The role of probability in solving the Monty Hall problem

[robvalue]

I'm really surprised you're persisting with this, pool. Your hypothesis is that it's 50/50, but the reality of the game shows that this is wrong. So your hypothesis is wrong. If it was 50/50, you'd win about 50% of the time by switching. And you don't.

This kind of observation is a way of estimating probabilities. Say you win 681 times out of 1000 games, it gives you an estimate of 68.1%. You will find it is going to be around 66%, and very rarely will drop as low as 50%. The more games you play, the more accurate the prediction becomes.

Instead of trying to understand why it's wrong, you're screaming at a ball for dropping down, telling it that it should be floating upwards instead.

If you threw a coin 10,000 times and got 6,476 heads, you would conclude that it was probably a weighted coin.