Philadelphia was up 27-10 at half. Cha-ching baby! Tomato had a winner!
However Tomato saw that the 2H line was PK at +110. He had a no-risk 10% win, and a 8 point middle! Considering Tomato had no risk, he took the middle. Bang bang!
Tomato knows you sharps select 2H bets a different way. What would your mathematical advice be towards 2H bets given that your 1H bet is a winner? When does it make sense to "go for the middle"?
This isn't directly a math question. If you handicap a team--perhaps through math, or perhaps observationally--as being poor at lead-holding or good at scoring garbage points then plan to take your middle of size X if available. If it didn't seem like a good idea before the game started, then there's no way to decide when the situation is suddenly in front of you.
In most cases it would be a bad idea. If your bet is winning at halftime, and it wasn't because of blind luck, let it ride. Unless, of course, you want to trade the game, in which case live betting may offer much better opportunities than a half time shot.
For me, the decision to hedge is made prior to the first wager. This allows me to allocate a much larger % of bankroll to the initial wager because I know that I am not going to let-it-ride and will hedge whether I have a profit or a loss.
I think the difficulty in making the decision after the initial wager is the following:
First, it will probably be a "normal" size wager and hedging will create a relatively small profit.
Second and my major concern is that if you don't make the decision to hedge profit or loss prior to the initial wager, you may find yourself hedging more of your winners and letting ride more of your losers.
This will at the very least reduce your profits and more than likely create losses even if your initial wagers would have been profitable.
The e.v. of the sum (of bets) is the sum of the e.v. You want to bet the halftime line if and only if you think that the halftime line is offering value. Yes, there are corner cases where it is worthwhile to control your risk and take a line that is marginally bad or break-even, but the gain from these is minimal if you aren't stepping out of line to begin with (and never comes up unless you are trying to bet Kelly). What your pregame bet can do for your halftime betting is enable you to bet more when you now like the other side by keeping your risk in check.