# Maths check - calling to split at best in sidepot

NetherlandsRed Chipper Posts: 642 ✭✭✭
edited May 2018
Ran into this hand the other day, and the maths are giving me a headache.

Main question is: which odds should I be getting to make a profitable call?

(This post is hence not so much about gameplay, just the maths behind the turn decision)

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 ?

(the turn bet puts me all-in if I call)

Let's for the sake of argument say that SB has a range of AA, AK, AQ and JJ after turn bet.
Also, MP called the flop all-in with all AT, A9, KT. It doesn't matter if this is accurate, I just wanna get the maths straight.

For the life of me I can't figure out how to do the maths on this turn decision. For what it's worth, my equity against SB is 26.35% and against MP is 53.33%. How do I use these numbers when the pot against MP stays the same no matter if I call and I'm splitting at best against SB?

## Comments

• NetherlandsRed Chipper Posts: 642 ✭✭✭
edited May 2018
Is it something like this?

I have 11.56% equity in the 3-way pot (against the two ranges)
So if I call I get 11.56% of the 40+3*19 side pot, which is 11.21BB.

I have 26.35% equity against SB
"Our" pot is 14 + 61 = 75, and after my call 75 + 61 = 136.
So on average I will get 26.35% of 136 which is 35.83BB.

So if I call I expect to make 11.21+35.83 = 47.04BB, which is less than the investment of 61BB, so I should fold.

Is this correct and does it correctly take into account those times I'm splitting?
• Red Chipper Posts: 2,396 ✭✭✭✭
LeChiffre wrote: »
For the life of me I can't figure out how to do the maths on this turn decision. For what it's worth, my equity against SB is 26.35% and against MP is 53.33%. How do I use these numbers when the pot against MP stays the same no matter if I call and I'm splitting at best against SB?

We can agree that SB is never bluffing. Because first he flop c-bet against you and short stack MP and wasn't scare to be called. Also he turn c-bet when he knew he was going to showdown: there is not much of a side pot to win by bluffing and pushing you out of the hand (14BB into 111BB).

HU with SB

I disagree with you having 26.35% equity. This is only if Villain turn c-bet all AK. And this power up our equity only bc we will split the pot many times.
Also I doubt Villain turn c-bet AK here: you called his 3bet preflop, called his flop c-bet... AK hasn't much of an incentive to bet turn here: your range is easily 2P+ (JJ, AQ, AJ; sometimes a lightly floated QQ); so I doubt he is value betting (thinking you could call with AT or worst) or, as said earlier, having a bluff with KK or TT.
If you take out these AK combos, your equity is more 13.18% (15% if he turn bets AhKh).

About your pot odds: you've to call 61BB to win a 233BB pot. Your pot odds are 26.18%.
So with 26.35% equity you're baaaaaarely +EV.

With 13.18% equity to 26.18% pot odds, calling is strongly -EV.

Including MP

Now if you input MP's range, you're losing even more equity.
I don't think MP will shows up with all KTs as you propose (too loose on the flop IMHO), but would have a range on the flop like JJ, A2s+, AT+, combo draws: gutshot+FD (KsTs, KsQs)

If you input it with both SB range and your range, your equity falls to less than 10% to win the main pot.

Conclusion

On the turn, it's folding season. No reason to call, either against SB or both SB+MP for main pot.

Now for the sake of this analysis I used your SB 3-bet range (preflop: TT+/AQ+). But we could easily disagree since it's 6max and online: could he have a wider range? If so, this would change our plan, both preflop and postflop.
• NetherlandsRed Chipper Posts: 642 ✭✭✭
Again, it's not about whether the assigned ranges are correct. I'm just interested in the maths of my turn decision IF those ranges are correct.

I am well aware that those ranges are subject to a lot of discussion. That's just not the point of my post. Just wanted to know how to compute the EV of a call and if it's positive. It looks like you did it the same way as I did so yay.
• NetherlandsRed Chipper Posts: 642 ✭✭✭
edited May 2018
So the EV of calling in general in such cases is:

(Equity in 3way pot * 3way pot + Equity HU * HU Pot after calling) - Bet

The fact that I'm splitting against part of SB range just means I have 50% equity against that.

