Hello,

I was trying to calculate the EV of a flop float and a possible turn-bet (we call flop and bet turn if checked to us), assuming two different turn-card scenarios.

I was setting up a formula but quickly noticed I was uncertain about it and would therefore really be happy if someone second checked my math. Its probably trivial to most of you




Here's the Situation: We've called a preflop raisethe flop comes Q72,preflop raiser c-bets 10$ into 20$ and we always call.



Now I want to look at 2 different turn scenarios:


1) turn card <8 hits (26 cards out of the remaining 47: 26/47 ~ 55.319%):

- villain 2nd barrels 25% of the time, we fold and lose the 10$ bet we've called on the flop, which happens in (0.25*0.553) 13.8%

- villain checks to us 60% of the time, folds to a 1/2 pot-bet and we win 40$(???), which happens in (0.6*0.553) 33.1%

- villain check-raises our 1/2 pot-bet all in the remaining 15% of the time, we fold and lose 10$(flop-call) and 20$(turn-bet) in (0.15*0.553) 8.2%


--->
EV(Turn<8)= -10$*0.138 + 40$*0.331 - 30$*0.082
= -1.38$ + 13.24$ - 2.46$
= +9.4$


Question: is this correct? I'm not sure if we win 40$ or 30$ the 33.1% times he check/folds to our turn-bet. Do we count in the flop-bet we've called or is that a mistake?







2) turn card >8 hits ( ~44.7% of the time):

- villain 2nd barrels 80% of the time, we fold and lose the 10$ bet we've called on the flop in (0.447*0.8) 35.7%

- villain checks to us 10% of the time, we bet 1/2 pot, villain folds and we win 40$(???) in (0.447*0.1) 4.4%

- villain checks to us 10% of the time, we bet 1/2 pot, villain goes all-in and we fold and lose 30$ in 4.4%


--->
EV(Turn>8)= -10$*0.357 + 40$*0.044 - 30$*0.044
= -3.57$ + 1.76$ - 1.32$
= -3.13$







EV(Total)= 9.4$ - 3.13$
= +6.27$




Would really appreciate if someone could have a quick look at it and tell me if I'm right, because usually I'm not .

i didn't give your assumptions any thought, just basically your methodology.

1st-- its my opinion that you should use $30 and not $40 for the amount you 'win' when he check/folds the turn. the expectation you are creating an equation to determine is your expecation of taking a specific line on the flop, therefore any money you contribute on the flop or after is your 'cost' and as your cost can't be your 'reward'. the $10 is the cost of getting to the turn.

2nd-- I'd write the equation as
EV =.533(.25*-10 +.60*+30 + .15*-30) + .447(.8*-10 +.1*30 +.1*-30)

you did the same thing but you distributed the frequencies(.533 and .477), you arrived at the correct answer if $40 was correct.

in case its not clear/obvious the ".533" in the post above should be .553.

apologies for the carelessness

alright, figured id have a mistake somewhere. thanks a lot dude!