Hi everyone, I'm curious about this c-betting situation I (theoretically) made up.
The fish are actual players in the 2NL player pool on Stars and the reason I know they are fish is because I have tagged them when I played a previous session against them and saw them call down very lightly - middle pair on 3 straight board on river, and bottom pair+gutshot on 1/2pot river value bet on a 3-flush board.
However, I have noticed I have a very high aversion to c-betting light, especially on dry boards where I don't c-bet very much with the bottom of my range, even though Villain's preflop calling ranges are so wide and weak, and thus miss the flop very often. Ex: I open preflop on the BTN with 5♠:5♣: or J♣:8♣: against fish in the blinds, get called and flop is K♦:9♥:4♠:. I check way too often in this spot and this depolarizes my check-back range (it includes many underpairs, some Kx, some 9x and 4x) and I tend to only cbet with hands with decent equity: gutshots, backdoor equity draws (T♠:8♠:, 5♦:6♦: etc), and strong Kx, two pair+ for value
So I tried experimenting with different flop types (in this case a Q♥:9♥:4♥: flop) to determine the bottom of the range of hands that can become profitable CBs in position against wide ranges, but I'm a bit stuck at where to construct such a range (I have a rough idea of hands: Qx, 2pr+ for value, any combo draw etc) though I feel there are more hands than those that fall in the categories above that can make +EV c-bets (ex. what about hands like T♣:T♠:, or K♠:J♠:?). I would appreciate it if someone math-savvy can check my calculations here?
I got the equities from equilab and the ranges from the HEM database info (it was over a small sample of hands though).
Thanks guys! 
-----------------------------------------------------------------------------
Hero is dealt ? ? on the Button five-handed
Hero raises and gets 2 callers (fish) from the blinds.
Flop: Q♥:9♥:4♥:
Calculate the profitability of a 2/3 pot size cbet in terms of the size of the pot P, assuming:
1) the sb and bb preflop calling ranges are as follows (assume 100% of their range checks this flop)
SB: 22+,A2s+,K2s+,Q4s+,J6s+,T6s+,96s+,86s+,75s+,64s+,54s,A2o+,K2o+,Q6o+,J7o+,T7o+,97o+,87o,76o
BB: 22+,A2s+,K2s+,Q6s+,J7s+,T7s+,97s+,86s+,75s+,65s,54s,A2o+,K6o+,Q7o+,J7o+,T7o+,97o+,87o
2) the continuance range for both fishy players (so assume if sb calls, bb will still call w/ middle pair+ even though theoretically most fish would still fold)
- any fd+any pair
- K-high fd, nut fd
- all open enders
- gutshot+any fd (KJ,KT,T8,J8 with heart)
- middle pair+ (TT+,9x)
- 2pr+,sets,flushes (monsters)
3) assume neither player will check-raise the flop
SB Range
306/600 hands continue (51%)
---
AA,JJ,KhKs,KhKc,KsKc,QdQs,QdQc,QsQc,TdTh,TdTs,ThTs,9d9s,9d9c,9s9c,8d8h,8h8s,8h8c,7d7h,7h7s,7h7c,
6d6h,6h6s,6h6c,5d5h,5h5s,5h5c,4d4s,4d4c,4s4c,3d3h,3h3s,3h3c,2d2h,2h2s,2h2c,AhKh,AdQd,AsQs,AcQc,
KsQs,KcQc,AhJh,KhJh,QdJd,QsJs,QcJc,AhTh,KhTh,QdTd,QsTs,JdTd,JhTh,JsTs,Ad9d,As9s,Ac9c,Ks9s,Kc9c,Qd9d,
Qs9s,Qc9c,Jd9d,Js9s,Jc9c,Td9d,Ts9s,Ah8h,Kh8h,Qd8d,Qc8c,Jh8h,Th8h,9d8d,9s8s,9c8c,Ah7h,Kh7h,Qd7d,Qs7s,
Qc7c,Jh7h,Th7h,9d7d,9s7s,9c7c,8h7h,Ah6h,Kh6h,Qd6d,Qs6s,Qc6c,Jh6h,Th6h,9d6d,9s6s,9c6c,8h6h,7h6h,
Ah5h,Kh5h,Qd5d,Qs5s,Qc5c,7h5h,6h5h,Qd4d,Qs4s,Qc4c,Ah3h,Kh3h,Ah2h,Kh2h,AhKs,AhKc,AdQs,AdQc,
AhQd,AhQs,AhQc,AsQd,AsQc,AcQd,AcQs,AhJd,AhJs,AhJc,AhTd,AhTs,Ad9s,Ad9c,Ah9d,Ah9s,Ah9c,As9d,As9c,
Ac9d,Ac9s,Ah8d,Ah8s,Ah8c,Ah7d,Ah7s,Ah7c,Ah6d,Ah6s,Ah6c,Ah5d,Ah5s,Ah5c,Ah4d,Ah4s,Ah4c,Ah3d,Ah3s,
Ah3c,Ah2d,Ah2s,Ah2c,KhQd,KhQs,KhQc,KsQd,KsQc,KcQd,KcQs,KhJd,KhJs,KhJc,KhTd,KhTs,Kh9d,Kh9s,Kh9c,
Ks9d,Ks9c,Kc9d,Kc9s,Kh8d,Kh8s,Kh8c,Kh7d,Kh7s,Kh7c,Kh6d,Kh6s,Kh6c,Kh5d,Kh5s,Kh5c,Kh4d,Kh4s,Kh4c,
Kh3d,Kh3s,Kh3c,Kh2d,Kh2s,Kh2c,QdJh,QdJs,QdJc,QsJd,QsJh,QsJc,QcJd,QcJh,QcJs,QdTh,QdTs,QsTd,QsTh,
QcTd,QcTh,QcTs,Qd9s,Qd9c,Qs9d,Qs9c,Qc9d,Qc9s,Qd8h,Qd8s,Qd8c,Qs8d,Qs8h,Qs8c,Qc8d,Qc8h,Qc8s,
Qd7h,Qd7s,Qd7c,Qs7d,Qs7h,Qs7c,Qc7d,Qc7h,Qc7s,Qd6h,Qd6s,Qd6c,Qs6d,Qs6h,Qs6c,Qc6d,Qc6h,Qc6s,
JdTh,JdTs,JhTd,JhTs,JsTd,JsTh,JcTd,JcTh,JcTs,Jd9s,Jd9c,Jh9d,Jh9s,Jh9c,Js9d,Js9c,Jc9d,Jc9s,Jh8d,Jh8s,Jh8c,Td9s,
Td9c,Th9d,Th9s,Th9c,Ts9d,Ts9c,Th8d,Th8s,Th8c,9d8h,9d8s,9d8c,9s8d,9s8h,9s8c,9c8d,9c8h,9c8s,9d7h,
9d7s,9d7c,9s7d,9s7h,9s7c,9c7d,9c7h,9c7s
equity vs this continuance range: ?
