backstory
I've been studying limit holdem with this guy for a long time. I posted this question:
He replied this: I've decided to put my response in the theory forum:

That's a decent way to think about TT, but why not try to think about it deeper away from the table? I think this is where you have the most potential for improvement. I've literally lost count of how many times I've been wrong in these forums, particularly in the more advanced forums like medium stakes holdem and poker theory. However, I learned much quicker by being wrong than I would have if I hadn't made all of those posts.

I think that if you put as much time thinking about the way ev shifts as a hand of poker progresses as you put in typing up all those bloggy style posts, that you'd have a better understanding of where the money is coming from.

To put it in perspective:

When two great players face off in a hand of cards, these players will only very rarely make a less than ideal decision; they will choose the most profitable play with astounding accuracy, precision, and frequency; they will rarely make a -ev decision even relatively speaking; For example:

we sit to play heads up limit holdem. I let you have the deal first hand just to be nice and we post blinds. How much of the pot do you think you own(a)?

you raise preflop. how much of the pot do you think you own without knowing your cards(b)? In other words, what's the average?

I call. how much of the pot do you think you own(c)?

etc as the hand progresses however you want to imagine it.

your guess is as good as mine, but there are a few things that come to my mind:



then the hand progresses until one of these outcomes occurs:

a) I fold.

b) You fold.

c) I call.

d) You call.

e) checks through*

eventually, one of these four things will happen. let's look at the ev distributions:

a) you win (pot*my fold frequency)

b) I win (pot*your fold frequency)

c) I win (my call) + (pot*% of value hands I beat)

d) you win (your call) + (pot*% of value hands you beat)

e) each player wins (equity*pot)

In situations (c) and (d) when blockers are involved, the evs look like this:

c) I win (my call) + (pot*% of extra bluff combos) ; what happens with that hand is that it's actually quite profitable, depending on the strength of the blockers and how bluff heavy the opponent becomes because of those blockers.

d) you win (your call) + (pot*% of extra bluff combos)

my ev is (b+c+e) and your ev is (a+d+e).

So what's the point? I'm gonna take a break from typing, but I'll be back.

lol what dude

It's funny to me too because that's the type of response I expected.

I'm still in the early stages of ev estimation <---- excuse.

I'm not always the best at conveying what I'm trying to say. <----reason.

-----

So where was I going? I think this is a rough outline of how players better than myself think about ev, but how can I know without putting it out there?

I think good players actually think about EV along the lines of your friend's response tbh

I agree. With enough study and memorization we can get pretty good at poker, but I also think that away from the table it's good to think about ev more in depth.

I think if you try to answer the questions I posted, it will make you think about pot distribution in a much deeper way. I'm still in the rabbit hole to be honest.

If you raise UTG with TT and take down the blinds, then you profit. If you raise UTG with TT and the BB defends, it could be +EV for you to raise and also for BB to call because you are chopping up the SB.

It sounds like you are ignoring the value of forced bets.

True.
Not sure why you came to this conclusion. It's not that I'm ignoring the forced bets, it's just that once they're posted, they're not ours anymore. They belong to anyone with cards still in the pot.

Calculating an accurate EV for a specific hand in a specific spot on a specific table is too many variables too even think about. You'd need 100million+ hand samples on everyone at the table.

All you need to know and the only value that is really relevant is that it is > 0

Not for a specific hand. I'm thinking about strategy vs strategy ev as a share of the pot.

you're wasting your time.

Ok, I'm gonna keep toying with the idea in my head, but I'm aware that it may not end with any useful conclusions. That's ok with me. People make sense of the world differently, thus what helps you learn might not help me learn. I'm very visually oriented and I used to be pretty good at spatial relation puzzles when I was a kid. So when I say that I'm thinking about owning a share in the pot, I don't have an exact number in my head. I'm imagining fractions of the pot being divided and rewarded to the players. Assuming that all are playing perfectly, every single play that they make will have an ev greater than or equal to zero.

So this is only a part of the equation that I have in my head:

strategy ev = (sum of all profitable and 0ev decisions)/(number of combos in range)

When experts face off in a hand of poker this is how the pot will be distributed:

No player may claim more than the existing pot with his or her strategy ev, lest the opponent makes a severely -ev decision.

Each player will receive a profit from the pot, not just sometimes, but any time the player continues. Even the nut low can river a pair and win the pot.

The only plays we make that are actually close to 0ev are these:

weak bluffcatchers calling

weak draws calling

fold is 0ev

and river bluffs out of position are 0ev.

