You make a great point. If you're offered a neutral EV hedge at ANY point, you should take it. In fact, if you take this to the limit then if you can get a neutral EV hedge before the game to lock in your EV on a +EV bet, then the correct play is to bet your entire bankroll and then hedge out because the risk is 0. Which is exactly what my formula predicts, because the parlay Kelly fraction is essentially a measure of your risk and if there's no event that has to happen for the first leg then p2 = p.

If you have to pay a vig to hedge out, then depending on the relative size of your bankroll, whether or not you should just comes down to price.

Next article in the series is up! This one talks about just these kinda spots where you shouldn't even wait to hedge...

Well done. As previously noted hedges are the easiest way to reduce risk and increase EG. All it takes is some math to realize it.

Thank you sir! You're absolutely right, and I plan to keep working out the math for many other spots as well.

Hi SGSpecial, Thanks for the articles they are very enlightening. I have a question: what is the formula for if we are laying rather than backing, for both doubling down and hedging?

Following up on this question SGSpecial?

An interesting thing happened in NFL last week. For those paying attention, 20 minutes before kickoff GB was -7.5 with odds adjust about 8-10c in their favor. CLE ml was around +320. Between that time and kickoff, the side odds stayed about the same, but CLE went up to +370 (+374 at BM, +379 at Pinnacle).

So the market at that moment apparently was thinking CLE was a bad bet to win outright, but +7.5EV was somewhat fair. Explanations aside, this seemed to be a good hedging opportunity. That is, play CLE +370, and play something on GB. Based on the market, teasing GB to -1.5 seemed to be the correct play. The question then is how much to bet on each.

I considered the following:
1. CLE ml +370 was fair (not likely, but possible)
2. CLE ml +300 was fair (not likely, but possible)
3. CLE ml +330 was fair (average of the 2 shading +300)

I went with scenario #3 as the most likely, and went ahead with the calcs. Because I would also need a 2nd leg to cash, I assumed I would be able to get a +300 dog (with 24% win rate) to hedge another -1.5 leg.

For $20k bankroll, the bet sizes are:
CLE +370: $1,157
GB -1.5 2 team teaser -110: $3,631
Leg 2 hedge: $1,409
EG: 0.67%

Teaser alone:
GB -1.5 2 team teaser -110: $981
EG: 0.11%

CLE ML alone:
CLE +370: $527
eg: 0.12%

With scenario #1:
CLE +370: $945
GB -1.5 2 team teaser -110: $4,492
Leg 2 hedge: $1,792
EG: 0.72%

With scenario #2:
CLE +370: $1,459
GB -1.5 2 team teaser -110: $3,768
Leg 2 hedge: $1,470
EG: 0.72%

The nice thing about this setup was that regardless what the true win rate for CLE was, hedging substantially increased EG.

For example, if I bet using scenario #2, but #1 was actual, EG would be 0.62%.