Beat the Banker & Know Your ”Enemy”

1. Conclusions: The Game: 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. • 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” Strategic Implications Discovering the Banker’s Formula • Example: What’s the Probability that future banker’s offers will be higher than current banker’s offer, given only 6 cases left? • We derived a model that compares current banker’s offer versus possible final round bankers offer. • If there are n boxes remaining, and a boxes that have amounts higher than the banker’s offer, then • keep playing if a / n < t • 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 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. U = bxb, where b=0.625 “Beating the Banker”: Expected Value MS&E 220 Project, Fall 2008 Elizabeth Martin, Michael Fan, David Wang jessi reel • 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. • 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: • 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)