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Raising this flop with QQ is a pretty blatant -ev play. I'm not going to spend a lot of time building a range for villain, but let's look at this situations from a few different perspectives.
Let's just assume that on this flop against villains betting range that we feel we are behind his betting range. That means that we feel we have <50% equity against the range of hands villain would bet in this spot. If this is the case, then we can immediately conclude that calling is a -ev play, unless we are intending to compensate on later streets (such as floating the flop knowing we are behind his range, but believe we can take the pot away often enough on later streets to make up for the initial call).
Therefore, if calling is -ev, then we shouldn't do it. So our other two options would be to either fold or raise (but as a bluff). Folding would be a 0ev play. That is, over the long run we do not expect to either make or lose money in this situation (because we aren't risking any).
I suggested raising as a bluff in the previous paragraph. I'm not really speaking towards this exact hand history, or even situations such as this. I'm just speaking from a theory based perspective, where raising in one of our options, and doing so in this situation would be as a bluff. The reason being is if we are -ev in calling against his betting range (we have <50% equity against the range he bets), then when we raise and narrow his continuing range even more, we are obviously going to experience a loss in equity (as his range of hands narrows and becomes stronger). However, if we feel he is folding enough hands in his betting range to make a raise +ev, then we should raise as a bluff in this situation. You would find this out by using math to determine how often villain needs to fold (based on the pot size, your raise size, etc), and then comparing that to his betting range vs. his continuing range.
Let's say that in this situation we DO NOT feel villain is folding often enough to make a bluff raise profitable. Therefore, that makes bluff raising -ev also.
Therefore, if our assumed situations is correct, and we are in fact behind villains donking range on this flop (as you alluded to in an earlier post), then our decisions would fall along this line: folding > calling > raising, where calling and raising can be interchanged based on their exact ev. Therefore, in this situation since both calling and raising are -ev plays, we would be correct in taking the 0ev play that is folding.
Now, if we assume we are ahead of villains donking range on this flop, then the situation changes a bit. First, we now know that calling is +ev. This is because we have >50% equity against his range of hands, and therefore a greater % of the pot "belongs" to us. Folding remains 0ev, as always. So as of right now we know that folding is incorrect, and we will be continuing in the hand. But the question is how, call or raise?
Well to determine how we continue in the hand we have to look at the EV of a raise from us. Note that if we raise we would no longer be dealing with just his donking range on this flop, but instead we have to adjust his range to a calling range. That is, what hands he would bet the flop with and call our raise. If we have >50% equity against the range that he is calling our raise with, then a raise is +ev. If that is not the case, and we actually have <50% equity against the range that continues against our range, then raising is -ev and we shouldn't do it.
We then must compare the EV of calling versus the EV of raising to determine which is more +EV, and from that we decide what our action will be.
Regarding this particular situation. If you feel you are actually behind his donking range (as I believe you do), then your only real options are to either fold or raise. Given his range, and the range he will continue with, I do not believe that a raise will cause him to fold enough of his range to be profitable, therefore you must take the 0ev route of folding.
If you felt you are ahead of his range, then your options are between calling or raising. I do not believe that you will be ahead of his calling range (that calls your raise), therefore, calling becomes your best option. Therefore, calling > folding > raising, where folding and raising can be interchanged based on actual ev.
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