How do you handle 7th heads up when you don't improve a hand you've lead the whole way?

Example:

Your holding:
A2:485K

Opponent holding:
xx:A7810

You've got an 8-5 low, and your opponent has 8-7 at best. Assuming your 7th card is garbage, and your still sitting on an 8-5 low, how often and what factors do you use for deciding to value bet or not?

From my limited experience, almost the only time your bet is called (assuming your not check-raised,) is when your beat.

Anyone else have thoughts?

i would bet that example every time, I have played about 4 hours of razz my whole life don't listen to me

It's like any other game when value betting on the river, bet when you're a favorite when you get called.

This means not betting against draws when your hand is obvious. If you have [A2]789T[x] don't bet the river against AAA2. You'll get raised when you're beat and get a fold when you're good.

It's pretty easy in razz, though. Figure out what hands your opponent will call with. If your hand is better than half of them, you can value bet.

In the case mentioned in the OP, Im going to bet 7th. Assuming you've been betting and getting called down all the way the pot is going to be decent sized where said player may be forced to make a crying call with an 87. If he hits then theres nothing you can do and you lose an extra bet, but I think the odds of you getting called by a hand that you can beat are more likely than the odds that he improves enough to beat you and you lose an extra bet.

Of course if you are playing against a player you know to be very good at razz then i would probably check the river, knowing that they can very easily throw away an 87 against a hand that almost certainly has them beat.

I play razz on full tilt in stakes ranging from .25 .50 to 3-6, and have not found many very strong players, and have seen a lot of donkey call downs when there hands miss on 7th.