Wow, such a long post. I'm glad you're willing to elaborate on this because I find this an interesting hand. 
Originally posted by Dawnfall26
If you make a third guy fold, part of his equity share is given to you.
On the flop after SB donks I would estimate your equity to be around 35-40%(lets say 37,5%). Once you make third guy fold your equity got bigger and is not at around 50%(lets even say 47%). So you got 10% boost with that raise. Math at this point I assume is not rly super easy since there are many variables to be considered.
I agree that your equity obviously rises when the third guy folds. But shouldn't your equity rise to at least 50% to be profitable? 33% equity is enough when you're playing with three in the hand, because you get 2 bets from them for every bet you make. Analogously, your equity should be at least 50% HU. So you go from a profitable situation (37,5% > 33,3%) to a slightly unprofitable situation (47% < 50%). Or am I missing something here?
Originally posted by Dawnfall26
But if we assume that we dont mind if the third guy goes for any additional action(and here we certainly dont) we can only focus on the case when he folds.
I agree, the ideal situation would even be a 3bet followed by a cap 3way.
Originally posted by Dawnfall26
In this case its pretty clear that we prefer to have 47% equity instead of 35% because in that 0,5BB raise that we make we are only loosing 3% of it but we are gaining 10% of the total pot.
Like I say above, I should think you go from a slightly winning to a slightly losing situation.
Originally posted by Dawnfall26
Now you may argue that it may be better to not make the third guy fold so that our implied odds are better for further streets. But is that really the case. What is the difference in the ranges that he will continue when we raise and when we just call.
He clearly will not fold FDs,9x+ in any case.
If we call he will continue super wide.He will call basically any two over,any Ax,Kx,any BDFD so I would guess 80%+
If we raise he most likely wont fold good Ax,pockets,maybe even 4x or even some Kx,Qx with BDFD.
I should say that the ranges are little bit tighter.
His range if we call: 2 OC's, FD, any pair and better made hand.
His range if we raise: FD, 9x and better made hands.
Originally posted by Dawnfall26
So the real difference between the two ranges is in random overcard,Ax,Kx. Are those really the cards where we gain a lot of implied odds...no they are not!... since these cards wont see the SD most of the time. But what these cards will do is they will only continue if they hit turn(and that is not very often) in which case our equity will go down a lot.
So in fact our implied odds are better vs his range when he continues in a raised situation than in a calling one!
The different in the ranges are indeed hands where we don't get a lot of implied odds, in the sense that they certainly won't raise if they hit a pair on the turn. But if they don't hit they will probably still call a lot of turn cards with overcards. And if they do hit we still have at least 33% equity because of the nut flush draw.
Originally posted by Dawnfall26
And the point about position is also pretty good one. If we raise and get it HU we will end up IP which is very very awesome since it will allow us to play perfectly vs him in most cases(which is to bet again turn and check behind river). Same is clearly not true when we just call since now he will dictate the tempo and there will always be another guy behind you to act.
But what if he bets the turn? 3way it should be a super easy call for value, you would even hope the third guy raises. HU on the other hand, you don't get the right odds to continue (only 12 outs, you would need 14). You can maybe call with implied odds, but it's an easier decision 3way if you should ask me.
And just in general, aren't draws the ideal hands to play multiway? Especially the nut FD? You get lot of implied odds and only small reverse implied odds. A made hand like TP on the other hand is something you prefer to get HU.
Originally posted by Dawnfall26
Oh and about seeing what he shows at SD. It is very important to note in this case whatever he shows you. If he shows you TP or set than I would probably think that this guy probably just donks when he has it and is passive otherwise. Sure a few more spots like this wont hurt but that certainly a hypothesis I would make after seeing it(since donking TP or set in this spot is obviously very bad). If he donks FD(which is also bad) that tells me that he probably likes to donk bluff so I would clearly be a bit more SD bound vs his donks next time. If he shows you mid or bottom pair(which is what I would suspect a lot of ppl have in this spot) then I assume he is more of a passive kind of guy who is afraid to c/r but at the same time doesnt want to give freecards.
If they fold at some point or you get to see a hand like Ax,random overcards then its a clear sign that this guy just likes to donk whatever on the flop and raises like this one become extremely profitable since your equity will be much higher than in our assumed case.
It seems to me that you're way overestimating the information you get from a single hand. For example if he shows you TP, you can't extrapolate that to 'he's passive unless he has it', it's possible that he would donk as well with a FD.
You also mention that it would be very bad for the SB to donk with a set. What would be the best value line? c/c F, b T? I don't like c/r here because it's such an 'action killer'.
Just a lost note: sorry for disagreeing with you so much. 
It's not that I want to be stubborn or so, I just feel that I'm learning a lot by discussing such hands extensively.