Can someone confirm? :P
• Red Chipper Posts: 2,396 ✭✭✭✭
LeChiffre wrote: »
(Equity in 3way pot * 3way pot + Equity HU * HU Pot after calling) - Bet

This seems very wrong to me. Also since you've 13% equity and 10% equity both HU (main pot) and MW (side pot), I don't understand how you get 50% equity.
• NetherlandsRed Chipper Posts: 642 ✭✭✭
edited May 2018
Why does that seem wrong?

If I call I get my share of the 3way pot (which is my equity * the size of that pot)

PLUS

I get my share of the HU pot (which is my equity against the SB * the new size of the pot)

Subtract how much I have to call and you get my EV.

Where do you reckon this is wrong?

And I know I don't have 50% equity against his ENTIRE range, just those parts that I'm splitting against (AKo fore xample).
• Red Chipper Posts: 2,396 ✭✭✭✭
@LeChiffre

First of all, you don't have a share of the HU pot plus a share of the MW pot. Because losing HU pot means also losing MW pot. SB and your equities in MW pot are the same as in the MW pot minus the share of MP's equity. So adding your equity both in side pot and main pot makes no sens (to me).
Also, your equation is reaaaally different to the EV formula which is : EV = (W%*\$W) – (L%*\$L) (see here).

Finally, as I said, I'm really doubtful about SB turn c-betting AK here.
• Red Chipper Posts: 5,003 ✭✭✭✭✭
You can't really do this at the table, you just have to guess based on your feel from doing these sorts of things away from the table.

You have to work with a hand calculator, and you have to calculate your main pot and side pot odds separately.

Your equity against the MP heads up is meaningless, as the pot will never be decided that way. You have 2 equities to look at - your equity against SB separately, and your equity against both of them together.

Your equity in the main pot against both players is only 12%, and this is the key number you left out. 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. We can already tell you can't win here no matter what else we calculate.

• NetherlandsRed Chipper Posts: 642 ✭✭✭
edited May 2018
Thanks Jeff!

It's annoying to find yourself spots at the bottom of the game tree where the maths are hard to do.

I realized after I posted this thread that indeed my equity in the 3-way pot is relevant (the 12%), not my equity against MP.

Actually your calculations are done in the same way as I did right? aside from rounding error. I also figured to get around 12BB in the 3way pot.

But:
jeffnc 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.

My guess here is you just took the 26% of the 75 in the pot after SB bet, which is indeed around 20. But shouldn't we include my call if we want to calculate what I am going to get out of it? So shouldn't it be 0.26 * (75+61) = around 35 BB?

So actually I should get around 12+35 = 47BB, which of course would still be -EV. Or am I wrong? Cause that's what I got when I tried computing it myself, too:
LeChiffre wrote: »
I have 11.56% equity in the 3-way pot (against the two ranges)
So if I call I get 11.56% of the 40+3*19 side pot, which is 11.21BB.

I have 26.35% equity against SB
"Our" pot is 14 + 61 = 75, and after my call 75 + 61 = 136.
So on average I will get 26.35% of 136 which is 35.83BB.

So if I call I expect to make 11.21+35.83 = 47.04BB, which is less than the investment of 61BB, so I should fold.

Also, @Red seems to suggest to ONLY include what we get from the 3way pot if we actually split against or beat SB. You don't seem to do that, but I could be wrong on that?

Looking forward to your reply!

• NetherlandsRed Chipper Posts: 642 ✭✭✭
LeChiffre wrote: »
Also, @Red seems to suggest to ONLY include what we get from the 3way pot if we actually split against or beat SB. You don't seem to do that, but I could be wrong on that?

We'd have to compute how often we split or win against SB, and multiply that probability with what we stand to get in the 3way pot? I think that's what Red is saying and that seems to make sense.

• Red Chipper Posts: 5,003 ✭✭✭✭✭
LeChiffre wrote: »
My guess here is you just took the 26% of the 75 in the pot after SB bet, which is indeed around 20. But shouldn't we include my call if we want to calculate what I am going to get out of it? So shouldn't it be 0.26 * (75+61) = around 35 BB?

If you want to include your call in your winnings, then you have to subtract the cost of the call as well. In other words, to call, you immediately lose \$61 from your stack, then you figure what you win from the pot later.

-61BB + .26(75BB+61BB) = -26BB

Or another way to do it is determine how often you lose your call and how often you win what's in the pot without your call. Remember, if you call and you win, you're simply getting your same money back.

.26(75BB) - .74(61BB) = -26BB

It would be kind of silly to write it like
.26(75BB + 61BB - 61BB) - .74(61BB)
• NetherlandsRed Chipper Posts: 642 ✭✭✭
edited May 2018
OK awesome, thank you man.

