ITH Poker Forum

[mash_tun]

I wrote this out last night as a pseudo-poker essay. It’s not a novel concept, but basically, I’ve always had an internal debate about whether traditional EV calculations were appropriate for use when considering situations in NL Cash where it’s pretty obvious that both players are committed to playing for stacks. I’m hoping to get some opinions that can either support or refute my thinking. Either way is fine with me!

A representative hand history:

Consider a full-ring 100NL game with $100 effective stacks. You end up playing a hand with a villain who is capable of raising from early-middle position with a range of something like 55+, AT+, A8s+, KJ+, QJ (about 13.6% of all starting hands). So, he’s not a rock, nor is he a LAG…basically, he tends to overvalue weaker Ax and broadway-type hands. Post-flop, he is more than willing to go to the felt with TPTK and TPGK-type hands, regardless of the flop texture. Of note, he also has check/raised these types of hands from OOP.

The villain makes a PFR to $3.50 from MP2, MP3 calls, and I decide to make a loose call on the button with .

I don’t want to turn this into a hand-history critique, but I decide to do this based on 3 factors:

1- I’ll have position for the rest of the hand
2- I may encourage SB and BB to enter, making for a nice multiway pot
3- I’m getting very good implied odds, as I’m calling here to try and take the villain’s stack.
4- It ensures a higher probability of closing the betting action, unless SB or BB have a strong hand.

The SB and BB fold, so it’s three players to the flop:

Flop (Pot size: $12):
MP2 (Villain) checks, MP3 checks, Hero bets $8., MP2 raises to $25, MP3 folds, Hero…

So, I flop a strong draw. Villain checks and MP3 checks. Based on Villain’s preflop range (of about 180 starting hands), this flop will improve his hole cards about 75/180 (42%) of the time (I also included KcQc, KcJc, and QcJc as “improved”). I decide to bet here because:

1- The majority of his hands were not helped by this flop.
2- I’m favored to win this hand by the river vs. both his PFR range (57.8% equity) and the hands in that range that were improved by the flop (51% equity). Also, the majority of his hands were not helped by this flop.
3- It will prevent a free card for the villain and MP3, who may be drawing to a stronger flush or stronger straight
4- It will potentially create a squeeze for MP3, further increasing the chances that he’ll fold a stronger draw.

The villain responds by check-raising me to $25. MP3 folds, which is a nice outcome. Although there is a small chance that the villain is doing this check/raise on a bluff/semi-bluff, his flop action indicates that he’s ready and willing to play for his stack.

How best to assess the EV of various lines, then?

Clearly, under these assumptions, I don’t have huge fold equity for a reraise push. I’d guess no more than 10-20% (accounting for bluffs/semibluffs with hands like TT-KK, for example).

The other 90% of the time when he calls, assuming he calls with AA,99,77,A8s+,KcQc,KcJc,QcJc,ATo+, I have 51% equity.

Here’s where things get fuzzled:


The “traditional” way of doing EV calcs:

Villain folds to the push: (0.10)*($45.00) = +$4.50

He calls, you win the current pot + his remaining stack: (0.51)*(0.9)*(+$116.50) = +$53.47

He calls, you lose the remaining $87.50 you pushed: (0.49)*(0.9)*(-$87.50) = -$38.59

Net EV per flop shove line = +$19.38


Looks great, right? Problem is, when everything is said and done, when you both get all-in, your stack will either be $105 larger or $100 smaller!!! The fact that you use your remaining stack and the total money in the pot in the traditional EV “push” assessment artificially inflates the true bottom-line profitability of the move.

In my view, if you’ve committed yourself to playing for stacks (and the villain has, too), this is the way you should address the hand:

Villain folds to the push: (0.10)*($33.50 <portion of flop pot that was not from your stack>) = +$3.35

He calls, you net profit a stack (plus blinds/MP3 pf $): (0.51)*(0.9)*(+$105) = +$48.20

He calls, you net lose a stack: (0.49)*(0.9)*(-$100) = -$44.10

Net EV per flop shove line = +$7.45


Clearly, shoving on the flop is going to be a +EV move. No disputing that. But how +EV it really is depends on what your view of the “end result” should be, right? The traditional EV calculation method gives you a 260% exaggeration of what your true profit per hand would be with this line.

