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Boem's picture
Ev calculation Flop and Turn

Hello i have a question about a calculation i don’t know if i’m on the rigth way.

Preflop

SB limp 20

BB check

Pot 40

Flop potsize 40

I want to donkbet the flop and i assume SB will fold 50% of the time and 50% Sb only call. My betsize is 30. My calculation

50% of the time i win the pot 40

50% of the time i loose my bet of 30

My expectation = (0.5*40)-(0.5*30)= 20-15 = 5 chips

My expectation is to win 5 chips with my bet.

Turn potsize 100

I assume that 30% of the turn cards are bad for me, so i check fold the hand.

I assume when i bet SB never fold and the river will be checked out. My equity in the hand is 25%.

If i don’t check i want to lead 30 in a pot of 100.

My expecation for the turn.

30% i loose the pot because i check fold -100

70% i bet 30 and i will win 25% the pot 130, 75% i will loose my bet of 30

My expectation is

EV = 0.3*100 + 0.7*(0.25*130 + 0.75*-30)

EV = -30 + 0.7*(32.5 - 22.5)

EV = -30 + 0.7*10

EV = -30 + 7

EV = -23

Expectation turn -23chips. Expectation flop +5chips

Is the expectation for the whole hand (flop 50%*5)+(turn50%*-23)= 2.5+ -11.5 = -9chips

So can i say my expectation of this play is -9chips?

Is the math for the donkbet rigth?

Is this a possible approximation for a turn hypothesis?

I hope you can help help me. Thanks

cdon3822's picture
Sort of but not really...

Go back to first principles:

For the discrete case, EV can be calculated using:

EV[X] = x1*p(x1) + x2*p(x2) + ... + xn*p(xn)

where:

x(1,2,...,n) = possible outcomes of X
p(x1,x2,...,xn) = probability of each outcome occuring

Consider your flop lead in limped pot:

Villain limps with a range of [A] and you check behind with range (or perceived range depending on what level your opponent is thinking on) [B].

The pot is 2BB going into the flop and comes down [F].

You want to know the EV of leading 1.5BB here with a perceived leading range of [C]?

To calculate the EV of leading this flop:

EV(lead) = f*2 + (1-f)*EV(not fold)

The fold equity (FE) you have is easily calculated:

FE = f*2

where f = % time villain folds

f is a function of a number of variables:

- How much equity does [A] have vs [C] on [F]?
- How much equity does [C] have vs [A] on [F]?
- How does villain react to flop leads in limped pots with:
- His hands that "hit the flop?
- His hands that "missed" the flop?

Your calculation assumes you have 0 equity when villain doesn't fold. "50% of time I lose my bet"

This is generally not the case.

Against your flop lead villain can [fold, call, raise, jam].

To calculate your EV, you need to estimate which hands he will take each of these actions with and calculate your equity against each of these ranges.

You end up with a decision tree incorporating all future actions, their payoffs and their associated probabilities. This would theoretically include all [actions,reactions] on all future streets.

It would look something like:

EV(lead) = f*2 + (1-f)[EV(lead,call)+EV(lead,raise)+EV(lead,jam)]

This requires a lot of assumptions about the hands in each of these segments of villain's range and practically becomes somewhat useless without reads to justify the assumptions you make.

In reality, most people calculate the results of discrete single street games to estimate the EV of a particular action.

For example, you may take the view:
- Villain limps a weak range [A]
- [A] usually misses [F]
- Villain plays fit or fold vs flop leads in limped pots
- I will bet out 1.5BB to pick up the dead money and give up if he doesn't fold.
- This will be profitable (EV > 0) if:

EV = f*2 - (1-f)*1.5
f > 1.5/3.5
f > 43%

So under these assumptions, if villain folds more that 43% of the time, your play will be +EV.

But it's not necessarily the most +EV play.

Note: I'm not going to try to address your turn and whole hand EV calcs because I think you would be better taking a different approach.

Picking arbitrary % on the turn will not help you make better plays at the tables.

Realise that you are now on the turn, conditional on previous streets play:
- Preflop went limp-check
- You lead out 0.75P and villain calls

Every time you bet, you affect villains range of hands on subsequent streets.

Going back to fundamentals: why are you betting?

- Value (can you be called by worse hands)?
- Bluff (can you make villain fold his equity share of the pot by betting)?

Reading your post I think you would benefit a lot from thinking about your decisions having first considered

- villain's range (+ tendencies)
- your perceived range (+ table image)

within the context of the:
- board texture
- effective stack depth
- gameflow.

Boem's picture
Really helpful, thanks a

Really helpful, thanks a lot.
I understand now more how to approach such situation and what the correct Ev calculations are. I've also posted this on the 2+2 forum where i also had instresting feedback
http://forumserver.twoplustwo.com/185/heads-up-sng/ev-calculation-flop-f...