[Justin7]

Early in the season, you bet 1400 to win 1000 on "Will Patriots go undefeated? No."

In the time since you made the bet, you went on the worst run of your life. Your new bankroll is now 5000 (3600 available to bet, and 1400 on the prop bet).

The entire Patriots team came down with an intestinal flu from a team meal, with a resulting new line of Pk. You can bet on either team at -102.

What is the optimal hedge? Ricky and Ganch, please wait 2 days...

I've seen many variations of this problem - especially when a player has a future that could win a big payoff pending.

[Ganchrow]

Early in the season, you bet 1400 to win 1000 on "Will Patriots go undefeated? No."

In the time since you made the bet, you went on the worst run of your life. Your new bankroll is now 5000 (3600 available to bet, and 1400 on the prop bet).

The entire Patriots team came down with an intestinal flu from a team meal, with a resulting new line of Pk. You can bet on either team at -102.

What is the optimal hedge? Ricky and Ganch, please wait 2 days...

I've seen many variations of this problem - especially when a player has a future that could win a big payoff pending.

There's insufficient information to properly answer this question as you've not defined the bettor's risk preferences.

[Justin7]

There's insufficient information to properly answer this question as you've not defined the bettor's risk preferences.

Assume Kelly risk management (which is what I assume in all risk management issues).

also, assume the market price for NE/NYG is accurate.

[HedgeHog]

Bet NE $1211.88 to win $1188.12, guaranteeing a loss of $211.88 either way.

[Ganchrow]

Bet NE $1211.88 to win $1188.12, guaranteeing a loss of $211.88 either way.

Your goal here isn't to lock in a guaranteed outcome but rather to determine an optimal strategy based upon Kelly preferences.

See Using Kelly to Determine Optimal Hedging Strategy and Overbets and Line Changes -- A Kelly Spreadsheet.

[HedgeHog]

Ganch: If the market price is corect at Pick -102, then the future bet is now a poor bet. Hedging out at the minimal loss seems to be the proper decision.

[Justin7]

Ganch: If the market price is corect at Pick -102, then the future bet is now a poor bet. Hedging out at the minimal loss seems to be the proper decision.

The future bet is bad... But so is laying -102 for something that should be +100. how much -102 should I buy?

[Ganchrow]

Ganch: If the market price is corect at Pick -102, then the future bet is now a poor bet. Hedging out at the minimal loss seems to be the proper decision.

That would certainly be true if hedging were costless. However, because the fair price of the PK bet is +100 yet you're paying -102, you're giving up 0.9804% in vig on every wager.

So the trick is to balance the risk reduction with the concomitant cost of the hedge. Determining the appropriate balance is determined via your utility function (in this case full-Kelly).

[HedgeHog]

The future bet is bad... But so is laying -102 for something that should be +100. how much -102 should I buy?

Depends on your tolerance for loss. As an extreme, you could let the original bet stand and risk losing $1400. But I would think that a +Ev better would rather try to preserve as much of his bankroll, and live to fight another day. Obviously Kelly will have something different to say, and I'll be very interested in the "right" answer.

[HedgeHog]

That would certainly be true if hedging were costless. However, because the fair price of the PK bet is +100 yet you're paying -102, you're giving up 0.9804% in vig on every wager.

So the trick is to balance the risk reduction with the concomitant cost of the hedge. Determining the appropriate balance is determined via your utility function (in this case full-Kelly).

I understand the cost of the bet. If hedging were free, wouldn't the correct bet be $1200 to win $1200 for a loss of $200 either way. With the very small juice here, the additional cost is just $11.88 to get out of a bad situation.

[Ganchrow]

I understand the cost of the bet. If hedging were free, wouldn't the correct bet be $1200 to win $1200 for a loss of $200 either way. With the very small juice here, the additional cost is just $11.88 to get out of a bad situation.

If hedging were free then yes.

Check out the spreadsheets referenced in the above-linked posts. Any one of them could be used to solve this in a matter of seconds.

[durito]

Bet $1,164.00 to win $1,141.18

[Ganchrow]

Bet $1,164.00 to win $1,141.18

Ding ding ding.

[HedgeHog]

Bet $1,164.00 to win $1,141.18

I got the same answer too using the Kelly worksheet.

PS Nevermind, Ganch posted at the same time. Makes sense.

[Gurni]

The future bet is bad... But so is laying -102 for something that should be +100. how much -102 should I buy?

If the player just wants to get rid of the bad future, he will either bet it like hedge said with the same loss amount on both outcomes..or make the amount a bit smaller or bigger depending on his feeling about what side will win.

So this may be interesting to math freaks (or maybe not, coz too easy?), but has nothing to do with the real gambling life.

[Justin7]

So this may be interesting to math freaks (or maybe not, coz too easy?), but has nothing to do with the real gambling life.

That one problem might not be that significant, but most serious gamblers know and understand it, and use the theory.

Here is a real life example that is similar:
I can bet on Phili -1.5 -241.
I can bet on Buffalo Pk +280, or
Buffalo +1.5 +250.

I can risk 100% of my balance on a pure scalp. But there is better way when you get these opportunities frequently (which we do in NFL). If you're going to tie up 100% of your money (or a large amount of it anyway) on stuff like this, you had better be perfect with it.

[Ganchrow]

So this may be interesting to math freaks (or maybe not, coz too easy?), but has nothing to do with the real gambling life.

The point is that if for an advantage player it should have everything to do with "real gambling life".

Whether you personally care about it or not doesn't change the fact that proper bankroll management is an essential component of advantage sports betting.

[HedgeHog]

This has been useful. I get the fact that the hedging bet needs to be reduced according to the disadvantage you're facing. Had the line been -105 a smaller bet is needed; even smaller for the unfortunate -110 player. Good question, Justin.

[Justin7]

Bet $1,164.00 to win $1,141.18

Congrats, Durito! You've been added to the "do not answer quickly" list!

If you're feeling nice, show the math for everyone.

[Santo]

If "real gambling life" paid attention to Math, less people would lose less money. Though that's probably not something those who understand the Math should encourage