----

all other bets, calls, checks, and raises are receiving a decent profit from the pot.

How do you suggest we visualize ev for these actions?

FWIW I don't think any mental exercise is a waste of time. Worst-case scenario conclusion is, "This is the wrong way to look at it" and you've gained more confidence in the alternative.

Also FYI Brokenstars I am exclusively a low-stakes live LHE player - if I'm at a table where my UTG raises are usually only getting action from the BB I rack up and go do something else.

Bob, out of curiosity have you read "The Intelligent Poker Player" by Phillip Newall? He does a lot of range vs. range analysis in that book and I think this may be what you're driving at.

I've read it more than twice. I've discussed some related concepts with Newall in the books and publications forum in this thread:

https://forumserver.twoplustwo.com/3...dem+discussion

which he hasn't updated in a long time. Shrug.

-----

But yeah he hits on lots of range vs range stuff in the book, which I should probably crack open again sometime.

Sure,

If the goal is to get better/gain better understanding, then I'd recommend just buying PIOSOLVER. This won't tell you the EV of opening a specific hand, but in HU situations it would be possible to do a summation of the EV of a specific hand over all boards. This obviously assumes a nash equilibrium, though.

The way you are thinking about it is correct, Bob. However, I don't really understand what use it is in asking the question since as I said previously to accurately know the absolute EV you'd need millions/billions of hands of all opponents and the EV would still only be relevant to THOSE players.

I wish to go a step beyond this and look at strategy vs strategy evs given a specific board.

Compare these two situations sticking with the limit holdem theme:

a) I raise preflop on the button huhu, big blind calls.

A62r

I bet, big blind calls.

Jo

I bet, big blind calls.

To

checks to me. Even before betting I think my share is pretty huge. Probably > (pot*70%).

---------

Or: I raise on the button, big blind calls.

458r

checks to me, I bet, big blind calls.

7o

checks to me, I bet, big blind calls.

6o

checks to me, I expect a much smaller share than the above situation, probably < (pot*60%)

If range vs range ev isn't indicative of how we should play these spots, specifically by betting often in the former and checking often in the latter, then I must be missing something.

aggregation analysis also gives and equity realization variable with PIO. This would be kind of what you're talking about.

Nice. Sounds like exactly what I'm talking about.

Was just a question to get the ball rolling.

I'm not claiming that average ev/hand expressed as a share in the pot is in any way instrumental to creating a strong poker strategy. If I may make an analogy:

Scientists have long studied supernovas by looking at them after they happen. Before the scientists were able to accurately and precisely measure these events as they occurred in real time, there was only theory based on the after effects of a supernova.

In a similar way, we are in a transitional period of poker theory where we have these near gto strategies that we study, without really understanding exactly where the ev is coming from. We can look at these near gto strategies and form theories based on the patterns we find, but it's still all just theory.

I think the next step now, at least for me, is to look at the resulting average ev/hand expressed as a fraction of the pot for clues in the after effects, so to speak.

2 thoughts:

1. All supernovae occur in the past (sorry couldn't resist :-)) though I do like the analogy of doing something and then going back and analyzing why it's that way.

2. I wonder if the probabilistic nature of the game and GTO strategies will create too much noise for you to draw significant conclusions about where the EV comes from?

I think if we simplify the problem, we may be able to see trends:

there are only two ways that we realize ev from the pot:

1) we have the winning hand at showdown

2) we win when everyone folds.

-------

We can achieve (1) in several ways:

a) checks through and we win.
b) opponent bets and we call.
c) we bet and opponent calls.
d) opponent bets and we raise and he calls.
e) we bet, opponent raises, we call.
f) opponent bets, we raise, he 3 bets, we call.
g) we bet, opponent raises, we 3 bet, he calls.
etc.

then the list gets messy from there.

So let's look back at some of the examples upthread:

Ok so we get to the river with this action and my range looks something like this:

KQ maybe 14 combos.
AA 3 combos
JJ 3 combos
TT 3 combos
66 3 combos
22 3 combos
AJ 9 combos
AT 9 combos
A6 9 combos
A2 9 combos
JT 9 combos
J6 9 combos
J2 9 combos
62s 2 combos
AK 12 combos
AQ 12 combos
A9 12 combos
A8 12 combos
A7 12 combos
A5 12 combos
A4 12 combos
A3 12 combos
A2 12 combos
KJ 10 combos
QJ 10 combos
J9 12 combos
J8 12 combos
J7 12 combos
J5 12 combos
J4 12 combos
J3 12 combos
KT 10 combos
QT 10 combos
--------------------
total value combos: 314

bluff combos:

43s 3 combos
53s 3 combos
54s 3 combos
73s 1 combo
74s 1 combo
75s 1 combo
83s 1 combo
84s 1 combo
85 4 combos
87 4 combos
93s 1 combo
94s 1 combo
95 4 combos
97 4 combos
98 4 combos
Q3 4 combos
Q4 3 combos
------
total bluff combos: 43

-----------------

value:bluff = 314:43 = 12.04% bluff frequency.