With the traditional EV calculation method, assuming a normal distribution of probability over 100 instances, your profit would be calculated as +$1,938. But, in reality, here’s what you’d have in your bankroll after 100 hands played this way:

10 x Villain folds = 10 x $33.50 = +$335.00
46 x allin, you win: 46 x $105 = +$4830.00
44 x allin, you lose: 44 x $100 = -$4400.00

Net change to bankroll = +$765.00


Thoughts? Did I make some silly calculation error? Was there something else in my beer last night that muddled my analysis?

[BigViking]

Hint: take a look at the change in your BR if you fold.

[mash_tun]

Hint: take a look at the change in your BR if you fold.

Not sure what you mean here, Viking...am I missing something? I'm thinking this through under the assumption that I'm only going to either push or call (not fold).

[BigViking]

You're not actually. You're just looking at the value of pushing. So instead of using traditional EV calculation which would have been 19$ or something, you calculate some return disregarding the money you've put into the pot. So what you're doing is saying that your bankroll would only be 8$ higher if you push so that's the number to look at. The discrepancy comes from the fact that your EV calculation is implicitly assuming push or fold. Your 'home made calculations' should have a BR change of 11$ or whatever when you fold while an EV calculation of folding is 0$.

[BigViking]

I think I found an easier way of saying this. Say your bankroll is 100$ when you start this hand. So you push and you get exactly your equity and your BR is 107.65$ which means the value of the push is 7.65$, right? Wrong. At the time you make the decision, your BR is 88.50$. So by making the push, you increase your BR by 19.15$ or whatever.

[emmapeel]

I think this is an incorrect way of looking at things.

You are trying to work out the best decision to make. Therefore you can't include any of the money that is already in the pot. It doesn't matter who's money it is or how much of it is yours.

All you can do in the situation is to make the right decision between Calling folding or raising. Working out how profitable a play is isn't so important as how it compares to the alternatives.

Looking at the hand overall is interesting though as it is possible to make +EV decisions after the flop and yet lose money in the hand. The reason is that you have spent money to play the hand preflop. I think maybe this is what has shown up in the example.

It is not possible to justify your previous contributions to the pot if there is no play that can do that. You can only choose the best play that is available. Even if the play you make is +EV then it is still possible that you can lose money in the hand overall. That's not a reason for choosing an inferior play though.

EP

[emmapeel]

I'll try and say it simpler too

The profitability of a decision and the profitability of a hand are two different things. A hand is made up of several decisions. The EV calculation is used to try to make a good decision and won't give you a reasonable idea about how profitable the whole hand has been.

I think this is a good question though.

Say hero bet the flop with the plan to push all in after being check-raised because he worked out that the push decision was very slightly +EV. This plan loses money though as the money used to bet in the first place has to be included as it was part of the initial plan. Sometimes you have to link decisions if they are part of a plan. I digress a bit though

EP

[janeg]

I think you are overstating the EV, not because you've included or excluded the amount you've put in the pot but because you haven't included the number of times you call and fold because you totally miss the flop.

Odds of flopping a flush or flush draw are about 7.5:1. So 7.5 times you call for 3.50 and miss and fold = $26.25. Since, by your own calculations, you are netting either 19.35 or 7.45 adding in the cost of the PF decision makes the move -EV.

You can't exclude the money you've put in the pot for the simple reason that once you've bet it, it's gone. The only way you can get it back is by winning the pot.

[Neilis]

It's too late at night for me to enter this discussion but I'm posting here so I notice the thread tomorrow. Then I'll edit this post. Good plan huh?

[Mordak]

Two options: all in or call. (I hate to go all in with a drawing hand because of the high variance, but it's a good option)

In the action, i think the best question to ask yourself is:

if I call flop and hit on turn, is he able to laydown considering that the turn card is a scared card for him.

My answer is, probably not. Because you bet 2/3 pot on flop with a drawing hand, it is more probable that he put you on a made hand that can improve. + he made a big bet on flop and he's probably emotionaly binded to this hand.

