An intuitive way to explain the Monty hall problem


#1

for the uninitiated heres a recap


when a mathematician 1st presented this problem on a talk show in 1990 she was met with a lot criticism and hate mail not just from common people of which only 8 % believed her result but from other mathematicians also of which only 35% believed … i dont know about you but even when it was explained to me i couldn’t rationally accept it so a few months back i thought of a new way to phrase the monty hall problem that makes it much more intuitive … heres the new problem : -
You have 100 doors only 1 of which has a car behind it , the host asks you to pick 1 then he discards 98 doors with goats behind them and asks if you want to switch to the only other door left… do you switch
i dont know why i haven’t seen anybody explain it like that it just makes so much more sense … its been bugging me for months thought i’d get it off my chest


#2

explain how is this relevent


#3

Its in offtopic section so it doesn’t have to relevant


#4

its pretty relevant if you want to win a brand new car :tada:


#5

But goats are so cool!


#8

I hope goat pictures don’t invade the forums… :goat:


#9

I wonder If we could some specs blind like this for the next project.

There are 100 screens. 99 of them are with light bleed 1 is without :))


#10

i think this belongs here


#11

The answer is that you should always switch, right? I saw a really good breakdown of the maths a while ago. The original is 3 doors, 2 with goats, 1 with the car. After picking the first one without opening, another door is opened and revealed to have a goat. The door you first chose has a 1/3 chance the car is behind it, so therefore between the other 2 doors there is a 2/3 chance of a car. Since the result of one of those doors has already been revealed, the 2/3 chance is entirely in the door you can switch to, so you should switch to it.


#12

yes thats correct but that wasn’t the point of the post :sweat_smile: its still counter intuitive even when explained like that as i pointed out even mathematicians didn’t agree with the result initially


#13

Does this result of always switching doors hold up in actuality though? I get why the math theory makes sense, but say this happened in real life. If the person switched doors a thousand times and kept their door another thousand times, I don’t think there would be a significant difference in the percentage of times you won the car instead of the goat.


#14

ya the woman who presented it was having a very hard time convincing everybody so she told everybody to go out and do it practically … if you read my version i don’t think you would be suspicious about a difference in the math and the practical result


#15

Great, entertainment and education.

Thanks

However I wouldn’t have been too worried if I got the goat.
Because, afterall goat curry is one of my most favourite food dishes in the world.


#16

I found this video put it really nicely


#17

Isn’t this what Deal or No Deal essentially plays on? So if you get all the way to the end and there’s a jackpot plus one other out there, then you should switch boxes?


#18

@Kee oh ya great point i didn’t think of that, im not sure, it gets a little more complex in that situation … the bankers use the same formula to calculate what offer to make you i think… ill post if i think of a solution


#19

So… do you switch? :smile: I really don’t think there’s a difference… All doors are equal, so now there’s 50% chance to find a car behind any of them…


#20

You pick wrong at first: The presenter picks a goat door and you decide to switch.

You pick right at first: The presenter picks a goat door and you decide to switch.

They say 2/3 if you pick wrong and 1/3 if you pick right at first, but the presenter just eliminated a possibility… So why is it still counted in the equation?


#21

i thought about it for a while and its not exactly the same as the monty hall problem and it doesnt make a difference if you switch ill post a full explanation if i can put it convincingly


#22

the difference between the monty hall problem and deal or no deal is that in monty hall 2 of the options can be counted as equal like 2 doors with goats behind them thats why you have a 2/3 chance of picking a door with a goat in deal or no deal two values cant be combined like that but say you started with only 3 suitcases 2 of which have 1 dollar in them (they dont have to be exactly the same as long as they are relatively the same it works) and 1 has 1 million dollars (this one has to be relatively different) then switching when one of the smaller values is revealed would give you the advantage

edit :- with some more thinking im not so sure about my logic so dont quote me… im pretty bad at probability that’s why i came up with the easy heuristic to understand the monty hall problem in the 1st place