Here's a game-theoretical idea that stems from a rather different analysis, but I just played a few HU matches with this in mind and really liked:

First, a value-bet is always being ahead of 2/3 of villain's range in a given situation--i.e., you have top 1/3 given villain's range.

So, the question is: How often should you bluff? And there's also a game-theoretical optimum, which I think is around 1/6 of the time with pot-sized bets.

However, in a given situation you also have or should have some assessment of fold equity.

I'll give PF play as an example, but the same actually applies on all streets--except that a betting sequence also narrows down your opponent's hand range. PF with position, his hand is random.

Now, if you're in SB and the blinds are 10/20, a VB is raising top 1/3 of your hands according to HU ranking. And if you raise to 50 (as I do here), you're paying 40 for a chance to win 30.

So, villain needs to fold a bit more than half the time (for simplicity's sake, I think we can call it 2/3) to make a bluff break-even.

Hence, as long as villain is calling >1/3 of the time, you should never bluff. And if he's calling <1/3, you should ALWAYS raise.

My conclusion is that you should be switching between these strategies until you feel like villain has changed his. And the same applies on every street.

Probably most difficult to play against PF should be raising actually a bit tight for a stretch (more like top 20% or randomized so as to define your hand less), then, as soon as you've achieved the goal of getting <30% calls, raise everything.

Similarly postflop: If he'll fold more than 50% to a pot-sized flop bet, you should be betting every flop. If not, you should be VBing only. Or with raises: If he'll fold often (defined according to your cost vs. gain) to a raise, you should be raising everything. If not, only value raises.

To red: The raising 100% is only good if all you lose is the amount of the raise. This is not good if you lose a CB.

Let's take your scenario: I raise my 32o and you're calling only with top 25%.

When I CB here, I need to consider whether I'm now in the top 1/3 of YOUR hand range on this flop, and I know you're only playing premium hands.

In other words, particularly if you're tricky and plan on CRing me a lot, I'm very rarely betting--a pair on an all rag board is probably a CB, but since you're playing better hands, I may even take a free card in that case, and most flops are very dangerous for me. So, I'm CBing here very rarely and only on a pretty hard hit.

I agree with you about position. I think that comes into play somewhere in the game-theoretical way of looking at it. But it's hard to create simplified models where the drawing aspect also comes into the picture.

Anyhow, if you're going to play with this kind of strategy effectively, you can normally assume that if they're playing tight (you're playing loose) and call, you give up immediately.

Another example from post flop from earlier today: Very early on, I made a light raise on the flop with position against this guy, he calls and keeps firing (I had some outs, but not enough, and I fold). Ok, my note here is that he's too tough on calls. So, now my strategy is never to raise light (unless he changes), but I can still get a lot in being ahead if I now raise only something like TP or better.

What I'm really driving at here is that in all situations, you should NOT be playing "theoretically optimally" but rather either too tight or too loose in the attempt to have your opponent play suboptimally as often as possible--because your opponent doesn't know whether you're too tight or too loose at the current time.

Several interesting ideas there for throwing them off.

One comment: If you raise to something like 50 in SB (blinds 10/20), you're risking 40 to gain 30. So, I think the reason for at least calling 30% of the time is that if you don't do that, raising 100% becomes profitable.

So, I don't think it actually has anything at all to do with hand ranges, just by basic pot odds. And of course, if you're calling 30%, you might as well choose the particular 30% that holds up best HU, and that's a pretty much known range--although I personally throw in low SCs here (both as raiser and as caller) even though 65s actually ISN"T in top 30%. I do feel like those are hands that are important for having some hands that potentially hit just about any board pretty hard.