I'm going to dedicate my first post ever on this forum to kurt! Thnx for the nice article!

How does this work? :

Your statement: A group of n players are each -EV going to the flop.

This implies: n-1 of the players are each -EV going to the flop.

But, if n-1 of the players are each -EV going to the flop (and the total EV must be 0, disregarding rake), the remaining player must be +EV going to the flop, and hence your statement is incorrect.

Your argument is complex, and I feel you can't have fully resolved all postflop scenarios, otherwise my reasoning above wouldn't work. Am I missing something?

Board:
equity win tie pots won pots tied
Hand 0: 43.450% 43.33% 00.12% 368614 999.20 { AcAd }

Hand 1: 20.044% 19.93% 00.12% 169512 999.20 { JcJd }
Hand 2: 15.052% 14.93% 00.12% 127040 999.20 { 6c6d }
Hand 3: 09.559% 09.44% 00.12% 80314 999.20 { 2c2d }
Hand 4: 11.895% 11.78% 00.12% 100192 999.20 { 4c4d }


---


equity win tie pots won pots tied
Hand 0: 52.810% 52.68% 00.13% 572108 1407.50 { AcAd }

Hand 1: 19.310% 19.18% 00.13% 208304 1407.50 { JcJd }
Hand 2: 16.116% 15.99% 00.13% 173618 1407.50 { 6c6d }
Hand 3: 11.764% 11.63% 00.13% 126348 1407.50 { 2c2d }

It has to do with your commitment.

Let's say you have AA. And let's say you get 20% of your stack in preflop.

Against a single opponent with a smaller pair you can commit you entire stack postflop and no matter what the outcome your play of the hand is +EV. They cannot make enough the 1 in 8 times they have 90% equity from the rest of your stack to make up for what they put in with 20% equity preflop. They are -EV.

Same scenario, your AA gets 20% of your stack in against 5 opponents with smaller pairs. You commit your stack post flop.

From the perspective of each of the villains, they are -EV for the same reasons they are -EV HU against AA. They can't make enough from your stack to overcome what they put in behind.

But you are not playing against one person. You are playing against a field. As a field they have 42% chance of flopping a set. If you commit your stack postflop you will be -EV because you will lose more postflop against the field than you got them to commit preflop.

So individually they are all -EV in setmining against you. But you are still -EV committing your stack.

The result is that you cannot commit your stack even though you got 20% in preflop.

In order to avoid this you have to put yourself in the uncomfortable spot of possibly putting half your stack in and then folding. And if you're going to fold, you will sometimes be folding the best hand. All of this adds up to making it a marginal spot at best... even though you got 20% of your stack in with the nuts.

small wins, big losses

comes to mind in this situation.

Total EV does not have to add up to zero.

So in first example, we have 43% equity in a 5way pot which is hugely +EV, and in second example 52% equity in a 4way pot, which is again hugely +EV. Of course, a stoved analysis is pretty irrelevant given there will be significantly complex post-flop action (the whole argument is about IO and RIO), so can't see the interest here.


Kurt, I don't disagree with the large part of your argument - raising bigger is clearly better to avoid this kind of horribly awkward spot.

My point is that everyone can't be -EV all at once, that's all - if an argument falls to a simple reductio ad absurdam as above, there's obviously a problem - this is really simple maths.

So, there must be significant scenarios that haven't been taken account of.

For example:

-We know they are all setminers (edit: obv in reality, they aren't always setminers, so postflop EV calcs change): we therefore won't commit our stack.
-If they are all setminers (a given), then if an overcard comes, and they don't hit, they may well fold to a cbet (and if one or two don't, there may well be very limited further action) (edit: clearly a multiway dead money argument here).
-If we are five way, there is a lot of dead money in the pot (4x our pfr). In this case, if we hit a set with our AA, we only need to 5x our pfr postflop to break even. Given that we stack anyone who hits a set (this happens ~25% when we hit our ace), we in fact have (edit:not insignificant, though ofc not sufficient) implied odds to oversetmine (edit: this would obv be an argument for raising to significantly less than 20bb if we were going to do it)

ofc ^^ is not exhaustive, but because it's impossible for everyone to be -EV, there must be something missing. That said, the spot is clearly marginal, as you say, and raising bigger is clearly more +EV.

EV before the flop is average money won over an infinite number of samples, given preflop action. So, if Total EV does not equal 0, where is the money going (obv disregarding rake)?

You have the +EV from preflop. In the form of IO a little piece of that +EV goes to each of your opponents. Individually, its not enough to make them +EV. But collectively you lose more in IO than you have banked preflop.

You have no idea how reluctant I am to argue with you, given your general awesomeness in these forums, but my original argument doesn't rely on totting up preflop and postflop EV (I believe your argument assumes we get stacks in everytime, which we don't), it simply relies on the fact that total money flow must be zero in the long run, and hence total EV must be zero in the long run, and hence *if* all your opponents are -EV you must be +EV. Otherwise money vanishes, which is impossible.

