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How to explain the Monty Hall problem to a disbeliever

michalpaszkiewicz.co.uk

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Re: How to explain the Monty Hall problem to a disbeliever

#21

Post by wanderingstan »

qumpis wrote: post #3
arnvald wrote: post #2

The most intuitive and simple explanation that worked for me is: * if on the 1st try you choose the correct box (33% chance), then the one you can switch to will be wrong * if on the 1st try you choose the wrong box (66% chance), then the one you can switch to will be correct one therefore your goal is to pick the wrong box on the 1st try and then switch, and you have 66% chance to do it

Or to just imagine a 1000 boxes with the same problem formulation

This was the one that worked when explaining it to my friends.

It gives a mental image of the host opening 998 boxes, leaving only your selected box and one other. From here it’s easier to see that there must be something special about that one box the host left un-opened!

(Though even then there were people who clung to the “2 boxes means 1-in-2 chance” fallacy, failing to see that the host has revealed information.)

Edit: an other version was to change the hosts proposal: what if he let you choose one box, and then said he would let you switch to having whatever was in the other 999 boxes? Of course you would switch! The crux is understanding that this offer is actually the same as in the first proposal, since the host is not opening the boxes at random.

Re: How to explain the Monty Hall problem to a disbeliever

#24

Post by fwlr »

Consider the Honty Mall problem: it’s like the original problem, except after you pick a box, Honty offers you both of the other boxes. It’s much easier to see swapping is better in this problem, and it’s also easier to see that the chance is 2/3 if you swap. Then you just have to show that the Honty Mall problem is equivalent to the Monty Hall problem, by stipulating that Monty will always open a box that’s empty.

Re: How to explain the Monty Hall problem to a disbeliever

#25

Post by acadapter »

There is a linguistic illusion at work here.

In the Monty Hall problem, you think you are choosing between one door and one other door. But in fact, you are choosing between one door and two doors.

The choice is between "this door" (1/3 probability for winning) and "all other doors" (2/3 probability for winning).

Re: How to explain the Monty Hall problem to a disbeliever

#26

Post by coldtea »

jstx1 wrote: post #12
qumpis wrote: post #3

Earlier quoted context omitted.

Or to just imagine a 1000 boxes with the same problem formulation

This doesn't do anything for me. (I understand the Monty Hall problem, I just don't see how changing the number of doors makes a difference to anyone's intuition.)

Because a 99/100 chance is much better than 2/3 to drive the point home...

Re: How to explain the Monty Hall problem to a disbeliever

#27

Post by adhesive_wombat »

GloucesterBoy wrote: post #11
adhesive_wombat wrote: post #5

The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. Imagine a universe with many simultaneous Monty Hall clones playing…

wow... what a grim approach!

Next on 4: Brian Cox presents Quantum Squid Game, in partnership with Academi.

Re: How to explain the Monty Hall problem to a disbeliever

#28

Post by TarasBob »

adhesive_wombat wrote: post #5

The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious. Imagine a universe with many simultaneous Monty Hall clones playing…

In the scenario where they are shot that you described, it is still better to switch!

Re: How to explain the Monty Hall problem to a disbeliever

#29

Post by curiousgal »

jstx1 wrote: post #12
qumpis wrote: post #3

Earlier quoted context omitted.

Or to just imagine a 1000 boxes with the same problem formulation

This doesn't do anything for me. (I understand the Monty Hall problem, I just don't see how changing the number of doors makes a difference to anyone's intuition.)

Imagine there are 999 boxes with nothing in them and one box with the keys. After picking a box, the hosts opens 998 empty boxes. Would you still stick with your initial choice?

Re: How to explain the Monty Hall problem to a disbeliever

#30

Post by brigandish »

jstx1 wrote: post #12
qumpis wrote: post #3

Earlier quoted context omitted.

Or to just imagine a 1000 boxes with the same problem formulation

This doesn't do anything for me. (I understand the Monty Hall problem, I just don't see how changing the number of doors makes a difference to anyone's intuition.)

It's because it makes the initial choice so increasingly unlikely (increasing with the number of doors) to be correct that when the doors are taken away and you're left with only two, one of which must be right, it means that the other door is incredibly likely to be the right one.
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