So if I hit on turn, I would bet 2/3 pot to give the impression that my hand have not improved but that I still think it worth to go.This is (for me) the best way to "trap" your opponent.

If you don't hit, I would check or bet light to hope to have a cheap card. It's a pot odds decision if he push.

If you don't hit the river, you minimize your loss. if you hit, you quickly bet all in to fake a bluff or you bet what you think he will call or shove depending on what you feel about your opponent.

[Soultwister]

Very interesting post, but I disagree that you should not factor in the total pot. Simply since the pot belongs to the winner of the hand, and not just the money the other person put in.

To analyze the hand, you called preflop because you expected the hand to hold positive expectation on average.Whether that's true or not is irrelevant, but when you get to the flop you are at a completely different stage of the game and the money you put in preflop should be forgotten. There's simply a pot now and remaining stacks.

On the flop you again put money in, this time by betting, because there's positive expectation. After the CR hand ranges change, but the money put in again no longer belongs to you and the correct result is based on ranges, fold equity etc and the pot size. You cannot lose $100 at this stage, because the money put in so far has both been put in with the idea it was profitable.

Two options: all in or call. (I hate to go all in with a drawing hand because of the high variance, but it's a good option)

This is a leak, though with very strong draws which may have some disguised outs the odds are often good enough to just call. But assume the last hand went different, and villain had cbet and villain raises. What is villain going to do on this board with KK or QQ? Or even AT? Strong draws are great because they are often ahead with two cards to come, may be a slight underdog, but the folding equity involved makes the hand a favorite.

Look at it another way, in my 217k hands database AKs is ahead of queens in profits, AKo still ahead of jacks. The reason for that is generally because of playing them the high variance way and generally 4-betting with it preflop especially OOP. When I played them more passively, they were only marginally profitable since I would often need to hit flops with them. The hundreds of times people fold 99/TT or even JJ preflop is what gives the hand it's value, not the times you are up vs AQ.

[Mordak]

If I understand you (not really clear), going all-in is the best option.
I guess I have good reading skills, and my desicions are often more read and logic based than pure maths.

But assume the last hand went different, and villain had cbet and villain raises.

If the hand went different then the decision is different.

You guys are trying to make general "rules" with maths to help your desicion making process. But all situations are different and recognizing logical patterns of play (read) on each hand is much more important than the fine details of a deep ev analysis. I agree that you need a good ev picture in the back of your mind. But the reading skill will give you much more $ than the fine details of the odds.

All in is good risk taking. But what if you can win more than what the odds offer with less risk ? I am willing to take that path.

[jeffnc]

mash_tun, I couldn't quite follow all of your post. Not sure if it's unclear on your part or a reading comprehension problem on my part.

I'm thinking that you're partially wrong and partially right. I don't think your EV numbers are really right, because as stated you have to look at the money that's already in the pot.

But, I think many traditional EV calcs are inherently wrong because they only teach you how to play from that point forward. You're right because there's more to it than that. You can't always justify a play based just on the postflop EV calculation, for example, because it doesn't take into account the cost of you getting to that point. It also assumes the money you put in preflop is gone. In fact, that was your money and there's a cost associated with that, and the money you win back has to get netted. A really good EV calc would take into account the cost of you getting into a situation to begin with, and if the return warrants the initial investment.

That's just too hard to do though - that's why no one can tell you if you should call a raise with suited connectors (as you did) is right preflop or not. All they can tell you is that getting your whole stack in on this flop is +EV.

[mash_tun]

Thanks for all the great feedback, everyone...lots of information and thoughts to digest and add to my already-convoluted thinking!

I think emma and BigViking started by identifying/clarifying a key point:

The profitability of a decision and the profitability of a hand are two different things. A hand is made up of several decisions. The EV calculation is used to try to make a good decision and won't give you a reasonable idea about how profitable the whole hand has been.

You're just looking at the value of pushing. So instead of using traditional EV calculation which would have been 19$ or something, you calculate some return disregarding the money you've put into the pot.

Take home message: When you assess EV, remember it's for one decision in a hand and may/may not relate to overall profitability of the hand.

