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This will be the first time I’ve tried to do this much math in an analysis so I may leave things out, please consider with caution, and if you can see and point out errors much appreciated as this is the first time i've tried to calculate all this.. apologies for the messiness. I realise this will likely be difficult to understand due to how untidy it is, I unfortunately dont really know how to set it out clearly on account of me lacking any math education beyond the middle of highschool other than my own common sense.
Pot 57c, facing 20c bet.
Villains range is 88+, AQ+
Plan of action vs range and maths is as follows
Combinatrics
villain holds –
12 combos of 88/99
18 combos JJ-KK
24 combos AQ+
6 combos TT/AA
On the turn villain check folds 88/99, check calls JJ-KK, bets AQ+, TT/AA.
On the turn hero calls a 70c bet if improved to two pair+, folds to any bet unimproved, and bets half of times when checked to, checks behind the remainder, checks down the river unimproved vs turn steals that villain calls.
Hero has 5 outs to 2pair/trips, chance to hit turn is ~10%
Following is the possible out comes-
45% of the time villain will bet and hero will not have improved, hero will fold. The EV for this is..
-0.20 x 0.45 = -0.09
22.5% of the time hero will be checked to and bet unimproved, if called he will fold to a river bet, or check behind. The EV for this is..
(+0.57 x 0.1125)+(-0.9 x 0.1125) = -0.036
5% of the time hero will improve and bet after villain checks. The villain will call and be behind 60% of times he checks, and check/fold the river. He will fold the other combos his turn check range (88/99) - EV as follows..
(0.05 x 0.6 x (0.57+ 0.7))+(0.05 x 0.4 x (0.57)) = +0.049
5% of the time hero will improve and call turn and river bets of 70c, then $1.5. in these hands hero will be ahead of villains AQ+ 80% of the time, and behind TT/AA 20%. EV as follows
0.05 x 0.8 x (.57+.7+1.5) = +0.11 0.05 x 0.2 x (.2+.7+1.5) = -0.024
22.5% of the time hero will check behind on the turn and river, 80% of these times he will lose, 20% he will improve and win, villain will fold to river bets in this situation. EV as follows
(.225 x 0.8 x-0.2)+(.225 x 0.2 x .57) = -0.01 Overall EV of flop call is +0.019
Don’t think you’d be able to arrive at that at the table though, and it seems barely worth it, if you make even the tiniest error your going to be –ev.
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