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.
Good
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