The odds may say, "No
deal!" and yet . . .
7 April 2006
By Mark Pilarski
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
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