I Know 2+2 Wants To Kill Me For This......

[StellarWind]

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What we do in EV neutral situations has a direct bearing on whether or not actions on the later streets are positive.

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The kurosh example is deceptive because the flop action is *not* EV neutral.

That thread floated all over the place, so let me recap some assumptions:

1. Preflop pot of 3 SB.

2. Hero has a draw with a 1/3 chance of completing by the river.

3. Hero has no fold equity with an unmade hand. He will always have two opponents unless he makes his hand.

4. Hero cannot collect any bets after he completes his draw.

5. Hero will be wringered on the turn and have to pay 4 BB to see the river. I added this assumption to clarify my point.

6. There is no cap on the flop.

Argument:

Each flop bet gives 2-1 odds and has a 1/3 chance of winning, therefore it is EV neutral (zero EV). Except for variance it would appear that it doesn't matter how many bets go in on the flop. The curious thing is that if no money goes in on the flop then Hero will not have pot odds to call the turn (1/5 chance to win), but if many bets go in on the flop the pot will become bloated and calling four bets on the turn becomes correct.

Paradox:

The "neutral EV" flop bets changed the EV mathematics of the whole hand.

Resolution:

Limit hold'em players are so accustomed to never folding flush draws that they accepted the "2-1 bet odds and 1/3 chance to complete draw means neutral EV" spiel without question. But it's wrong and if I redid the example with a big table full of callers and a gutshot people would see it immediately. We all know you can't count on two pulls at a gutshot. The odds on turning the flush draw are only about 4-1 and the 2-1 bets on the flop are clearly negative EV.

Only when the pot becomes sufficiently large that Hero is river committed do the well-known flop 2-1 bet odds come into play.

A similar effect occurs with gutshots. If I drop Ed Miller's famous $1000000 into the pot preflop, then I can start value-betting the flop at roughly 5-1 odds with a nut gutshot because I'm guarenteed to see two cards.

Stellar,

You deserve to be commended, as you did a phenominal job throughout this whole thread.

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The "neutral EV" flop bets changed the EV mathematics of the whole hand.

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This is a very important concept. There is a standard argument that money you put in the pot belongs to the pot and is no longer yours. This argument is usually brought up when evaluating correct "chasing" odds. At the time of the decision (flop, turn, river, etc.) the argument is valid. The money in the pot doesn't belong to you and therefore the pot is already bloated. However, there are certain preventive measures that can be taken at the "time of bloating" which will allow us to make correct folds when we're supposed to (Kurosh's thread illustrated this idea).

In the current hand, I believe capping preflop with AKo will give us correct odds to call on the turn fairly often....and won't allow us the opportunity to make the right fold in that spot, as exemplified in Kurosh's thread. Just calling preflop may or may not do this and for that reason, I believe calling to be a better option than capping.

There's one other thing from Kurosh's thread that can redefine the way we look at decisions. Bloating to give correct odds for a later call is bad when we're currently -EV. As the thread pointed out, there are situations where pumping the pot can hurt us when we're currently "EV neutral". Using that line of logic, there have to be situations where pumping can be a detrement EVEN IF WE'RE SLIGHTLY +EV!! This can happen any time the value we get by pumping is less than the value we lose by not being able to make a correct laydown. It's a VERY interesting concept.

All of this is separate from implied odds or reverse implied odds. Kurosh completely removed those from his example and the paradox still existed. The way we assess EV on any given street has to include the (-EV now, +EV later) possiblity of future calls when we don't currently have the winning poker hand.

[StellarWind]

Here is an example that I made up a long time ago in a preflop EV thread.

You are playing heads up hold'em but the deal is rigged. One of you will flop TPTK. The other player will receive a standard gutshot. It is completely random as to who will receive what.

Scenario 1: Both players are perceptive and skillful and will play FTOP-correctly postflop. Whoever gets TPTK will bet and his opponent will compute pot odds and act accordingly. There are no implied odds because no one ever chases a made straight. There are no redraws to full houses.

Analyze the preflop play.

Scenario 2: Exactly like scenario 1 except that Villain has a bit of gamble. He will always peel one card to try and make his straight. Other than this he plays properly.

Analyze the preflop play.

I'll post again later after you've had some time to absorb this. This example has great significance when a good player is considering raising the field for value with some mediocre hand like QJs that has a small PokerStove edge over the marching nitwits. Specifically I am thinking of opponents who only play their cards and don't consider pot size or what hand the PFR is representing.

[kurosh]

I still don't fully understand the concepts in my old thread. There is a lot more to it than what is there. It has a lot of implications on PF play. I wish Sklansky had touched on this so I wouldn't have to figure it out piece by piece over time.