BB Range
275/526 hands continue (52.28%)
---
AA,JJ,KhKs,KhKc,KsKc,QdQs,QdQc,QsQc,TdTh,TdTs,ThTs,9d9s,9d9c,9s9c,8d8h,8h8s,8h8c,7d7h,7h7s,7h7c,
6d6h,6h6s,6h6c,5d5h,5h5s,5h5c,4d4s,4d4c,4s4c,3d3h,3h3s,3h3c,2d2h,2h2s,2h2c,AhKh,AdQd,AsQs,AcQc,
KsQs,KcQc,AhJh,KhJh,QdJd,QsJs,QcJc,AhTh,KhTh,QdTd,QsTs,JdTd,JhTh,JsTs,Ad9d,As9s,Ac9c,Ks9s,Kc9c,Qd9d,
Qs9s,Qc9c,Jd9d,Js9s,Jc9c,Td9d,Ts9s,Ah8h,Kh8h,Qd8d,Qs8s,Qc8c,Jh8h,Th8h,9d8d,9s8s,9c8c,Ah7h,Kh7h,
Qd7d,Qs7s,Qc7c,Jh7h,Th7h,9d7d,9s7s,9c7c,8h7h,Ah6h,Kh6h,Qd6d,Qs6s,Qc6c,8h6h,7h6h,Ah5h,Kh5h,7h5h,
6h5h,Ah3h,Kh3h,Ah2h,Kh2h,AhKs,AhKc,AdQs,AdQc,AhQd,AhQs,AhQc,AsQd,AsQc,AcQd,AcQs,AhJd,AhJs,AhJc,
AhTd,AhTs,Ad9s,Ad9c,Ah9d,Ah9s,Ah9c,As9d,As9c,Ac9d,Ac9s,Ah8d,Ah8s,Ah8c,Ah7d,Ah7s,Ah7c,Ah6d,Ah6s,
Ah6c,Ah5d,Ah5s,Ah5c,Ah4d,Ah4s,Ah4c,Ah3d,Ah3s,Ah3c,Ah2d,Ah2s,Ah2c,KhQd,KhQs,KhQc,KsQd,KsQc,KcQd,
KcQs,KhJd,KhJs,KhJc,KhTd,KhTs,Kh9d,Kh9s,Kh9c,Ks9d,Ks9c,Kc9d,Kc9s,Kh8d,Kh8s,Kh8c,Kh7d,Kh7s,Kh7c,Kh6d,
Kh6s,Kh6c,QdJh,QdJs,QdJc,QsJd,QsJh,QsJc,QcJd,QcJh,QcJs,QdTh,QdTs,QsTd,QsTh,QcTd,QcTh,QcTs,Qd9s,
Qd9c,Qs9d,Qs9c,Qc9d,Qc9s,Qd8h,Qd8s,Qd8c,Qs8d,Qs8h,Qs8c,Qc8d,Qc8h,Qc8s,Qd7h,Qd7s,Qd7c,Qs7d,
Qs7h,Qs7c,Qc7d,Qc7h,Qc7s,JdTh,JdTs,JhTd,JhTs,JsTd,JsTh,JcTd,JcTh,JcTs,Jd9s,Jd9c,Jh9d,Jh9s,Jh9c,Js9d,Js9c,
Jc9d,Jc9s,Jh8d,Jh8s,Jh8c,Td9s,Td9c,Th9d,Th9s,Th9c,Ts9d,Ts9c,Th8d,Th8s,Th8c,9d8h,9d8s,9d8c,9s8d,9s8h,
9s8c,9c8d,9c8h,9c8s,9d7h,9d7s,9d7c,9s7d,9s7h,9s7c,9c7d,9c7h,9c7s
equity vs this continuance range: ?
equity vs both continuance ranges combined: ?
probability of time they both fold = 0.4772*0.49 = 0.233828
probability of time SB calls, BB folds: 0.51 * (1-0.5228) = 0.243372
probability of time BB calls, SB folds: 0.5228 * (1-0.51) = 0.256172
probability of time SB and BB both call: 0.26628
EV(cbet) = (both fold) + (SB calls, BB folds and we win) + (SB calls, BB folds and we lose) + (BB calls, SB folds and we win) + (BB calls, SB folds and we lose) + (both call and we win) + (both call and we lose)
for EV > 0:
?