What about Red's comments on that we need to take into account that we only get our share of the equity in the 3way pot if we split or beat SB?

So shouldn't we get:

EV in HU pot + (probability of splitting against or beating SB * EV in 3way pot) ?

So 20 + (that probability * 12)?
• Red Chipper Posts: 5,003 ✭✭✭✭✭
LeChiffre wrote: »
What about Red's comments on that we need to take into account that we only get our share of the equity in the 3way pot if we split or beat SB?

Well that's technically true - obviously we can't win the main pot if we don't beat SB. It just seems like a red herring to me in terms of figuring our EV. We've got our EV against SB, and we've got our EV in the main pot, I don't see anything else as being necessary.
LeChiffre wrote: »
So shouldn't we get:

EV in HU pot + (probability of splitting against or beating SB * EV in 3way pot) ?

That's barking up the wrong tree. There is no sense in trying to calculate your chance of beating SB in the in the 3 way pot. It will simply come out wrong. The existence of the MP's cards will change things. This can only be calculated with a hand calculator with all cards accounted for and all money accounted for.

Example. You hold , SB holds , MP holds , with MP being shortstacked.

The flop is and the 3 of you go all in. In the side pot your equity against SB is 72% and his is 28%. Now go to the main pot with all 3 players. SB's equity stays at 28%, and yours drops to 28%!! Think about that, it's pretty amazing. MP picks up 43% and almost literally all of it comes from you. That is how much difference it can make to throw another hand in there. So how can it possibly help you to know your heads up equity against SB while in a 3 way main pot? It's way, way off.

So again, there are simply two things to figure out here. Your equity against SB in the side pot, and then your equity against both other hands together in the main pot. Everything else is a distraction.
• NetherlandsRed Chipper Posts: 642 ✭✭✭
Sorry I think you misunderstood what I meant. I was never talking about my equity against just SB in the 3 way pot. That indeed makes no sense.

I agree that we should only look at my equity against SB in side pot, and equity against both in the main pot. That's how we got to the conclusion it's a negative EV play to call.

Really the thing that bothers me is the idea that we only contend for the main pot if we split against or beat SB. Could you maybe explain further why you say we don't need to consider this, contrary to Red?

I'm sorry for being so investigative but I'd really like to get this down and get a full understanding of the compuation of my EV in this situation. Once we settle on a formula of some kind I can play around with ranges and pot sizes etc. to gain a better understanding and feel for the situation.
• Red Chipper Posts: 5,003 ✭✭✭✭✭
LeChiffre wrote: »
Really the thing that bothers me is the idea that we only contend for the main pot if we split against or beat SB. Could you maybe explain further why you say we don't need to consider this

I don't really understand the question. It's like a tautology because you're saying the same thing in 2 different ways. What does "contend" mean? Basically it means "engage in order to win". So what you're trying to say is that you can't win money from the main pot unless you tie or beat SB. You could also say you wan't win money from the main pot unless you tie or beat MP. That seems pretty obvious, so I don't understand why it's an issue.

I guess Red was trying to get you away from adding equities together that never needed to be added together in the first place. But it's not something you need to calculate. It's a boondoggle.
• NetherlandsRed Chipper Posts: 642 ✭✭✭
edited May 2018
Got ya, thanks Jeff. Sorry for the confusion :)

Follow-up question:

(if it's too small you can open in new tab)

How come the EV of turn call is -19.4 when according to our calculations it's actually around -30? (being asked to put in approx. 60 to get approx. 30 back in expectation).

I put the same ranges as I described in OP.
Started the flop with 40 in the pot and correct remaining stacks.
Followed the line of actions as if they did it with their entire range.

Some CREV intricacy I'm not familiar with? Did we miscompute? Probably the former.
• Red Chipper Posts: 5,003 ✭✭✭✭✭
I've never used CREV so I'm not really sure how it works. Off the top of my head I'd say it's computing something different than we are. It's almost like it's calculating the equity against both opponents, but forgetting that MP is all in at just a portion of the turn bet. Possibly a glitch in the software, but it doesn't sound like the kind of bug a well written program would have.

Maybe post a new thread and ask if anyone with CREV understands that? Unless I made some math error I can't see right now. I'm very tired :)
• NetherlandsRed Chipper Posts: 642 ✭✭✭
Alright, will do. Cheers!

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