CardRunnersEV computation of EV does not match my computation

NetherlandsRed Chipper Posts: 326 ✭✭✭
Hi all,
In this thread I asked how to compute hero's EV of calling turn in the following hand.

PokerStars - \$0.02 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 131.5 BB
SB: 114 BB
BB: 112 BB
Hero (UTG): 100 BB
MP: 32 BB
CO: 192 BB

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has

Hero raises to 4 BB, MP calls 4 BB, fold, fold, SB raises to 13 BB, fold, Hero calls 9 BB, MP calls 9 BB

Flop: (40 BB, 3 players)
SB bets 26 BB, Hero calls 26 BB, MP calls 19 BB and is all-in

Turn: (111 BB, 3 players)
SB bets 61 BB, Hero ?

After some discussion with @jeffnc we arrived at an EV but this does not match the one computed by CREV.

For the sake of argument I assumed the following ranges of the villains:
SB: AA, AK, AQ and JJ
MP: A9, AT and KT

Of course these ranges don't make much sense, it was just about the pure maths behind calling, so it is not about gameplay elements, strategy or hand reading.

This is the tree that I created in CREV. I am of course only interested in the EV of the turn call. I just picked the above ranges and recreated the line of actions, taking into account correct stack sizes and what have you.

As you can see the EV of a call on the turn is -19.4.

The problem is that this does not match the EV we computed by hand.
We looked at the EV in the main pot and side pot seperately.

Quoting Jeff here in the original thread:

"Your equity in the main pot against both players is only 12%. There were 40BB in the pot preflop, and an all-in for 19 more for a total of 97BB. So you figure to get about 12BB there.

Your equity in the side pot against SB is 26%. There is 14BB in the side pot plus the 61BB for a total of 75BB. So you figure to get about 20BB there.

Your total equity is 12+20=30. You are being asked to put in 61BB on the turn with an expectation of getting 30BB back."

So that would mean an EV of around -30, which is not the -19.4 computed by CREV.
There are three possible reasons for this in my estimation:
1) CREV did something wrong
2) Our EV computation is wrong
3) I did something wrong entering the tree in CREV

Any help would be greatly appreciated here :) cheers!

Tagged:

• Red Chipper Posts: 4,424 ✭✭✭✭✭
LeChiffre wrote: »
Quoting Jeff here in the original thread: "Your equity in the main pot against both players is only 12%. There were 40BB in the pot preflop, and an all-in for 19 more for a total of 97BB. So you figure to get about 12BB there.

Your equity in the side pot against SB is 26%. There is 14BB in the side pot plus the 61BB for a total of 75BB. So you figure to get about 20BB there.

Your total equity is 12+20=30. You are being asked to put in 61BB on the turn with an expectation of getting 30BB back."

Actually I think that's wrong, but the question is still valid because I can't come up with the number CREV comes up with.

It's a little confusing because you're putting \$61 into the side pot, but not into the main pot, and yet you still have to pay \$61 to get any of either pot.

So I think the right thing to do is add your \$61 to the side pot, but not the main pot, and then subtract your \$61 call from everything, as a cost. In a normal pot you wouldn't need to do this because you'd just be adding and subtracting the \$61, but here it's only associated with one of the equities and not the other.

main pot equity * main pot\$, plus side pot equity * side pot\$ (including your call), and subtract out the cost of your call.

.12(\$97) + .26(\$14+\$61+\$61) - \$61 = -\$14

I think that's right, but still doesn't match CREV. Calling @SplitSuit ?

• NetherlandsRed Chipper Posts: 326 ✭✭✭
edited May 2018
LeChiffre wrote: »

Your equity in the side pot against SB is 26%. There is 14BB in the side pot plus the 61BB for a total of 75BB. So you figure to get about 20BB there.

FWIW this not entirely true either. We would have 26% if MP was not in the hand. The thing is that with every holding in his KT,AT,A9 range he changes my equity cause of blockers.

