I have a future bet on Tampa Bay to win the Super Bowl at 10-1, now effectively a simple +EV bet on today’s game. That raises the perrenial question of hedging the bet and betting some on Kansas City. The standard answer that many gamblers will give you is that if you felt it was a good bet (+EV) then, you would not hedge it. However, several things have changed since then. First and most significantly, Tampa Bay hasn’t lost so the bet is still live. Next, the odds are certainly different today. Finally, the outcome probabilities have changed. It seems to me that there are three possible approaches.
1. Be a gambler and do not hedge with another bet on Kansas City.
2. Bet enough on Kansas City to cover your first bet, insuring no loss.
3. Bet enough to create a certain and equal return eliminating the gamble.
If I take the third option, find the best odds, and wager an amount to get the same return regardless of the outcome, what is that amount? First you compute the expected return on the initial wager. That would be ExpRet1=Amount1*Odds1*Probability1. The expected return on the second wager would be the same formula with different values (note: Probability2 would equal 1-Probability1). Set the two equal to each other, plug in the known values; Amount1, Odds1, and Odds2. Estimate the current probability and solve the resulting equation for Amount2.
I’ve used the average book’s moneyline to estimate the probability of Tampa Bay winning at 0.40. I won’t detail the calculations. However, if the initial bet was $1 to win $10, the expected return of that bet would be $4.40. if the best money line I can find on Kansas City is -155, then the amount bet on them should be $4.46. That expected return would also be $4.40. I don’t yet know what I’ll do, but at least I know the numbers.