Dear Mark,
There is a new game show called Deal or No Deal. The participant selects a brief
case containing anywhere from 1 cent to 1 million dollars, and there are 26 cases
to choose from. Then, all non-selected cases are slowly revealed until there are
just three left, two on the board and the one the player has selected. My wife
believes at the end of the game, when only 3 cases are left, the player has a
1 in 3 chance for the highest prize, assuming that the 1 million has not been
seen yet. I believe the true odds are still 26-1, which is what they were when
the case was selected. Which is it? Dick D.
Dear Mark,
Do you watch Deal or No Deal, and what is your take on the game in general and
when should you take the banker's offer? Cheryl A.
Yes, Cheryl, I've watched Deal or No Deal a bit, although not a lot since I
really don't see it as much of a game, since neither skill nor trivia is involved,
just an ambiguity, a bellowing brother-in-law, the prickle of greed and a baseless
guess.
My take on it, Cheryl: I find Deal or No Deal excruciating to watch because
of its tortoise pace (an exercise in Job-like patience), not to mention all
those dreary commercials to keep the suspense alive (huh?). When they finally
return from pushing products, we get to watch five more minutes of a brother-in-law
in the wings yelling, "Take the Deal, you Putz!" Now that Nielson
knows what I think of the show's staging, plot and general entertainment value,
and because of my resultant limited exposure to it, I really can't answer your
Banker offer question with 100% certainty.
From what I have seen, I am sure that probabilities are re-calculated by the
anonymous silhouetted banker, based on what values remain in play, which allows
me to put Dick's question to bed. At the onset, Deal or No Deal offers the best
odds for winning $1 million on national TV -- 1 in 26. But once only three cases
remain, those odds are improved to 1 in 3. Your wife is right, case closed.
Back to you, Cheryl. From my limited observation of Deal or No Deal, the banker
seems to start with offers well below the expected value of the remaining suitcases,
getting closer to the expected value near the end. A smart player would refuse
the banker's offer until it is close to or exceeds the average of the remaining
suitcases. If the contestant just wants to maximize the expected value of their
winnings they should always turn down the Banker, and yet, it seems most players
end up accepting the Banker's deal before all the brief cases are opened. So,
are they well advised by their brother-in-law to take the money and run? Probably
yes, because it seems their decisions are made based on what we call in the
gambling business risk aversion.
Given the choice between two gambles: Gamble A making the weak promise of a
very high payoff, and Gamble B making a more likely promise of a more modest
payoff — the gambler showing "risk aversion" will choose Gamble B,
preferring to take the lesser risk. The "risk seekers", familiar at
casino tables, accept a negative expected return or the thrill of financial
risk and a possible immense payoff.
Also factored in is that the amount of money involved in Deal or No Deal is
a significant fraction of the contestant's net worth. As we crunch the banker's
offer in our heads at home in the comfort of our Lazy Boy, the banker's stingy
offer may be far more than the contestant makes in a year. It's easy to see
why many players become risk averse and are willing to accept a sure amount
rather than a possibly higher amount by taking additional risks. Let's face
it, taking risks is . . . risky.
Just like those million-dollar figures on a progressive slot machine, Deal
or No Deal taps into the most basic human emotions: greed, a desire to improve
one's situation through a get-rich-quick scenario. It's something we can all
relate to, and one we all play in life differently.
Gambling Wisdom of the Week: When a man with money meets a man with
experience, the man with experience leaves with money and the man with money
leaves with experience. -- Anonymous
