Saturday, March 03, 2007

The Brier: Predictions and Bets
An Algebraic Summary of Our Selections

Last night at our curling club, Ms. Eclectic and I entered the pool to predict who would win the 2007 Tim Hortons Brier. Ms. Eclectic thinks it will be a toss-up between Glenn Howard (Ontario) and Kevin Martin (Alberta). Deep in my heart, though, I predict Glenn Howard will win.

Who did we pick in the club pool? Not Glenn Howard; and our choices were reasonable because of how the pool works: the pot is split between everyone who correctly picks the winner.

Given that we curl in Ontario, and (as a result) given that we expect most of our fellow club members would pick Howard to win the Brier, we realized that if we also picked Howard, and Howard won, then the size of the prize (split among everyone who picked Howard to win) would be pretty small.

So, even though I think there's a somewhat higher chance Howard will win, I picked Brad Gushue (NF/L) to win in the pool, and Ms. Eclectic very reasonably picked Kevin Martin.

Algebraically, E(W) = (pS)/N, where
  • E(W) is each bettor's probablistic, expected dollar winnings,
  • p represents that bettor's subjectives guess as to the probability that his/her selection will win the Brier;
  • S is the size of the pot that is to be divided between all those who correctly pick the winner; and
  • N is the number of people each bettor thinks will have selected the same winner s/he did.
For Howard, p might be high, but N is expected to be high, too, offsetting the high value of p. For Martin and Gushue, we expect that N will be much lower so that if we do pick the winner, we will win more money.

Note: this strategy assumes risk neutrality on our part. It also assumes that nobody else (or not many others) in the club have the same betting strategy.

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