A revisit to discussion about pot equity (NO hand)

On a post yesterday, Deranged gave the best explanation I've seen about calling/raising decisions and pot equity vs calling decisions and pot odds. I had a further question that never was answered so I will pose it again. Here is Deranged's post, my question follows
"In situations when you are deciding whether to bet or raise for value (rather than to call), you need to consider whether you have above-average equity , not whether you have sufficient pot odds .
The point is that, when you raise this turn, you are choosing to put extra money in the pot . This only makes sense if the additional bets that you are putting in the pot are profitable. The fact that you could conceivably call two bets profitably here (getting like 11 to 2 or whatever) does not mean that it is correct to raise.

In order to determine whether it's correct to raise, don't compare the size of the total call+raise to the total pot size.

Instead, ask yourself the following question: Am I going to win more than my fair share of the extra bets that go into the pot ?

You have three opponents. Your nut flush outs give you about 20% equity. Your overcards might be good. Say they are worth about three outs. That's 12 outs total. That's slightly more than 25% equity. The average equity for the pot is equal to 100%/the number of players; so here it's 25%. In order for a raise to be correct, you need to be confident that your equity is above average .

We deduced that your equity is probably a little bit above 25% here, but notice that if you raise you might get three-bet and the pot might not have 3 opponents anymore. Because of that fact, your equity needs to be considerably higher than 25% to assure that raising is going to have value. I'd say you would want to assure like 35% to make a raise correct here.

So in my opinion calling is clearly better than raising, as raising is about equivalent to calling if everything breaks your way and is clearly worse if you get three-bet and some opponents fold."
My question is regarding when you are HU on the turn and facing these decisions. By the above reasoning, you would need to feel you have a better than 50% equity to raise, which isn't going to be the case for most hands (even a nut flush draw and clean A overcard outs is only 25%). However in a HU situation, I would think you would often raise to either get a free SD or because you think your hand might be good with the A high. So my question is, how do you adjust your thinking of pot equity to HU situations?

[mack848]

You can raise for value HU, as your equity is not simply the % of the time that you improve to a winning hand. In HU pots especially, the combination of the equity of your draw + the chance you are ahead + fold equity could well be >50%.

You are correct that it is extrememy unlikely that your draw alone will give you sufficient equity to raise the turn HU. A semi-bluff raise could well be correct though – if you suspect that your opponent might fold a better hand, or that you are ahead. You need to estimate whether the cost of raising is worth it. This would need to be based upon your read of them (can they fold?), their possible holdings (TPTK or middle pair?) and the size of the pot. They will only need to fold very occasionally in a medium sized pot for a semi-bluff raise it to be +EV.

thanks, that was a good explanation