Shamelessly stolen from you-know-where.
Sorry fam, I don’t negotiate with game theorists.
Jigsaw Trolley Problem
Submitted 1 day ago by TauZero@mander.xyz to science_memes@mander.xyz
https://mander.xyz/pictrs/image/59479a02-e6c7-4915-9a40-1f8d1187a377.png
Comments
pennomi@lemmy.world 1 day ago
SkyezOpen@lemmy.world 1 day ago
So the only winning move is not to play? Caught you, game theorist.
Redex68@lemmy.world 1 day ago
I think the ball is at C3.
Albert knows that Bernard doesn’t know where it is exactly, that means the ball can’t be in the first two rows, because if it was that would mean there’s a chance for the ball to be in column 5 or 6, in which case Bernard would known right away where it is exactly (as those columns have only one ball). This means the ball must be in row C or D and column 1, 2, 3 or 4. We know Bernard was able to deduce the exact position of the ball from this information, which means it can’t be column 1 (as there are 2 balls still remaining there). That means it must be in column 2, 3 or 4. We know Albert was able to deduce the exact position if the ball from this, and since row D has 2 balls still in play (collumn 2 and 4), meaning Albert wouldn’t be able to guess which one it was, that means it’s in row C, as row C has only one ball left in play.
Now idk what the correct choice would be statistically. If I remember correctly, the Monty Hall problem states that there’s 2/3 of a chance you’ll get it correctly if you switch doors, but since a gold ball was pulled out from behind the first door (the ball at C3 is gold), I think that means there’s a 2/3 chance of the first door (the one from which the ball was pulled out of) being the one with all gold balls (since it contains 2/3 of all gold balls). In that case I think the probabilities cancel out? Which means it doesn’t increase your chances whether you switch or not.
TauZero@mander.xyz 1 day ago
Beautifully written!
I think the probabilities cancel out?
My conclusion as well. Except that since Jigsaw has taken one gold ball out, door 2 must have slightly better chance of gold ball remaining on average (75% vs 72.2%?).
y0kai@lemmy.dbzer0.com 1 day ago
I’m so confused by the added complexity here. If there’s a gold ball behind every door, the choice of door doesn’t matter.
We were asked to pull a ball from behind one of three doors, not figure out what two dudes know about balls in a grid.
I choose the following option:
Kick the madman in the nuts, open all the doors and take all of the balls, switch the trolly track myself, save the people, sell the balls, then go back and tie the madman to the tracks and ask him to pick the door with the black and blue balls. If he doesn’t choose his own fly as the door, TROLLEY.
Redex68@lemmy.world 14 hours ago
I’m think it’s implied that you can only take pull out one ball at random from behind a door.
y0kai@lemmy.dbzer0.com 8 hours ago
We don’t even get that far. Everytime we try, the dude does something before we get the chance and then changes the rules lol
brisk@aussie.zone 1 day ago
Commenting before reading other comments
::: solution to grid puzzle The henchmen’s discussion implies that the letter row and number column both have at least two balls in them (required for “I don’t know, but I know you don’t know)”. B’s statement to A makes it clear to A that the letter must be either row C or D depending on the number he knows.
:::
rooroo@feddit.org 14 hours ago
I had the grid solution wrong, but your explanation is sound! Thanks!
Rentlar@lemmy.ca 1 day ago
Hoping to select the door with a goat, that will headbutt the switch for me.
monk@lemmy.unboiled.info 15 hours ago
I don’t see no question.
hodgepodgin@lemmy.zip 1 day ago
C3.
woodenghost@hexbear.net 1 day ago
Yes and because C3 is a golden ball, you should confidently switch to the second door. Because now it’s just the Monty Hall problem with balls instead of goats. When the madman chose a door to opened, he deliberately chose a bad (mixed) door, otherwise he would have given away the correct location. The fact, that he opened the third instead of the second gives you new information, that you can take advantage of by switching, increasing your chances. Had the ball been silver, it might have been revealed to come from a bad door.
hodgepodgin@lemmy.zip 17 hours ago
I have no idea what the ball thing is about. I just assumed that since he was a madman, he was just doing madman things.
flora_explora@beehaw.org 14 hours ago
Thanks for the explanation, but I cannot follow on this line
Since he knows that Bernard doesn’t know given just the row, each ball in that row is in a column that contains more than one ball.