Odds of flopping a flush or flush draw are about 7.5:1. So 7.5 times you call for 3.50 and miss and fold = $26.25. Since, by your own calculations, you are netting either 19.35 or 7.45 adding in the cost of the PF decision makes the move -EV.

Jane takes this a step further with some real #'s. For what it's worth, I'm actually getting a bit better odds than 7.5:1 to make a call here and "hit" the flop in a meaningful way. I'm hoping to hit a flush draw, straight draw, flush, straight, and/or two-pair or trips. This will happen about 20-25% of the time, so my odds are about 3:1 or 4:1 to get a good flop. So, before I even get to the situation at hand, I need to remember that 3 or 4 times, I'll be folding, to the tune of about -$11 to -$14 net loss. So, when I do hit the flop, I need to make an average of at least $15 to show a long-term profit. The question, then, is:

What is the best way to assure yourself of getting this profit?

Mordak and Soultwister shed some good light on this question:

Two options: all in or call. (I hate to go all in with a drawing hand because of the high variance, but it's a good option)

In the action, i think the best question to ask yourself is:

if I call flop and hit on turn, is he able to laydown considering that the turn card is a scared card for him.

My answer is, probably not. Because you bet 2/3 pot on flop with a drawing hand, it is more probable that he put you on a made hand that can improve. + he made a big bet on flop and he's probably emotionaly binded to this hand.

So if I hit on turn, I would bet 2/3 pot to give the impression that my hand have not improved but that I still think it worth to go.This is (for me) the best way to "trap" your opponent.

...with very strong draws which may have some disguised outs the odds are often good enough to just call. But assume the last hand went different, and villain had cbet and villain raises. What is villain going to do on this board with KK or QQ? Or even AT? Strong draws are great because they are often ahead with two cards to come, may be a slight underdog, but the folding equity involved makes the hand a favorite.

The key points here to assess overall profitability are how much fold equity you can expect vs. the villain given the action up to this point, combined with the strength of your draw vs. villain's range.

...all situations are different and recognizing logical patterns of play (read) on each hand is much more important than the fine details of a deep ev analysis. I agree that you need a good ev picture in the back of your mind. But the reading skill will give you much more $ than the fine details of the odds.

All in is good risk taking. But what if you can win more than what the odds offer with less risk ? I am willing to take that path.

Agree 120%. In fact, what started me thinking about all this in the first place was a recent re-read of Largay's NL Cash book. In one section, he talks about looking at lines that give you the best opportunity to exploit your villain's errors, as it will give you the highest profitability. The "strong draw" situation is one of the most obvious examples, since your read on you villain is, I think, the most crucial determinant to how you should play it.

But, I think many traditional EV calcs are inherently wrong because they only teach you how to play from that point forward. You're right because there's more to it than that. You can't always justify a play based just on the postflop EV calculation, for example, because it doesn't take into account the cost of you getting to that point. It also assumes the money you put in preflop is gone. In fact, that was your money and there's a cost associated with that, and the money you win back has to get netted. A really good EV calc would take into account the cost of you getting into a situation to begin with, and if the return warrants the initial investment.

That's just too hard to do though - that's why no one can tell you if you should call a raise with suited connectors (as you did) is right preflop or not. All they can tell you is that getting your whole stack in on this flop is +EV.

This is pretty much the dilemma I was struggling with...so you did understand my post just fine!

[janeg]

Finally reading PNLHE and wondering if this wouldn't be better approaced using SPR. It's only my first read so not sure I understand it correctly but given the above scenario, the SPR is 8 (smallest stack 100-3.50 / pot 12).

As a rule of thumb, the text advises a largish SPR (20 or so) for drawing hands OR a medium SPR (13 or so) if you plan on raising your opponents off a top pair hand. The basic concept is you either expect to win 20 times the pot or 13 times the pot if you hit the flop. The hand you're most likely to flop with 86s is a draw (sometimes you'll flop the str8 or a flush or a full house but mostly you'll miss or flop a draw).

The example doesn't fit either scenario, the SPR being too low for either. It calls into question your 3rd assumption:

I’m getting very good implied odds, as I’m calling here to try and take the villain’s stack.

Given the SPR values, that doesn't look true.

Rather a weak analysis but it still looks -EV to me.