are.
Sorry if I appear belligerent, but I just cant see the logic in the proposed probabilities.

You don't appear belligerent - just mistaken.

Consider the following nine cases, all equally likely:

You picked A; prize in A. Either B or C has been opened. Switching is bad.
You picked A; prize in B. C has been opened, switching is good.
You picked A; prize in C. B has been opened, switching is good.
You picked B; prize in A. C has been opened, switching is good.
You picked B; prize in B. Either A or C has been opened, switching is bad.
You picked B; prize in C. A has been opened, switching is good.
You picked C; prize in A. B has been opened, switching is good.
You picked C; prize in B. A has been opened, switching is good.
You picked C; prize in C. Either A or B has been opened, switching is bad.

2/3 chance that switching is good, because if you picked wrong first, you were given new information.

If you won't accept the word of a Statistics instructor, then I suggest that you actually try it. Run 1,000 cases in which you choose randomly, Monty opens a worthless door, and then you switch.

[jaydubs]

How about this. You've got some kind of pachinko type machine, where a steel ball drops down into one of two funnels. The left funnel is half the size of the right funnel, so the ball is twice as likely to land in the right funnel. The left funnel eventually drops the steel ball into box 1, while the right funnel eventually drops the steel ball into box 2.

So even though there are 2 boxes, and the ball could end up in either, it's more likely to be in box 2.

That's basically the Monty Hall problem, except instead of funnels you have a door elimination process. The door you initially choose is box 1, and the door you haven't chosen (and that Monty hasn't opened) is box 2.

[BRC]

I think the issue with the Monty Hall problem is how it is normally presented.

"You pick Door A, Monty opens Door B, revealing a goat. Should you switch to Door C?"
Which makes it sound as if you are standing in front of three physical doors labeled A, B, and C from left to right. What is described is not a sequence of events so much as the rules of the game.

There will ALWAYS be a Door A, which you picked, a Door B, which is opened to reveal a goat, and a Door C, which is neither picked nor opened.

[Milo v3]

I've been in situations where players essentially say 'Bow before me, for I am High Lord of Something, and kiss my feet. Else you suffer', and keep true to their promise. It is realistic, but...

Has any one encountered this kind of DM?

Yeah, I didn't last long in that game though (in-character and out-of-character).

[Mr Beer]

But... on the second choice, don't you also have a 50% chance of having the right door if you don't switch?

No. You are better off switching doors.

[Amphetryon]

Between two campaigns I'm currently playing in I can recall at most three "challenges" where a relatively clean victory didn't seem like a foregone conclusion (at least to me), and there most certainly haven't been any major tragedies in either, yet the whole group is still having a blast. Why? Because things have been sunshine and rainbows despite the DMs maintaining what at least seem on the surface to be reasonable difficulty and drama levels.

When the dice are consistently stacked in the protagonists' favor in a story it's generally due to poor writing. When the dice are consistently stacked in the protagonists' favor in an RPG it's generally (or at least hopefully) because the players made it so,* and it usually feels damn good.

* There is a line to tread here; if the players are so soundly blowing through everything that they no longer feel like they have to be trying to do so, then the game should be harder.

If you make the game harder, then you're increasing the amount of suffering - certainly the amount of potential suffering - the characters are undergoing. Given that causing them any suffering is apparently contrary to the point, and those that disagree are

twit[s]. . . so far off base he scored a touchback... and it's not even relevant to RPGs

, it matters not if the GM is causing the suffering, or if the players/characters are voluntarily "throwing themselves at pathos." If causing suffering of any sort - and, note there was no nuance given in the quoted statement, so assuming any is putting words in Sartharina's mouth - is not relevant to the game, and doing so makes one a 'twit,' then I'm still genuinely curious as to how one progresses any game of this type without it. Conflict is not viable, because conflict is a type of suffering.

[Solaris]

If you make the game harder, then you're increasing the amount of suffering - certainly the amount of potential suffering - the characters are undergoing. Given that causing them any suffering is apparently contrary to the point, and those that disagree are , it matters not if the GM is causing the suffering, or if the players/characters are voluntarily "throwing themselves at pathos." If causing suffering of any sort - and, note there was no nuance given in the quoted statement, so assuming any is putting words in Sartharina's mouth - is not relevant to the game, and doing so makes one a 'twit,' then I'm still genuinely curious as to how one progresses any game of this type without it. Conflict is not viable, because conflict is a type of suffering.

You're confusing 'challenge' and 'suffer'. Stop doing that.

A challenge is when you make something hard. Suffering is when you're making something hard on someone.

[Jay R]

But... on the second choice, don't you also have a 50% chance of having the right door if you don't switch?

No, but until you study conditional probability, and learn Bayes' rule, it will always seem counter-intuitive. (Or take the easy way and try 1,000 trials.)

I just ran 10,000 trials. By always switching, I won 6,592 times. That gives a 95% confidence interval of .6500 - .6685 for the probability of winning with that strategy.

But don't take my word for it. Run the trials yourself. It only took me about twenty minutes in Excel.

[comicshorse]

Or let James May do the experiment for you (with beer !)

https://www.youtube.com/watch?v=tvODuUMLLgM

[Nagash]

I've been in situations where players essentially say 'Bow before me, for I am High Lord of Something, and kiss my feet. Else you suffer', and keep true to their promise. It is realistic, but...

