So I want to run a dungeon full of logic problems.  I figured out how to do the prisoner's delima.  I can do the Monty Hall problem.  Serries of doors in sets of 3.  Put your key in the first one it gets locked in, then the other 2 light up.  Choose one of those and goat walks out and your key falls out of the first door.  Make your selection again.  Either its a safe path onwards or the goat transforms into a terrible weargoat that they fight.  Link them in a serries of 6 or so to make the right choice pay off. 


Anyone else have any good logic problems?   I mean the true and false doors but what else.

Quote from: Headless on August 14, 2022, 04:02:07 PM
So I want to run a dungeon full of logic problems.  I figured out how to do the prisoner's delima.  I can do the Monty Hall problem.  Serries of doors in sets of 3.  Put your key in the first one it gets locked in, then the other 2 light up.  Choose one of those and goat walks out and your key falls out of the first door.  Make your selection again.  Either its a safe path onwards or the goat transforms into a terrible weargoat that they fight.  Link them in a serries of 6 or so to make the right choice pay off. 


Anyone else have any good logic problems?   I mean the true and false doors but what else.

Your definition of a Monty Haul dungeon is way different than what it used to be.

It used to be that a Monty Haul dungeon was one where you could gain incredible riches for taking on very little danger. Like only kobolds guarding a +5 Vorpal Sword.

Quote from: jeff37923 on August 14, 2022, 04:49:44 PM
Your definition of a Monty Haul dungeon is way different than what it used to be.

It used to be that a Monty Haul dungeon was one where you could gain incredible riches for taking on very little danger. Like only kobolds guarding a +5 Vorpal Sword.

Indeed. I think the OP is talking about a dungeon that implements the Monty Hall Problem. Tricky. The intentional misspelling in the historical Monty Haul is perhaps noteworthy here.

Quote from: jeff37923 on August 14, 2022, 04:49:44 PM

Quote from: Headless on August 14, 2022, 04:02:07 PM
So I want to run a dungeon full of logic problems.  I figured out how to do the prisoner's delima.  I can do the Monty Hall problem.  Serries of doors in sets of 3.  Put your key in the first one it gets locked in, then the other 2 light up.  Choose one of those and goat walks out and your key falls out of the first door.  Make your selection again.  Either its a safe path onwards or the goat transforms into a terrible weargoat that they fight.  Link them in a serries of 6 or so to make the right choice pay off. 


Anyone else have any good logic problems?   I mean the true and false doors but what else.

Your definition of a Monty Haul dungeon is way different than what it used to be.

It used to be that a Monty Haul dungeon was one where you could gain incredible riches for taking on very little danger. Like only kobolds guarding a +5 Vorpal Sword.

Greetings!

*Laughing* Exactly, Jeff!

Running a "Monty Haul" dungeon or campaign is *bad*. Generally speaking, Noob DM's that don't know better and don't have the experience to equip them with broader knowledge and skill in running a D&D game successfully. Baby DM's all pretty much go through a "Monty Haul" phase. With study, learning, and experience, hopefully such ideas fall away and are rejected by even the modestly-experienced DM.

I didn't post such an observation, because being charitable and confident in Headless's nature, I didn't think this is what he has in mind.

Having said that, like you, Jeff, I only know one definition of a "Monty Haul" campaign or dungeon, so I honestly am at a loss for what our friend Headless is really getting at.

Geesus, Jeff! Talk about getting "Back in the day!". It's been so long since I have heard such an expression!

Semper Fidelis,

SHARK

The Monty Hall Problem is a counter-intuitive result in probability. Long story short, given three doors one with the Big Prize and two with goats, you pick one. Hall reveals a goat behind one of the other two and gives you an opportunity to stick with the door you've already chosen or switch to the other unopened door.

It seems like switching should make no difference, that there's a 50/50 chance of getting the Big Prize, but in fact switching increases your chances from 1/3 to 2/3, so you should always switch doors.

This is easy to prove but it's difficult to get people to believe it because it's so absurdly counter-intuitive. I know it took me a while to accept it.

ETA: Let me try to prove it. When you first pick one of the three doors, there's an equal chance that any of them can be the Big Prize, so the chance you picked correctly in 1-in-3, and the chance you picked incorrectly in 2-in-3. Hall opens one of the latter two doors and reveals a goat (there's a goat behind at least one of them, so he can always do this). The key is that this hasn't changed the probabilities, it's simply eliminated one of the wrong options. So at this point the probability you chose correctly is still 1-in-3, and the probability you were wrong is still 2-in-3, but now there's only one wrong option instead of two. So by switching, you get the full 2-in-3 probability of winning the Big Prize.

If that still doesn't do it for you, consider an alternate scenario. Suppose after picking a door, Hall offers you to chance to open both of the other doors, and you get the Big Prize if it's behind either. Then obviously you should do it, because opening two doors is obviously better than one. Well, in the original scenario, by switching you are effectively opening both of the other two doors.

Also if you really want to do a Monty Hall dungeon right, you need to give the PCs bonuses for dressing in Halloween-style costumes.

Quote from: Zalman on August 14, 2022, 05:02:34 PM

Quote from: jeff37923 on August 14, 2022, 04:49:44 PM
Your definition of a Monty Haul dungeon is way different than what it used to be.

It used to be that a Monty Haul dungeon was one where you could gain incredible riches for taking on very little danger. Like only kobolds guarding a +5 Vorpal Sword.

Indeed. I think the OP is talking about a dungeon that implements the Monty Hall Problem. Tricky. The intentional misspelling in the historical Monty Haul is perhaps noteworthy here.

Sorry I might have been too far up my own ass. I used to be impressed with my own cleverness and think no one knew what I knew.  Now I have made the oppisit problem and think everyone is in my head.