Well, then thank you for arguing.

I think...

Its a matter of perspective. From your perspective you're -EV. From villain's perspective he is -EV. From God's perspective, its all 0EV.

I don't have time for a long post right now. But I'll do some thinking over the next day or so and see if I have to recant or if I can explain it better.

Sick dude, props for being easy to talk to - not many discussions end (well, to be continued...) in such a civil manner here lol

I used to limp a lot when I first started playing, but raising first in seems to speed up the game a little more.

I limped in utg with QQ. Dude raises middle position with aces to 6x. Another guy flats with 89 offsuit. I flat call.

Board: Q99

I check, aces bets, late position raises, I flat aces shoves allin, I call. So that is the only situation where it worked out. This situation is rare though, but sweat to triple up.

Doesn't this have something to do with the 50-50 propositions? I mean, I look at a situation where $$$ is equal and if I have the best of a 51-49, I have a +EV.

It gets mess with when we are up against multiple stacks and multiple players (as you premise). In that case, I believe we can have the best of it with AA.....but still be behind the field.

Think of it this way. You are playing a NL holdem game with a table of 13 players. You hold AA, the next KK, the next QQ....and so on until #13 holds 22.

You have the best of it against each individual... but I like the field's chances

(((hatfield... not appropriate thread post..... again)))

Yes, but we don't mind, because we only put in a little money, and the field (collectively) put in a lot of money: we don't have to win very often to be profitable (as long as we don't insta stack off with our overpair that is).

In your extreme example, we can simply wait to hit our ace. If our opponents are willing to put in money when they hit their set (two other players will always hit their set when we hit ours (disregarding paired boards, when we know they have quads)), we will make a ton of money in the long run.

People often talk about the 3 edges one can have in poker: skill, position, and card. Skill and position being equal (say we run the test multiple times in different positions), we simply have the best cards - when we hit a set, we win near everytime (ie we loose when a flush or straight comes for a villain) - when they hit a set and we hit a set, they loose. When they don't hit a set, and we don't hit a set, we win. We only loose out if somehow we play worse than the field postflop, and there is no reason why we should - our hand is of the exact same type as the villains' - there is no sense in which it is less playable.

There is part one of The Rub. Again, small win, big loss.

Part Two???? They aren't always setmining with pairs.

I will argue.

You are assuming the end game is finite, which is not. Just because a player enters the pot doesn't mean all the money will flow. So a player can have a -EV, but the combination of the field can be +EV, which means you will be +EV overall, but -EV for that particular situation, since any player can end the game early "fold"

There are in fact a finite (but very large) number of ways the hand can be played out (finite combos of flop, turn and river cards, and finite combos of possible bets, given that money is discrete).

A player's EV in entering the hand is determined both by the initial conditions, and their "strategy", in the game theoretic sense: A Strategy is defined as a "complete specification of a player's actions choices at all possible paths the hand might follow" (Mathematics of Poker, Chen & Ankeman)

This discussion is becoming fairly complex - I feel that one thing which is clouding the discussion is the concept of a "field" of players: There seems to be a suggestion by some posters that the EV of the field of setminers (or players with lower pocket pairs) is somehow different to the sum of its parts. This is clearly incorrect. Each player entering the pot has an Expected Value for the money they will win in a hand. Over a large number of samples, they will each individually average a particular "EV", determined from initial conditions (their hand, their position and the presence of the other players at the table, with their own strategies) and their strategy.

As such, we can add up the EV for each of the other players in the pot, and this will give us the EV of the field. Our EV is exactly the negative of the field's EV - this is in line with the "Conservation of Money":

Conservation of Money (EV): Given initial conditions and strategies, each player who has been, or is, or may be involved in a particular hand has an Expectation Value for their winnings in that hand (this is applicable at any point in a hand, even before cards have been dealt). The sum of all player's Expectation Values is zero, otherwise there is a net flow of money out of or into the game (We are disregarding rake).

I hope it is clear now that this EV is independent of observer, and is simply the average value of a player's winnings over an infinite sample, given initial conditions and strategy. So, this is not correct:
As you say (Sammy), certain strategies are -EV, for example, open folding the flop in all situations.

I contest that given AA, it should be possible to create a strategy on the flop (this is a hypothetical strategy, we don't need to write it out) that will be +EV vs a group of players with lower pocket pairs, given any possible preflop action.

There must be such a strategy, because if there is not, then we are -EV, while at least one of the players with a lower pocket pair will be +EV (by Conservation of Money), and this is absurd.

I agree with what you say. As far as a strategy for AA, yes we can create a strategy that is alway +EV no matter how big the field is (off the top of my head calcs, assuming 9 handed, if you raised to 34% of effective stacks assuming no rake), but this may not be the most EV (which can only be dictated by each players strategy). Plus the set of hands we play preflop may be actually -EV using this strategy....I think the discussion is moot at this point as we are almost in full agreement.

