So I think some of the confusion stems from that is only three goats.

If you think about more goats, you will think I definitely want to switch.

I know this is very tricky, so now let's look at a Monte Carlo

simulation of this problem in a spreadsheet.

I'm now going to simulate this game 1,000 times.

And from the simulation create data,

create proportions of winning by switching or winning by not switching.

And then, let's have a look at those numbers.

So now, because we're looking at data,

we're back to probability definition number two.

So let's go to the spreadsheet.

Here's now a scratch sheet where I simulate this Monty Hall game

show problem for you.

Let's have a look at what I've done here.

First, prize this rand between 1, 2, 3.

So this is a random number between 1 and 3, and

that's the number of the door where the prize is.

So here, in this example right now, it's a 2.

The candidate chooses a 2.

Again, a random number.

I assume that the candidate is completely clueless and just randomly picks a number,

then the host has to open a door with a goat.

Now here, this is quite a complicated Excel formula.

You can ignore this, I know.

Many of you can code this very elegantly and

much faster than I did using Excel Macros or Visual Basic.

I deliberately did not do the CSO, this will hopefully, run on anyone's

spreadsheet on any type of computer, even all your computers in the world.

Then, we look at what happens if the candidate does not switch,

keeps the same door, or what happens if the candidate switches.

And then, here we see with a simple if, question whether he or she wins or loses.

Now, if I recalculate my sheet, every time I do this 1,000 times,

1,000 times I say, he is a prize, he is a candidate, he chooses this site, the host

open something and then we see what happens with switching or not switching.

Here, for example, right now on my sheet it says,

if you do not switch, you win 33.9% of the time.

If you yes, you switch, you win 66.1% of the time in these 1,000.

Now, let me click recalculate sheet.

Notice the numbers change.

34.6% not changing, 65% probability of winning, yes when you change.

Here's now 30.3%, 69.7.

So you see, our relative frequencies are indeed close to the one-third,

two-third cutoff that I explained to you earlier.

We can't expect that we hit it exactly, but we get very close.

And I hope this convinces the last doubters among you that indeed,

the probability of winning after switching is twice as high

as the probability of winning when you don't switch.

So if you ever in that situation, please do me a favor, switch that door.