Deal or No Deal: The Banker’s Secret

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April 28th, 2006

“Deal or No Deal” a popular game show on NBC has captured audiences with its large prize amounts, and unorthodox game show structure. Game show fans have become accustomed to trivia, dating and stunt –based games. “Deal or No Deal” presents a new format for game shows, but what is the secret behind the banker’s offers?

I love watching this show because the whole concept of the banker’s offers tempting the players to abandon the game and walk away with some amount of dollars really appeals to me. I play the game in my head, telling the players which offers they should accept, and which they should walk away from. There is an easy way to figure out which offers are good (and which are bad) through a simple financial principle.

Expected Value
Expected value is one of the very first concepts taught to finance students. It is a math technique which allows some limited prediction of future events.

Essentially, this principle relies on knowledge of two variables: the amount you stand to gain, and the probability that you will make that gain.

For a classic finance example: let’s say you have a stock valued at $50. Tomorrow, there is a 50% chance it will go up to $100, at which point you can sell it. If it doesn’t go up to $100, you will sell it for $50. So: your probability is 50% and your potential gain is $50.

To find the expected value, we simply multiply the probability of the result by the potential gain.

0.50 * $50 = $25

Therefore, the value of your stock today (knowing what you know about the future) is $75. If someone offered you $80 for the stock today, should you accept?

The answer is yes. If you were to run this example 100 times over, half the time you would gain $25, half the time you wouldn’t. So you’d end up with $1,250.

If you accepted the $80 offer during those 100 times, you would have a $3,000 profit at the end.

So, expected value allows you to determine what something with be worth tomorrow. How does it apply to “Deal or No Deal?”

Deal or No Deal: How to decide
The real point of the game is to approximate, at any given point, what the expected value of the suitcase in your hand is.

Step 1: What is the potential gain? At any point in the game, you can determine the potential gain. The highest values left on the board are the maximum amount you can gain from playing. At the start, this would be the $100,000 through $1 million prizes. As the game progresses, and cases are eliminated, the potential gain adjusts downward.

Step 2: What is the probability of that gain? There are 26 spots on the game board. The probability of you having the highest-value case in your possession is simply the number of “high-value prizes” (greater than $100,000) left on the board divided by the number of cases remaining.

For example: you’re playing the game, and there are 9 cases left (plus the one in your hand). The board has the $100,000, $400,000 and $750,000 prizes left, with 7 other smaller prizes also available. The probability that you have the case with one of these three prizes is 10%.

0.10 * $100,000 = $10,000
0.10 * $400,000 = $40,000
0.10 * $750,000 = $75,000

Summing these values, the approximate expected value of your case is $125,000. If the banker offers you anything less, you should say, “No deal!”

So how does the show keep from losing money on every player? The banker almost never offers anything over the expected value when there are still large amounts on the board. Players compare a paltry $150,000 to the possible million-dollar prize and they can’t resist.

So now you know how to play. And how to ‘beat the banker!’

Entry Filed under: Finance Examples
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