Re: 10/20 Q9s
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I have twenty outs to an almost sure win. That gives me ~40% equity in this pot.
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Jason, I think you need to discount pretty much here, you don't discount at all.
Counting outs:
Hands those loose passives could have that makes you forced to discount:
<u>UTG:</u>
KQ: 11.5 outs
J9: 18 outs
87: 14 outs
Other reasonable hands he could have: JT
I also think it's reasonable he's called the flop with a set trying to bet the turn to get raised by the flop aggressor and trap you, bad players tend to do that a lot (against these hands we have 14 outs). But what hands will a loose/passive bet this turn with after the aggression shown on the flop? The only one that you have 20 outs against is JT unless he's a über-fish and calls preflop in UTG with J3.
If we add some hands such as J3s and the fact that he might be donking with AJo or something like it (not very likely a loose/passive will do that after the flop got betted and raised) I would still say you'll only have ~17.5 outs against UTG.
<u>Then we need to worry about MP2:</u>
KT: 17 outs
TT/99/33: 14 outs
QT: 15 outs
T8: 17 outs
Other reasonable hands: Hard to put on a range but since he's passive it's not terribly wide. Of course it's made up by more hands we're having 20 outs against than those I've already mentioned, but he'll still kill a decent ammount of outs.
Put together I think it's obvious that estimating more than 17 outs would be too optimistic.
EV-calculations:
17 outs gives us 37% equity (first [...] is EV for the flop and 2nd is for the river).
<u>EV (turn raise):</u>
[(2+2x)*0.37 - 2*0.63)] + [(1+x)*0.37*0.935 - 1*0.065]
x = the chance of MP2 calling the turn raise.
I assume if MP2 calls the turn he'll call the river too and so will UTG. If we hit and miss it will cost us 1BB on the river, if we miss the river we'll check/fold. I estimate x=80%.
[(2+2*0.8)*0.37 - 2*0.63] + [(1+0.8)*0.37*0.935 - 1*0.065] = +0.48BB (x=90% would give +0.66BB)
<u>EV (turn call):</u>
[2*0.37 - 1*0.63] + [(2+2y)*0.935 - 2*0.065]
y = the chance MP2 will call 2 cold on the river, I assume he'll always call the turn. I estimate y=65%:
[2*0.37 - 1*0.63] + [(2+2*0.65)*0.935 - 2*0.065] = +2.4BB
Of course this is a very simplistic calculation for a complex situation, but I don't think the assumtions made will swing the results much in favor for one of the 2 lines and I think it's a decent approximation.
I really can't see how we could change those approximation so a turn raise would be correct. Why would we want to push a tiny edge on the turn, risking to lose costumers and maybe get 3-bettet when we can wait for the river to raise when we hit. These are loose/passive player, we can't count on them giving any action when we hit the river if raised the turn. They might even check the turn when the flushdraw hits depending on how strong their hands are which would swing the calculation a little, a turn raise will become a little better, but not close to making it correct.
EDIT: another benefit for raising is the folding equity, but that's about zero here.I also think folding the river ui after calling the turn would be very safe.
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