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Wow, ok I just assigned the villain this range on the turn that he might call with if we shove:
JJ, 99, 77, AJ-A7s, KTs, QTs, J9s, J7s, T8s, 97s, 86s, AJo-A7o, KTo, QTo, J9o, J7o, T8o, 97o, 86o.
Against this range we have ~37% equity.
Obviously, I elminated pretty much all the gutshots with out a pair, and some of them with a pair, like JT which he still MIGHT call us with, but I think this is a fairly solid range of what he would call with if we shoved the TURN.
Now I figure that the other gutshot and single pair hands that he wouldn't call us with = ~10% of his total range. So he will fold 10% if we shove and he will call with this 90% that I assigned him.
Note: I just estimated that the part of his range would fold = 10% its not an exact figure.
So here's how much we will make if he just folds the 10% of his range.
.10*2.27= $0.23 per decision.
Now with the other 90% of his range that he would call with we have 37% equity.
.37*4.37= $1.62 per decision.
.63*2.10= $1.32 per decision.
$1.62 + $0.23 = $1.85
$1.85 - $1.32 = +$0.53 per decision for shoving the turn.
Now lets figure out how much we will make for just calling the $0.95 on the river.
I'm using Micro2Macro's range for the river when he bets out that range is:
JJ, 99, 77, AJs-A9s, A7s, KJs, K9s, QTs, J9s, AJo-A9o, A7o, KJo, K9o, QTo, J9o
Against this range our hand has ~35% equity.
.35*3.22= $1.13 per decision.
.65*.95= $0.62 per decision.
$1.13- $0.62= $0.51 expected value for calling 95 cents on the river.
So when we shove the turn we can expect to make 53 cents per decision.
When we just call on the river we can expect to make 51 cents per decision.
So technically, shoving the turn makes us 2 cents more on average, but it's really marginal either way. The important thing is, they are both profitable decisions and that we really aren't going wrong by doing either.
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