Why is that? Why couldn’t it be A2 or A3? In this case neither Albert nor Bertrand could tell what row/column this was either, because it would be in a row/column with another ball. How can you exclude any row with overlap with any single-ball columns?
hodgepodgin@lemmy.zip 1 hour ago
It couldn’t be row A or B because there would then be a possibility the ball was in A6 or B5 and that Bernard actually did know where the ball was. Albert says he knows Bernard doesn’t know where the ball is, which means he is 100% confident, and the only rows that allow for that confidence are rows C and D, because each ball in each row is not alone in its column.
Dyskolos@lemmy.zip 1 day ago
Can I try again until I get a silver ball? Please.
TauZero@mander.xyz 1 day ago
Yeah, problem doesn’t specify whether you want your family to live. Common mistake.
TheFogan@programming.dev 1 day ago
That’s like the old joke of the CIA loyalty test.
A CIA recruit reached the final stages, at the last step he found his mother tied to a chair and gagged. His prospective boss hands him a gun and says "To prove you are ready for this job and will follow any orders, You’ll need to kill your mother, I’ll be outside.
10 seconds after leaving the recruiter hears the bang of a gun… followed by other bangs, clangs of metal.
Prospective recruit walks out the door… “The god damn gun you gave me had blanks in it, so I had to beat her to death with the chair”
NeatNit@discuss.tchncs.de 1 day ago
Sounds to me like you’re allowed to see the color of the ball before you take it out. This means it doesn’t matter which door you open, a gold ball will be available to pull and you win. Checkmate.
slippyferret@lemmy.blahaj.zone 15 hours ago
Smullyan would be proud.
chaos@beehaw.org 1 day ago
I'm pretty sure the ball landed in
C3. Albert is very sure that Bernard doesn’t know either. Bernard would know the location if it was in 5 or 6, indicating to all of us that Albert was told a row that isn’t A or B. Now that Bernard can also deduce that it’s not A or B, he’s narrowed it down to one possibility. That means all of us now know it can’t be column 1 either, because if it were, he wouldn’t have gotten anything from that new fact. Finally, now that column 1 is eliminated, Albert has deduced the location. Row D would’ve left two more possibilities, but row C leaves just one. Albert must know it is in row C.
For the rest, well, there isn’t even actually a question, I suspect you’d open a door and pick a box and hope that you’ve got a gold ball to pick, and it’s not clear that he’s following Monty Hall rules and always opening a bad door, but I think knowing which ball got thrown would make the rest of the odds fall into place.
TauZero@mander.xyz 1 day ago
it’s not clear that he’s following Monty Hall rules
Whenever I see a badly-specified Monty Hall Problem, I always imagine the host saying something like “Oh, you want to pick door number 1? Well, guess what - the car was behind door number 3 all along! You get nothing but a goat!” And only when you initially pick a door with the car does the host ask “Are you sure you wouldn’t rather switch to door number 2? Look, there is even a goat behind door number 3!” Switching doors 100% gurantees you get a goat… or 50% silver balls in this case.
wolframhydroxide@sh.itjust.works 3 hours ago
Uh, deal? I walk up to the third door and pull a gold ball from it.
TauZero@mander.xyz 2 hours ago
Doesn’t say the trolley is a runaway. Don’t even need to make deals, you can safely walk away.
wolframhydroxide@sh.itjust.works 2 hours ago
It also doesn’t say that the track isn’t already headed away from the people.