Topic: Episode #280

[GodSlayer]

The difficulties people have with the Monty Hall problem are symptoms of a fundamental misunderstanding about probability, namely:-

An event does not, in general, have a fixed, a priori, probability, but the probability depends on what prior knowledge you have of the outcome.

In this case, Monty Hall knows where the car is, and betrays part of that knowledge by opening the door. This makes the probability of winning different from what it would be if choosing with no prior knowledge at all.

I wish there was a podcast that was full of these sorts of useful little self-contained nuggets of information.

[MountainManPan]

Let's face it: the biggest issue with the Monty Hall problem isn't the sample space or the trials or not getting that Hall knows where the car is ahead of time, it's that something - and I can't quite put my finger on what - about this trick is counter to human intuition. The only reason it makes sense is that everything works out mathematically and logically.

Lots of probability is very counter-intuitive.  Just look at the thread about the 'letter problem'.

[Puppet_Master]

If you want to get an intuitive understanding for the MH problem, I suggest doing a short experiment (that's what finally made it click for me).  Just get a piece of paper and write 1,2,3 about 30 or so times and then circle doors at random (using a die would be best):

1 2 (3)
(1) 2 3
(1) 2 3
1 2 (3)
1 (2) 3
...

Then get someone to randomly write a column of 1, 2, or 3 (or roll a die).  This is the prize door:

2
2
1
3
1
...

Now, you can put the two pieces of paper together and use the switching method and mark if it was a hit or miss.  So, for my above example, the prize is behind door 2 and I picked door 3 so you would "open" door 1 and switch to door 2 then put a check mark next to that trial since you got the prize.

I started "understanding" the pattern after about 15 trials into the experiment.  I understand this is a crude experiment that isn't methodologically rigorous, but it accomplishes the goal.