Decided to just go through every combo in his range and make each individual hand dead in Equilab. My equity for every combo in MP's range against SB is then:

AhTh 23.81
KdTd 20.66
KhTh 21.43
KsTs 20.66
Ah9h 25.40
AhTd 23.81
AhTs 23.81
AhTc 23.81
Ah9d 25.40
Ah9s 25.40
Ah9c 25.40
KdTh 20.75
KdTs 20.66
KdTc 20.66
KhTd 21.43
KhTs 21.43
KhTc 21.43
KsTd 20.66
KsTh 20.75
KsTc 20.66

Which is an average of 22.7%, not 26%. So I should get 17BB from the side pot, not 20.

• Red Chipper Posts: 4,424 ✭✭✭✭✭
LeChiffre wrote: »
FWIW this not entirely true either. We would have 26% if MP was not in the hand. The thing is that with every holding in his KT,AT,A9 range he changes my equity cause of blockers.

Decided to just go through every combo in his range and make each individual hand dead in Equilab.

Yeah that's absolutely true, I was going to mention that at some point that we were actually "rounding off" the dead cards so to speak. And I was going to mention there's no way to enter a range of dead cards in Equilab, so it's too much trouble, so kudos for doing all that manually, lol

• NetherlandsRed Chipper Posts: 326 ✭✭✭
=)
• Red Chipper Posts: 2,636 ✭✭✭✭
Why don't you just write to Scylla instead ?
• NetherlandsRed Chipper Posts: 326 ✭✭✭
What do you mean?
• NetherlandsRed Chipper Posts: 326 ✭✭✭
OK, I figured it out. I narrowed villains' ranges to the following:

MP:
AhTh
KhTh

SB:
AhKh

Then I went over every possible scenario and computed the EV according to Jeff's formula:

main pot equity * main pot\$, plus side pot equity * side pot\$ (including your call)

Not possible

Not possible

-SB has AhKh
36.9% of 97
+
39.29% of 136
Total = 89.2

MP has AhTh:

Not possible

38.10% of 97
+
50% of 136
Total = 105

-SB has AhKh
Not possible

MP has KhTh:

- SB has AdAh
3.57% of 97
+
7.14% of 136
total = 13.2

- SB has AdKd
2.38% of 97
+
50% of 75+61
total = 70.3

- SB has AhKh
Not possible

Possible outcomes:
70.3
13.2
105
89.2

Average:
69.4

The call to make is 61, so the EV is +8.4
This matches the one from CREV:

Now the question is whether there is a quicker way to do this =)
• Red Chipper Posts: 2,636 ✭✭✭✭
LeChiffre wrote: »
What do you mean?
Write to support.
• Red Chipper Posts: 4,424 ✭✭✭✭✭
Yeah that's a good idea to narrow down the range to test out the answer. And no I don't think there's a faster way to do it.

So like I was saying, I had thought of this, but at the point I was going to mention it, I was off on that side experiment with giving MP a hand like 22, and of course the blocking there is so minimal it couldn't have explained the difference between our answer and CREV's, so I put it on the back burner. But of course the blocking of MP's real range is very significant when it blocks most of the cards we need, so I'm sure that explains it.

So, looks like you have it figured out, CREV was right and we just had no good way to write an equation. Programs like that don't figure things out with equations and probabilities, they use brute force techniques (basically what you did). They either run all possible combinations out when the numbers are reasonable, and when the combinations of runouts gets outrageously large, they use things like Monte Carlo algorithms, which are way too complicated for us to deal with unless we get paid to do it :)
https://en.wikipedia.org/wiki/Monte_Carlo_algorithm
• NetherlandsRed Chipper Posts: 326 ✭✭✭
Yup, so it seems. I guess that's it then. CREV provides the answer, so I will just play around there with ranges and pot sizes, etc.

Thanks for the help!
• RCP Coach Posts: 3,936 -
jeffnc wrote: »
I think that's right, but still doesn't match CREV. Calling @SplitSuit ?

I'm not the CREV guy =(
My new book lays out the playbook for AK. Grab your copy and start Optimizing Ace King!
• Red Chipper Posts: 4,424 ✭✭✭✭✭
No I know, but you do combo math pretty well, lol
• RCP Coach Posts: 3,936 -
jeffnc wrote: »
No I know, but you do combo math pretty well, lol

:blushes:
My new book lays out the playbook for AK. Grab your copy and start Optimizing Ace King!