More Deal or No Deal
I know this article is old, but I hate it when people write articles about how people don’t understand probabilties when they themselves don’t understand probabilities. Plus, I love Deal or No Deal. If you are not familiar with how the shows work, click here for my first effort on the show.
Here is an article by Chuck Jaffe, printed in the Bayou Business Review, where he laments the choices people are making on Deal or No Deal.
“Take the case of a recent participant, who was down to four possibilities, two under $250, then $50,000 and $500,000. He was offered nearly $140,000 to walk away, and he had a 75 percent chance of leaving with an amount much lower.”
Oh really? I’m not so sure.
Jaffe has made a mistake – or is at least making some very strong assumptions about what the person will do in the future.
If the person were to refuse all future offers, and thus take the contents of their suitcase, then indeed Jaffe would be correct to say there as 3/4 chance the person will walk away with less than $140,000.
But Jaffe is neglecting the fact that the person has the right to take a cash offer after opening the suitcase after each round. The person doesn’t have to play until they open the suitcase.
In fact, if the $140,000 offer is a refused, there are four possibilities. One suitcase must be revealed:
Possibility A = $500K is revealed
Possibility B = $50K is revealed
Possibility C = one of the <$250 is revealed
Possibility D = the other <$250 is revealed
Now, consider what the bank will offer in each case.
Possibility A = $50 K and both small amounts remain, so the offer is roughly $17,000.
Possibility B = $500 K and both small amounts remain, so the offer is roughly $170,000.
Possibility C = $500 K, $50K, and one small amount remain, so the offer is roughly $187,000.
Possibility D = $500K, $50K, and one small amount reamin, so the offer is roughly $187,000.
So if we know the player will stop after one more round, there is a 75% chance the person will end up with more than $140,000.
In fact, as long there is some chance the person will stop upon receiving an offer better than $140,000, Jaffe's statement is inaccurate.
In all fairness, Jaffe does get one thing right...
The point he makes about the hot hand - people seeing patterns where patterns are not - is, for lack of a better term, on point. See my previous post on roulette wheels here.
But another person quoted in the article also gives us this pearl of wisdom.
“The point often depends on someone’s circumstances. A person with a lot of money can take more chances; to them, a few thousand dollars difference is probably not a life-changing event.”
You mean like someone who just “won” $140,000?
–CT
Note: If the player gets past the first suitcase wihout revealing the $500K, and rejects that offer, then person will get a better offer. If that one is rejected, there will be a 2/3 chance the person will receive an offer better than $250K.
At this point, I am reminded of one of my favorite lines from the movie “The Naked Gun”. Nordberg (played by OJ Simpson) is in the hospital recovering from several gunshot wounds. Someone tells his wife there’s a 50/50 chance that he’ll survive, but then adds, but there’s only a 10% chance of that.