An EV calculation

pok3rplaya

So I was up at 4am last night (as you do) and I decided I'd try and do my first EV calculation ever. I'm not sure if this is even close to right because I couldn't find a good calculation I could work off but how and ever I'm going to put it up here.

If you would like to discuss any part of this analysis (aka show me where I went wrong) please feel free to do so in this thread. I'd especially like criticism of the various assumptions I make later on in the calculations.

The Situation

The situation it relates to is calculating the EV of floating with gutshot draws.

Say this is 100NL 6max with effective stacks of $100.

Opponent in UTG+1 raises to $4.
We call OTB with 6 Heart 7 Heart .
Blinds fold.

Pot: $9.50
Flop: J Heart 3 Diamond 4 Spade

Opponent bets $7.
Our decision wheather or not to call $7 into a $16.50 pot with a gutshot.

How do we go about calculating the EV of this call?

To be able to tell what we should do, we need to look at what could happen on the turn if we decide to call. There is one major factor which will influence the action on the turn, that is wheather or not we hit our gutshot.

We have 4 outs to hit our GS which means that out chances of hitting are roughly 8%. Lets start creating our equation.

EV = (chance we miss our GS)(turn action 1) + (chance we hit our GS)(turn action 2)
EV = (0.92)(turn action 1) + (0.08)(turn action 2)

Now we must examine the various actions that could occur on the turn card. Our opponent has four options available to him on the turn:

1) He can lead out,
2) He can check with the intention of folding,
3) He can check with the intention of raising,
4) He can check with the intention of calling.

I'm going to make some assumptions now in order to simplify the equation a bit.

1) I'm assuming that when we get checkraised we are blown off our hand, in a pot odds sense.
2) Everytime our opponent checks the turn, we bet $16 in attempt to take the pot.
3) When we get check/called we have no chance of improving on the river.
4) If we make our straight on the turn, we can only win the money in the pot plus the initial lead bet, call or check/raise. In other words, if we get check/called on the turn, we cannot amke any more money on the river.

The turn actions when we miss our draw are as follows:

(x)(-$7) <-- y is the % of times the villan leads the turn. We fold, losing our %7 flop investment.
(y)($16.50) <-- this describes the situation when our opponent checks the turn and we win the pot with a bet. x = the percentage of times he checks the turn with the intention of folding.
(z)(-$23) <-- z is the % of times our opponent checks, we bet to try and take the pot and he then raises, forcing us to fold. We lost our $7 flop call and the $16 we bet on the turn to try and take the pot.
(r)(-$23) <-- r is the % of times our opponent check/calls us on the turn. We lose our $7 from the flop and our stab at the pot on the turn. Remember that we can't improve on the river.

turn action 1 = [(x)(-$7) + (y)($16.50) + (z)(-$23) + (r)(-$23)]


Similarly, the turn actions when we hit our draw on the turn are as follows:

(x)($32.5) <-- Here I'm assuming that we will win $32.5 (including what is already in the pot) when we hit and he leads into us with a bet of $16.
(y)($16.50) <-- same as in the turn action 1 situation.
(z)($101.5) <-- This time when he check/raises us, we have the nuts and we win his stack. Note that I'm assuming that he never draws out on us after the money goes in.
(r)($32.5) <-- Here our opponent check calls us when we are ahead. He calls a bet of $16 on the turn and we win that.

turn action 2 = [ (x)($32.5) + (y)($16.50) + (z)($101.5) + (r)($32.5) ]


Now, subbing in to the first equation:

EV = (0.92)[(x)(-$7) + (y)($16.50) + (z)(-$23) + (r)(-$23)] + (0.08)[ (x)($32.5) + (y)($16.50) + (z)($101.5) + (r)($32.5)]

But what does all this mean?

At this point we can set about assigning various turn action percentages to the opponent.

Remember:
x = the percentage of times our opponent leads out on the turn.
y = the percentage of times our opponent check/folds the turn.
z = the percentage of times our opponent check/raises on the turn.
r = the percentage of times our opponent check/calls on the turn.
Also: x + y + z + r= 1


Here are some examples:

with x=25%; y=40%; z=5%; r=40% (A passive calling station)
The expected value of the move is -$4.98

with x=25%; y=60%; z=5%; r=10% (A passive weak player)
The expected value of the move is $4.4

with x=25%; y=50%; z=5%; r=20% (A passive, slightly less weak player)
The expected value of the move is $0.77

with x=35%; y=25%; z=15%; r=25% (A tricky, aggressive TAG)
The expected value of the move is -$6.84

Conclusion

The biggest thing I've noticed from playing around with this equation in a spreadsheet is that the opponent tendancy that effects the EV of the move the most is y, the percentage of times he check/folds on the turn. If you can find an opponent who likes to do this, then using this move on him is very profitable.

I think it's also important to notice how unprofitable this move is agains a tricky opponent who has a large range of lines he can use on the turn. If he varies his actions, regardless of his hand, it becomes very difficult for us to play against him.

fuzzbox

Wow, I didnt read all that .... but raising on that board > calling !!!

pok3rplaya

fuzzbox wrote:

Wow, I didnt read all that .... but raising on that board > calling !!!

The specific hand was just some arbitrary cards to set the scene, I didn't really think about it. Obviously I can't go through different specific boards and do calcualtion on each one.

I'm interested though as to why you say raising > calling?

Gholimoli

i didnt read all of it but spotted a couple of mistakes which i think are mistakes in it:
first on is you EV is how much you win or how much you lose untill the turn card comes and the action before that and not the action after that.
the action after that is by no means certain so i dont think you can say EV=92%(turn action 2) + 8% (turn action 1).
the above makes no sense to be to be honest.
you have to calculate the EV of you calling his flop bet and then you can calculate the EV of your turn play after the turn comes .

also you made an assumtpion that if you get check/called on the turn your hand can never improve to be the best hand .
i dont see how that can happen as you will still have your got shut which if it comes in could or could not make the best hand.

pok3rplaya

Gholimoli wrote:

the action after that is by no means certain so i dont think you can say EV=92%(turn action 2) + 8% (turn action 1).
the above makes no sense to be to be honest.
you have to calculate the EV of you calling his flop bet and then you can calculate the EV of your turn play after the turn comes .

I think if you read on you'll see that turn actions 1 and 2 each have their own calculations which cover all the possible turn actions that could occur and address the possibility of each one.

Gholimoli wrote:

also you made an assumtpion that if you get check/called on the turn your hand can never improve to be the best hand .
i dont see how that can happen as you will still have your got shut which if it comes in could or could not make the best hand.

I suspect this could be a language thing but what I'm saying is that I know it's not a realistic situation and leaving the river action out makes the calculation less accurate but I'm going to do it anyway because it makes things much easier.