------------------

My checking range on the river is then Q4 (1) or anything better up to QT and everything in between that I would play that way up to the river:

Q4 1 combo
Q5 4 combos
Q7 4 combos
Q8 4 combos
Q9 3 combos
K3 3 combos
K4 3 combos
K5 3 combos
K7 3 combos
K8 2 combos
K9 2 combos
K6 6 combos
77 3 combos
88 3 combos
99 3 combos
------
total check combos: 47 combos + 357 bet combos = 404 total range combos: 47/404 = 11.63% checking frequency complemented by 88.37% betting frequency.

I'll have to come back later and pick apart the big blinds strategy to complete the ev calculation.

The big blinds strategy probably looks something like this after this action:

JTo maybe 5 combos
T6 maybe 9 combos
T2 9 combos
J5s 3 combos
J4s 3 combos
J3s 3 combos
----above this line can beat some of my value hands.
K6 12 combos
Q6 12 combos
96 12 combos
86 12 combos
76 12 combos
65 12 combos
64 12 combos
63s 3 combos
33 6 combos
K2 12 combos
Q2 12 combos
92 12 combos
82s 3 combos
72s 3 combos
52s 3 combos
42s 3 combos
32s 3 combos
K9 16 combos
K8 16 combos
K7 16 combos
K5 16 combos
K4 16 combos
K3 16 combos
Q9 16 combos
Q8 16 combos
Q7 16 combos
Q5 16 combos
-----------------
total combos that can beat a bluff = 336 combos

hands that only beat part of my bluffing range:

Q4 16 combos
Q3 16 combos
-----------------
this means that my Q4 will win the pot 6.52% of the time and thus the big blind should fold at frequency that allows my bluffs to profit exactly 6.52% of the pot. Here's some math for fun:

before I bet, the pot is 6.25 big bets. 6.52% of 6.25 = 0.4075 big bets of profit must be allowed for my bluffs (Q4) or else I could exploit by not bluffing the bottom of my range.

This equates to 80.59% calling frequency for the big blind on that river and a complementary 19.41% folding frequency, which is admittedly higher than i expected. Let's see what that works out to for a call or fold strategy:

19.41% * 368 combos = 71.43 fold combos.

so:

big blind should fold 7 combos of Q7 and anything worse in order to make me indifferent to bluffing the river with Q4. big blind calls 9 combos of Q7 and anything better for ev greater than or equal to zero.

So what does this mean for long run final pot distribution? Looks like this imo:

when I check 11.63% of the time, I win a fraction of the pot that is greater than or equal to the ev of checking Q4o = 6.52% of the time I win (pot) = + 0.4075 big bets profit or more up to the ev of checking with my 99, which is apparently quite high: 91.3% equity = +5.70625 big bets of profit. It would take me a while to figure the avg value of checking, but I think that knowing it's somewhere between 0.4075 big bets and 5.70625 big bets is useful. So multiplying that by the checking frequency we get this as the checking range ev source: 0.0486 big bets/hand minimum up through 0.6808 big bets/hand maximum ev for checking. The mean, although not quite the same as a pure average here, would be about 0.3647 big bets/hand

when I bet my 314 value combos: my ev is at or above the ev of value betting QT.

331 calling combos: 32 of which beat QT. QT has 90.33% equity when called 80.59% of the time: (8.25*.9033*.8059) = 6.006 big bets of profit/hand when called.

Also, a seemingly hidden ev source is that of winning the whole pot when the big blind check folds the river:

19.41%*7.25 = +1.407225 -1 big bet invested = 0.407225 big bets of profit/hand with value hands when big blind folds the river.

So if all of that is true, then that means my pot share adds up as such from the two ev sources of having the best hand at showdown, and winning when the opponent folds:

6.777925 big bets realized at minimum per hand on the river.

That equates to a minimum 93.49% pot share for the button on the river after I bet.

a correction: see bold:
Q7 was wrong. It's Q8.