The NCAA basketball championship game is tonight.  If you bet on either North Carolina or Villanova to win, then you now have the opportunity to hedge your bet and ensure some profit.  But should you?  We’ll go through tonight’s game as an example to explain how you should make your decision.

Back in January, I tabbed Villanova as a good bet at +1500 to win the national title.  So we’ll use the assumption that you are an avid reader of this blog and bet \$100 on the Wildcats at 15-to-1 odds.  That means your total return would be \$1600 on your \$100 bet.

If we look at the current market for tonight’s game, we’ll see that North Carolina has a 53.9% chance to win the game tonight, thus giving Villanova a 46.1% chance.  So you have a 53.9% chance of walking away with zero dollars, and a 46.1% chance of walking away with \$1600. Your expected value for this bet is (.461)(\$1600) = \$737.60.  So if someone walked up to you and offered you \$1000 for your betting slip, then it would actually be a correct decision to sell the ticket for the guaranteed money.

But I would imagine you would have a lot of trouble getting that \$1000 offer.  So let’s say you want to take the Tarheels at -130 tonight to hedge your bet.  You can bet \$130 to win your original \$100 bet back to make sure you don’t lose anything.  So now your futures bet that was worth \$737.60 goes down to \$607.60. (Technically the value of that bet doesn’t change, it’s the combination of the two bets that adjusts your value if Villanova wins, but that sounds complicated and stuff.)  But instead of getting \$0 if UNC wins, you get \$230 for a value of (.539)(\$230) = \$123.97.

So you lose about six bucks of value by hedging.  So if that \$100 is really important to you, then it’s obviously worth the hedge, but strictly looking at this situation from a mathematical standpoint, you should let your initial bet ride.  Any time that you are making a bet that is -EV (negative expected value) to hedge your bet that is already in good shape, you are costing yourself money in the long term.

The only way that you would want to hedge (mathematically speaking) would be if you determine that North Carolina was a bigger favorite than the market is currently offering.  In that case you would be getting a positive expected value on both sides of your bet.  Me personally?  I’m riding Villanova +1500.

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