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rec5 - ORIE 321/521 RECITATION 5 Spring 2007 The aim of...

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ORIE 321/521 RECITATION 5 Spring 2007 The aim of this recitation is to apply dynamic programming techniques to compute (after the fact) an optimal betting strategy for a pool to wager on the outcome of the 2001 NCAA men’s basketball tournament. For those unfamiliar with this tournament, 64 teams compete in a single elimination bracket consisting of 6 rounds. In each game, the winner advances and the loser is eliminated. (There are 32 winners that advance to round 2, 16 to round 3, etc., until the finals, in which only two teams compete for the championship.) So there are 63 games total, and a team must win 6 games in a row to become the champion. The bracket is split into four regions of 16 teams apiece, and each team is given a seed from 1 to 16 (where this “seed”ing is a hypothesized ranking of these 16 teams from best to worst). The teams that have played the best during the season are rewarded with the lower numbered seeds, so the four #1 seeds are the favorites to win, while the four #16 seeds are perceived to have little chance of winning. The following novel pool was invented by Robin Lock and popularized by former Cornell ORIE faculty member Rick Cleary. The teams are each given a price based on their seed, according to the table below. The costs
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