As far as the discussion of -EV strategy being absurd, that is not the case as these are conditional games vs rigid strategies. We can have an overall strategy that is +EV preflop no matter the overall conditions with even though each Post flop street strategy is -EV....I think that is the overall confusion here. Our overall preflop strategy is +EV no matter the decions post flop, but our postflop strategy could be greatly -EV. So our overall strategy could be +EV, but <<<< than a non-rigid post flop decision matrix.

Before getting on with the post, for clarity, can we define Postlop EV as: The difference between our true preflop EV (that takes account of all postflop paths), and our EV if there is no further betting once the flop comes down (our AIEV).

I'm not sure what "postflop EV" has meant so far, but I think this is the most sensible definition.

Yes, I have just realised that I hadn't been taking into account the asymmetric information in this hand. In Kurt's original example, the villains were setminers, ie the villains has us on a very tight range (Say Aces, Kings, Queens), while we have each of the villains on much larger ranges, giving them an obvious edge. I had assumed that we knew the villain's range, but forgotten to take into account the range the villains had us on.

Given the villains' precise knowledge, we will be -EV postflop: the villains can bluff us unexploitably (ie infrequently enough such that we cannot bluffcatch profitably), while we can never get value from the villains. Kurt basically said this in OP - the villains are getting value from their superior knowledge of our range. (Here, we are neglecting the scenario where there are high cards on the board, that could conceivably give us a set - we could further simplify our range to exactly AA to remove this complication.)

So, just as we are -EV post flop, because the villains can bluff us unexploitably, and we can never get value, the villains are in fact +EV post flop. (Of course there will be a certain point at which enough of the stacks are in that our preflop card advantage dominates over this informational advantage, as stated in OP)



I believe the confusion in the OP (ie the factor that caused my initial problem) was that it claimed that the villains were only setmining - ie that they would not bet when they didn't hit.

(If this is were the case, postflop EV would in fact be completely neutral for each player, as the villains wouldn't bluff us, and we couldn't valuebet. This (idealised) situation would obviously leave us massively +EV overall)

The OP then claimed the villains were -EV overall because they didn't have odds to setmine, which is obviously true if they are simply setmining (and never bluffing), as stated above. It also claimed (in contradiction) that the villains could bluff us, but this then makes them +EV postflop, possibly +EV overall, although this would be horribly complex to calculate. This minor contradiction (and possible confusion of overall and postflop EV) led to the claim that both we and the villains were -EV, which is, of course, impossible.



Edit: I've neglected the fact that when we bet on the flop, and the villains all fold, they fold out their equity of hitting a set on the turn or river. I reckon other EV aspects of our betting the flop will dominate, so this is probs a good approx.

I'm really spamming this board, because I have way too much time on my hands atm.

Sammy can I ask what you mean by a non rigid postflop decision matrix, as opposed to a Strategy?

As defined, a Strategy tells you exactly how to respond to the board, and any set of Villain actions. An optimal long term Strategy will include elements of randomisation: for example : "when we hit top set on the flop, and a villain (with a particular history, and given particular preflop action) donks, we raise 60% of the time, and call 40% of the time."

If I'm OP and have a marginal hand I'm almost always punishing limpers. Well it also depends on the other players, but if I can I'm always punishing them hard! NO LIMP!

(from post #5)

Repeating a falsehood does not make it true. Ignoring the rake, it is impossible for everyone in the pot to be -EV (even if there were not two average hands in the blinds putting some chips in as well). Allowing for blinds, if anyone has an above average hand, someone must have +EV. If everyone who has limped in and yourself have below average hands, it's difficult to know what to say...

Look at it this way. Over a million plays of the hand from a particular situation, each player will get a portion of the pot as it stands. These portions add up to 100%. Some player has to be getting more than they put in (neglecting the influence of the rake). This is clear since (1) no-one else is getting any of it, and (2) the pot came from the players (including the blinds, which is why I needed to mention the quality of the hands above). [If we are taking account of the way players will play later in the game, it is possible to have EV over 100% of the pot. And for someone else to have expected losses greater than if they simply checked and folded. But it still all has to add up to 100%]

What would make more sense might be to say that each of the other players made a decision which gave less EV than the alternative of raising and, for you, calling might give less EV than raising. Both of these might be true.

This is a technical point which does not undermine Kurt's advice in any way.

Having made my last rather curt post, I realised how confusing the use of the term "EV" can be. To me, it can mean:
(1) The fraction of the pot that a hand would get on average if there was no further betting to showdown
(2) The fraction of the pot that someone would get on average, assuming styles for each player which would determine future decisions
(3) The fraction of the pot that would be gained on average by a particular choice of play compared with another choice (must be assuming the way players will behave in all possible future scenarios). Eg "raising is +EV compared to calling"
(4) allin EV (some people confusingly refer to this as EV, which seems inadvisable)
(5) any more? any comments on what is correct/sensible usage of the term?

The passage from Post #5 is confusing, to say the least. As for your second question it is usually a variation of your option (3), where folding is considered to have zero expectation. So "+EV" is used as "has a better expected outcome than folding".