Deal or No Deal

I was doing some chores tonight - bleh, and my wife was watching the show Deal or No Deal in the other room. I was half listening to it. It doesn't seem like a very good show. However a situation came up that was somewhat interesting.

There were 5 cases left. One was worth $1 million. One was worth $200,000. The other three were not worth very much. The show offered the contestant $119,000 to quit. The contestant at the strong urging of her family accepted the offer and walked away with the $119,000.

For most people, certainly me, 119K is a great score that would make a real positive difference in your life. So I can understand why she was risk averse and took the guaranteed cash.

Now for a really wealthy person, it was not the correct move to accept the 119. A poker player would tell you the correct move was to decline the 119 and play through the end to get one of the cases. A wealthy person doesn't care about the $1M or the $119K as such, he only cares about making the most profitable move. The correct choice is the most profitable choice. Then it's a simple expected value calculation.

The player is guaranteed to get one of the cases at the end. One of them is worth $1M. One is worth $200K. Let's say the others are worth 0. Each outcome is equally likely. So the expected value E of chasing to the end is

E = 1/5(1,000,000) + 1/5(200,000) + 3/5(0)
E = 200,000 + 40,000 + 0
E = 240,000

So NBC wisely offered her only half of what it was worth to her to stay in the game and chase. Good financial move by NBC.


A Texas hold'em player is faced with pot odds situations all the time. A poker situation similar to the one on Deal or No Deal would be something like this.

Suppose you have a nine out flush draw on the turn. If you hit your flush on the river you win the pot. If you miss your opponent wins. Your opponent has bet $120 to bring the pot to $1000. Should you call?

Well the answer is of course yes. You have about a 1 in 5 chance of hitting the flush on the river and winning the pot. So your expected value is 1/5($1000) = $200. It only costs you $120 to chase and see the river card. So it is profitable to call. It would have been more profitable for the Deal contestant to chase.