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That's nice, albeit unrelated as fuck to this hand.
Edit: Put cliff notes first, math explanation last.
A good portion of the time we're already drawing dead, and if he has a king that isn't a boat yet, we're going to both improve on the river one-eighth of the time, which will equally suck. Overall, when we improve on the river, we're still probably losing almost half of the time, so our 8 heart outs (excluding the 9) are really only worth about half an out each.
With that noted, I'm probably folding to anything bigger than a $0.20 bet with a plan of when I hit to call a pot-sized or less bet on the river and bet half the pot or so if I'm checked to in an attempt to get value from bare trips.
--- MATH ALERT ---
At 10nl, villain will likely go to the felt on any river with any king, two pair turned full house, or set turned full house. Now, obviously sometimes he might get away from K2 on this flop or something, but other times he might have a lower flush draw or bottom two pair on the flop, so I'll assume those cases approximately cancel each other out.
So here are the possibilities from this example range:
* Group 1: 6 possible combinations of 55 or 99 each.
* Group 2: 6 possible combinations of K9 or K5 each.
* Group 3: 8 possible combinations of KJ, KT, K8, K7, K6, K4, K3 or K2 each.
* Group 4: 6 possible combinations of AK or KQ each.
For any holding in Group 3, if we make our flush on the river, from our remaining 8 outs, there is a 12.5% (1/8th) chance villain also improved to a full house. Now, let's throw out a couple of fantasy scenarios to get a feel for how much value we have against this particular range.
Let's say villain let's us draw for free on the turn, and always makes a pot-sized bet on the river. We'll call this bet if we get there with one of our 8 outs, and we'll fold if we don't. When we miss our flush draw, we simply fold, so there's nothing to compute about the times we miss our draw.
So we need to know what percent of the time we'll be losing on the river if our clean hearts hit. Since 12 times out of 26 he has his full house by the turn, we're already losing 46.2% of the time. In 12.5% of the remaining 53.8%, our opponent will make his full house on the river, which accounts for 6.725% of the time. This means that against this range, if we get the river for free and call a pot-sized river bet, we'll lose 52.925% of the time, which will be a negative profit for us.
Let's say villain bets 1/4th of the pot on the turn, which we call getting 5:1, and always makes a 3/4th pot-sized bet on the river, to which again we'll call if we make one of our 8 outs, and fold if we miss. We'll get there on the river 17.8% of the time, so the other 82.2% of the time we're down one-fourth of the pot value. In that 17.8%, we'll be behind 52.925% of the time to a 3/4th pot-sized bet. The other 47.075% of the time, we win a pot the size of 2.25 times the size of the pot on the turn. Sooo....
Times we miss: (.822)(-.25) = -0.2055
Times we hit and lose: (.178)(.52925)(-.75) = -0.070654875
Times we hit and win: (.178)(.47075)(2.25) = 0.188535375
For a grand total of -0.0876195 times the size of the pot on the turn.
Note that these are fantasy scenarios, but prove a point: you generally don't have nearly as much equity here as you think you do.
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