Has any one encountered this kind of DM?

players like the characters say that to an NPC? If so how does it involve the DM?

[Milo v3]

players like the characters say that to an NPC? If so how does it involve the DM?

Players (that were effectively DM's for the medium he was in) said it to his character iirc.

[goto124]

players like the characters say that to an NPC? If so how does it involve the DM?

Players (that were effectively DM's for the medium he was in) said it to his character iirc.

Milo's right. Technically player-to-player, but the effectively-DM players were indeed High Lords/Ladies of Something, and wielded huge power over other characters. The real DM (the person who actually controls the game) had intentionally set things up that way. They would've said the same thing IC and OOC: 'So you don't want to kiss my character's feet? Bugger off to another game'.

[comicshorse]

At which point you bugger off (or start long term planning for assassinating their characters)
Though was it that bad, I've played in a game where half the P.C.s were ghouls in service to the other P.C.s Vampires and there is all the difference in the world between 'pay respect to my high position' and 'grovel like a worm'.

[goto124]

At which point you bugger off (or start long term planning for assassinating their characters)

I wonder how that would've worked. Suffice to say that if you hate them, you'll probably get sick of the game long before your character's strong enough to even think about assassinating them.

Though was it that bad, I've played in a game where half the P.C.s were ghouls in service to the other P.C.s Vampires and there is all the difference in the world between 'pay respect to my high position' and 'grovel like a worm'.

It's a blurry line I guess. What is 'pay respect to my high position' to one person is 'grovel like a worm' to another. There's also the thing that it's an imaginary game, not an actual society, so I set the bar for 'grovel like a worm' to be much lower than RL. Especially when dealing with PCs, who are there for the sole purpose of having fun.

That said, how does your game work to solve that problem? Mutual respect between players would be essential, but how would the system encourage such a thing?

[comicshorse]

I wonder how that would've worked. Suffice to say that if you hate them, you'll probably get sick of the game long before your character's strong enough to even think about assassinating them.

You only need to be as strong as them if you're in a fair fight. Poison their drinks, hire assassins, back stab them in their sleep, etc. That said if the GM is happy with this power disparity any plan is probably going to be made to fail no matter how good it is

It's a blurry line I guess. What is 'pay respect to my high position' to one person is 'grovel like a worm' to another. There's also the thing that it's an imaginary game, not an actual society, so I set the bar for 'grovel like a worm' to be much lower than RL. Especially when dealing with PCs, who are there for the sole purpose of having fun.

That said, how does your game work to solve that problem? Mutual respect between players would be essential, but how would the system encourage such a thing?

Indeed the particular group this occured with have been playing for years and so trust each other not to abuse the position of being in power over the other players. This wasn't a single time we've had this challenge though in lots of games we've had to have a team leader : in Serenity the owner of the ship everybody worked for, in 'Warhammer' the Count that employed the P.C.s as his retinue, etc. The thing is to wield the authority while still respecting the other P.C.s and it can lead to some interesting RP'ing. Again this has to be with players you trust, I've had some storming arguments IC with other players but then still been able to laugh about it after the game is over..
In the Vampire game the system really worked against such a thing as not only are the Vampires much more powerful than the Ghouls but the Blood Bond ensures the Ghouls are emotionally manipulated to care for their master. It raised some interesting RP'ing, particularly as my Ghoul was a huge Mafia thug in a game set in the 50's in service to a bookish, female Vampire.
Fundamentally it isn't something that can be forced, the players must be willing to accept that somebody will be in a position of authority over them for the game to work. If they're not comfortable with it then its time for the GM to rethink the game

[goto124]

You only need to be as strong as them if you're in a fair fight. Poison their drinks, hire assassins, back stab them in their sleep, etc. That said if the GM is happy with this power disparity any plan is probably going to be made to fail no matter how good it is

The mechanics of the game were... unforgiving. Poison? If you even know how to make a successful poison without killing yourself - you're going to find very little help on 'forbidden skills' like thievery. Hire assassins? Who? Caan you even find an NPC who'll do this sort of thing? Other PCs? Money's useless when you risk losing your hard-earned character. Back stab in their sleep? Good luck getting into their castles, which have real defenses for exactly this reason. Also, how are you going to learn to backstab? Again, forbidden thievery skills means it's the HIGHER-UPs who have them (because no one can stop them, and they're the ones who made the skills 'forbidden' in the first place). They will dodge your attack and then kill you. Which goes back to the 3rd sentence in that quote I guess.

You can wait for the person to go out alone, throw a spell at the person and kill him instantly (funnily enough, viable in game). But then you'll have to hide his soul somewhere, otherwise all his underlings (all exprienced PCs not to be trifled with) will go all out to look for him, and ressurect him. They can find his soul even if it's in the depths of a dangerous dungeon. You could opt to try destroy his soul, since you're going to die anyway. If you can figure out the methods to do this. Good luck.

(What is it called when you hate a game, and love to rant endlessly about it?)

Indeed the particular group this occured with have been playing for years and so trust each other not to abuse the position of being in power over the other players.

*takes notes*

Fundamentally it isn't something that can be forced, the players must be willing to accept that somebody will be in a position of authority over them for the game to work. If they're not comfortable with it then its time for the GM to rethink the game

I guess it also depends on how much power the authority has? This can vary wildly from game to game. Authority may actually mean nothing in one game, and almost completely dictate your IC life in another.