[jncfhnb]

> If I understand correctly, you’re saying Monte’s intention (randomly picking an empty box vs purposely picking an empty box) is effecting the odds that the box in hand has keys?

Sort of. If you’re saying the next box is chosen at random then there are 2 of 6 possible end games in which the key is chosen; 2 of 6 in which you pick an empty box and can switch for the keys; and 2 of 6 that both of the remaining are empty.

Since the prompt says that you did in fact open an empty box, that removes the 2 where you open the keys. So it’s 50/50.

When you know for a fact that the keys will never be chosen, the probability of picking an empty box when you chose an empty box goes from 50% to 100%. Meaning it now occupies twice the probability space. That’s now it’s 2/3 chance of winning.

You truly learn nothing if Monte randomly opens one of the doors and it is not the keys.

> Also, do you have any evidence that this isn’t the original?

The quote in the article?