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Argh. I see now that I mis-stated the EV equation in the other thread. What you've posted above is correct.
Just beware that beating both villains individually is not what you're trying to accomplish with a shove OTF, there. You're trying to beat them concurrently, at the same time. This is a similar case to calculating your bet sizing to open from the BTN to steal the blinds based on the calling frequencies of both blinds combined. There's a square root in that one, IIRC, and thus one of the more frustrating calculations to study in poker.
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A donk bet will mean different things from different people. I really don't donk bet much at all, and would only do so in a multi-handed pot where I have 2-pair+ OTF and I'm just too nutted to take a chance on giving everyone a free turn card. There's very little of that in my range from MP1(really count it as MP2, since it's 8-handed. It's always about distance from the BTN, not the BB), though, certainly no straight draws on that board. You could safely put me on a pocket pair or NFD. and you block a lot of my range for NFD, and so does the board. At 8-handed, I'm not playing 22-44 without a read that the table will almost certainly pay off a set, so you may discount those combos in my range.
So my range to donk bet from MP1 (really MP2), is 66+, AKs, but you can rule out KK+, AKs, 'cause I'm gonna bet/raise every opportunity PRE with KK+, AKs. My range PRE is capped when I call.
ATss is 1 combo that may be in there or not, and when I outflush you, here, it's just a big cooler. It's literally the only FD in my range from PRE that isn't blocked by your hand, and it's not in my default range, only in my adjusted range.
So my range to donk bet is 66-QQ. 39 combos out of my starting range of ~120 combos. (quick estimates, not using equilab) You wouldn't know the specifics, but you can guess that less than 25% of my range to see the flop will donk-bet that board.
Maybe I x/c overpairs on that board, too, but your 3-bet PRE makes me think you have a lot of big PP in your range, too, so I'm not as enamored with my 77 - JJ.
Your pre-flop range is not capped, after all.
But I'm not your standard micro-stakes mouth breather (I'm my own unique brand of such), so that's probably not hitting the nail on the head.
It simply illustrates that a good place to start when trying to figure out a villain's range is to consider your own range.
Then ask, how much better/worse than me do I think villain's reasoning is in this spot?
Are they even nittier than you with a donk bet? Are they much wider than you with a donk bet?
Understanding your own range and where it draws the line and just recognizing which side of that line villain is probably on is an important early step in learning to put villains on ranges.
Do you think villain's range to raise/call PRE is tighter or wider than mine?
How much / attach a range to that guess.
Do you think the villain that donk bet the flop is more or less tight with that play than I am?
How much / attach a range to that guess.
Then we ask what combos in villains range (after they donk the flop) might fold if you raise OTF. For me, it's going to be hard for me to continue with less than a set. I'll probably call 1 or 2 bets with QQ, JJ, but I'm really not confident in TT-77 if there's a 3-bet OTF. Not without some read that Villain 3-bets super wide when their C-bets get push back.
So you'd basically be folding out all of my hands but the 3 combos of sets and the 1 (maybe) NFD. Me dropping from 39 hands in my range to only 3, maybe 4 hands in my range is a huge win for you, even if you always expect to be shown that set of 6's when I call. That's why I have to call 1 or 2 bets with QQ, JJ. That's 6 combos each in my range and if I don't call with more than 4 hands, then my ranges are so out of balance that you can start raising that donk bet with impunity and a wide range. As such, I just turned 2 of the top hands in my range into bluff catchers, and that's not too good. I shouldn't be donk-betting out with QQ, JJ all the time, but I can't do it never, or my donk-bet is just a faceup set to someone like you who's paying attention to that stuff.
Maybe it doesn't matter at the micros, 'cause almost no one is going to notice that pattern. ABC poker is so valuable at the micros because villains just wont exploit huge gaping leaks like that.
Does this help you see how to start constructing Villain's ranges in study? First figure out what you'd do and why. Then when you find a leak in your own play, like I just did, you ask, "How can villains exploit this leak?" and "Is this Villain likely to have the same leak?" and "Can I exploit this weakness?"
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