Download Beat the Banker & Know Your Enemy

The Game:
Conclusions:
•Deal or No Deal is an NBC hit TV show
where the contestant picks a suitcase from 26
each with a value that ranges form $.01 to
$1,000,000.
•Each round the contestant opens a certain
number of the remaining suitcases to reveal
the values inside.
• At that point a mysterious banker offers the
contestant some amount of money to stop
playing.
Beat the Banker & Know Your ”Enemy”
MS&E 220 Project, Fall 2008
Elizabeth Martin, Michael Fan,
David Wang jessi reel
Discovering the Banker’s Formula
To do this, we first recorded 35 data points. Recorded were the suitcases removed, the expected
value, and the mysterious banker’s offer. Data collection was done by playing the game online.
Data was analyzed in search of a pattern in the banker’s formula.
“Beating the Banker”:
Expected Value
One strategy is simply to “beat the mean”—or
rather only take the banker’s offer if it is bigger
than the current expected value of the deal. With
26 suitcases, there is a uniform distribution of
what suitcase will be pulled next. Its expected
value would simply be the average of all the
amounts:
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
If no cases have been opened, then this value
computes to approximately $131,477.54.
As cases are removed, the formula for expected
value updates to:
E[x] = 1/n (x1) + 1/n (x2) + 1/n (x3) …. 1/n (xn)
U = bxb,
where b=0.625
Optimizing game strategy is
more than beating the expected
value of the deal. By deriving and
anticipating the future banker’s
offers, we can plan strategically
based on the probability of
improving that offer.
Strategic
Implications
Example:
What’s the Probability that future banker’s
offers will be higher than current
banker’s offer, given only 6 cases left?
1. We derived a model that compares current
banker’s offer versus possible final round
bankers offer.
•A chart showing the utility
function as a function of
suitcase value
•Comparing our predicted
banker’s formula to the actual
data collected gave the accuracy
shown in the following chart.
This is the % probability
distribution of our Certain
Equivalents about the actual
banker’s offers.
2. If there are n boxes remaining, and a boxes
that have amounts higher than the banker’s
offer, then
1. keep playing if a / n < t
2. stop playing if a / n >= t.
This 2nd method does not work flawlessly for
rounds farther from endgame. Possible
solutions could take into consideration (r,t),
that modifies strategy given which round r