I was referring to the Monty Hall Problem as described very well above.

Strange. I knew immediately what OP meant by a "Monty Hall" dungeon, especially after mentioning three doors, but I had NO CLUE wtf a "Monty Haul" dungeon was until today. *shrug*

I've used Monty Hall doors in dungeons before. I've also had rotating/counter-rotating rooms, where a series of levers would move a room 3 spaces clockwise, 2 spaces counter-CW, etc., and players had to figure out the pattern to align the opening with the exit. I've had "Simon" rooms, where a floor would consist of colored flagstones and player had to remember the order of colors encountered previously in the dungeon to proceed. I've used word puzzles/riddles.

Ultimately, I've discovered that unless the players are acutely aware they're entering a "logic dungeon" in advance, they fukken hate such things. Before the dungeon even begins, tell them they'll need to pay very close attention to things you say, because you WON'T REPEAT THEM. Then when you describe rooms, put a little special emphasise on details you want them to remember. Give them a chance to write it down before continuing. It might "cheaper" the mystery of some puzzles, but it'll be more fun for the players.

As for other logic puzzles, Knights and Knaves is a classic, but surprisingly I haven't run into a group yet that already knew it.

Another that might work is the puzzle called Down in the Cellar or 3 Bulbs and 3 Switches.

Quote from: Headless on August 14, 2022, 05:56:27 PM

Quote from: Zalman on August 14, 2022, 05:02:34 PM

Quote from: jeff37923 on August 14, 2022, 04:49:44 PM
Your definition of a Monty Haul dungeon is way different than what it used to be.

It used to be that a Monty Haul dungeon was one where you could gain incredible riches for taking on very little danger. Like only kobolds guarding a +5 Vorpal Sword.

Indeed. I think the OP is talking about a dungeon that implements the Monty Hall Problem. Tricky. The intentional misspelling in the historical Monty Haul is perhaps noteworthy here.

Sorry I might have been too far up my own ass. I used to be impressed with my own cleverness and think no one knew what I knew.  Now I have made the oppisit problem and think everyone is in my head.

I was referring to the Monty Hall Problem as described very well above.

I got what you meant from your description. I think the technical term is the "Three Doors Problem" or somesuch. Works exactly the same with 3 cups too.

And I was one of those people who very did not believe that switching was a good idea till it was both explained to me and I performed the puzzle with cups 100 times and recorded the results.

As was explained above the trick is one of probability. When you first choose a door or whatever you have a 66.6 chance of having chosen wrong. So statistically you are always better off taking a chance and changing doors. It took actually seeing it to get it.

If you need more ideas, Raymond Smullyan's puzzle books are a great resource. In this context I particularly recommend The Lady or the Tiger and Satan, Cantor, and Infinity. As the latter's title suggests, it involves some pretty nerdy math but the build up to those problems is gentle.

I stil

Quote from: Cat the Bounty Smuggler on August 14, 2022, 05:16:43 PM
The Monty Hall Problem is a counter-intuitive result in probability. Long story short, given three doors one with the Big Prize and two with goats, you pick one. Hall reveals a goat behind one of the other two and gives you an opportunity to stick with the door you've already chosen or switch to the other unopened door.

It seems like switching should make no difference, that there's a 50/50 chance of getting the Big Prize, but in fact switching increases your chances from 1/3 to 2/3, so you should always switch doors.

This is easy to prove but it's difficult to get people to believe it because it's so absurdly counter-intuitive. I know it took me a while to accept it.

ETA: Let me try to prove it. When you first pick one of the three doors, there's an equal chance that any of them can be the Big Prize, so the chance you picked correctly in 1-in-3, and the chance you picked incorrectly in 2-in-3. Hall opens one of the latter two doors and reveals a goat (there's a goat behind at least one of them, so he can always do this). The key is that this hasn't changed the probabilities, it's simply eliminated one of the wrong options. So at this point the probability you chose correctly is still 1-in-3, and the probability you were wrong is still 2-in-3, but now there's only one wrong option instead of two. So by switching, you get the full 2-in-3 probability of winning the Big Prize.

If that still doesn't do it for you, consider an alternate scenario. Suppose after picking a door, Hall offers you to chance to open both of the other doors, and you get the Big Prize if it's behind either. Then obviously you should do it, because opening two doors is obviously better than one. Well, in the original scenario, by switching you are effectively opening both of the other two doors.

l still don't believe it, and I've had several graduate level courses in probability.  I figure that is something is that massively counterintuitive then there's something wrong with the proof.  Just because I'm not smart enough to point out the flaw doesn't mean it's not there.

Quote from: Mishihari on August 18, 2022, 12:23:29 AMl still don't believe it, and I've had several graduate level courses in probability.  I figure that is something is that massively counterintuitive then there's something wrong with the proof.  Just because I'm not smart enough to point out the flaw doesn't mean it's not there.

More proof college is just a waste of time.

Quote from: Effete on August 18, 2022, 12:52:16 AM

Quote from: Mishihari on August 18, 2022, 12:23:29 AMl still don't believe it, and I've had several graduate level courses in probability.  I figure that is something is that massively counterintuitive then there's something wrong with the proof.  Just because I'm not smart enough to point out the flaw doesn't mean it's not there.

More proof college is just a waste of time.

Not really.  I certainly get paid a heck of a lot more than I would without multiple grad degrees.

Quote from: Effete on August 18, 2022, 12:52:16 AM

Quote from: Mishihari on August 18, 2022, 12:23:29 AMl still don't believe it, and I've had several graduate level courses in probability.  I figure that is something is that massively counterintuitive then there's something wrong with the proof.  Just because I'm not smart enough to point out the flaw doesn't mean it's not there.

More proof college is just a waste of time.

Nonsense; it's a often a waste of both time and money.