I jumped in the middle of a “Deal or No Deal” episode at my family’s house during the holidays. The contestant had 3 remaining briefcases in addition to the one she had chosen.

Howie Mandel said, “You have a 1/4 chance.” …. That doesn’t sound right. According to the famous Monty Hall problem, it isn’t.

Let’s apply the logic of the Monty Hall problem to the game show “Deal or No Deal” to determine the actual probability of our case containing the $1 million. Let’s start at the beginning.

There are 26 cases. The contestant chooses 1.

What are our probabilities here?

We can group the 25 on the left into one block. It has a 25/26 chance of containing the $1 million. We count the chosen case on the right as a block of its own. It has a 1/26 chance.

Now let’s speed forward in the game. Several more cases have been eliminated.

There are now 3 cases on the left and 1 case is still on the right.

The trick here is that the probabilities have not changed. The left block still has a probability of 25/26 and the right block has a probability of 1/26.

Now, the left block’s 25/26 probability is spread between the three remaining cases instead of the original 25.

So where’s the money? Probably not with you! Sorry.