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I have a question about equity here. If you are HU at the turn, then theoretically, you need better than 50% equity to raise according to your argument. Now if you have an overcard and four card flush draw heads up, and say your overcard outs are all clean, so that gives you 12 outs or 25% equity so you shouldn't raise, but I would think in a HU situation, you quite often would want to raise here. Do you need to adjust for HU situations or would you play be the same criteria no matter what.

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Quite often, HU and short handed pots have a certain amount of Fold equity that you can add to your hand equity to move your play from call to raise.
You also have to factor the chance that your hand is ahead into the mix.

But the requirement of 50% or fair share stays the same.