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Scenario 1: Both players are perceptive and skillful and will play FTOP-correctly postflop. Whoever gets TPTK will bet and his opponent will compute pot odds and act accordingly. There are no implied odds because no one ever chases a made straight. There are no redraws to full houses.

Analyze the preflop play.

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I'm a little confused. I guess we're assuming that we can't tell anything from the cards we're dealt? What I mean is if we're dealt 32 preflop, we know we're the one who will flop the gutshot because 32 could never be TPTK.

If we're not allowed to see our cards until after the flop, then it doesn't matter because this would be a complete coin toss every time.

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Scenario 2: Exactly like scenario 1 except that Villain has a bit of gamble. He will always peel one card to try and make his straight. Other than this he plays properly.

Analyze the preflop play.

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Assuming the same deal (we can't see the cards preflop):

The idea here is to keep the pot as small as possible at either 0 or 1 bets. In other words, we check or we call. This allows our "gambling" opponent to make the biggest mistake on the flop by peeling when he has the gutter.


EDIT: Hopefully, I understood the question correctly.

[StellarWind]

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I'm a little confused. I guess we're assuming that we can't tell anything from the cards we're dealt?

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Correct, you cannot predict who will flop TPTK based on your preflop cards. Assume you cannot see your hand preflop.

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If we're not allowed to see our cards until after the flop, then it doesn't matter because this would be a complete coin toss every time.

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Correct. These are straight even bets on a 50-50 chance. They have zero EV. Bet and raise if you enjoy gambling.

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The idea here is to keep the pot as small as possible at either 0 or 1 bets. In other words, we check or we call. This allows our "gambling" opponent to make the biggest mistake on the flop by peeling when he has the gutter.

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Suppose Villain bets preflop. You can call this bet or you can raise in which case assume Villain will call.

Thus the preflop pot can be 2 SB or 4 SB at your option. The preflop raise carries zero EV.

Now consider the postflop play. A gutshot should be folded on the flop irrespective of whether the pot is 2 SB or 4 SB. Hero will play the hand exactly the same postflop regardless of what he did preflop. For his own reasons Villain will also play the hand exactly the same postflop.

Since the postflop action will be identical in every respect, it follows that the preflop action cannot change the winner of the pot nor the amount of postflop bets won by the winner. We also noted above that the preflop raise has zero EV.

So why do you think it is more profitable not to raise preflop? If the bigger Sklansky mistake means you make more money, then where is the extra money coming from? It's not preflop and it's not postflop either.

There is a way out of this apparent paradox. The Fundamental Theorem is not wrong.

[waffle]

hi stellar,

does it have to do with the idea that all of the PF equity is not realized because the chaser does not get to see all 5 cards?

edit: or is it something to do with not knowing if we'll flop tptk or the gutshot when we raise pf?

or does it have to do with a donation of .5 bb that i make when the gutshot hits post?

this paradox is really confusing me and it disturbs me how uncomfortable i am thinking out this bit of theory. [img]/images/graemlins/crazy.gif[/img]

[Guruman]

It looks like I misunderstood your premise a little there Stellar. I'll take another whack.

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Suppose Villain bets preflop. You can call this bet or you can raise in which case assume Villain will call.

Thus the preflop pot can be 2 SB or 4 SB at your option. The preflop raise carries zero EV.

Now consider the postflop play. A gutshot should be folded on the flop irrespective of whether the pot is 2 SB or 4 SB. Hero will play the hand exactly the same postflop regardless of what he did preflop. For his own reasons Villain will also play the hand exactly the same postflop.

Since the postflop action will be identical in every respect, it follows that the preflop action cannot change the winner of the pot nor the amount of postflop bets won by the winner. We also noted above that the preflop raise has zero EV.

So why do you think it is more profitable not to raise preflop? If the bigger Sklansky mistake means you make more money, then where is the extra money coming from? It's not preflop and it's not postflop either.

There is a way out of this apparent paradox. The Fundamental Theorem is not wrong.

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I think that there is no edge one way or the other when both players consider the odds. regardless of the size of the pot, the one who flops top kicker will automatically take down the pot uncontested.

With the gambler, the edge has to come from position, but only because this hand will be won on the turn every time.

I think a critical question is, what will top pair do on the turn those times that the gutshot connects?

will he recognize the straight board and opt to check/fold?
will he bet if he is checked to?
will a made gutshot lead every turn?
if a made gutshot checkraises, will the top pair pay him off?

I can’t figure this one without accounting for the turn here.

[Guruman]

--also, I made an assumption on the position of the button and the blind structure. Having the BB become the dealer seems like it would be significant.

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There is a way out of this apparent paradox. The Fundamental Theorem is not wrong.

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I don't see much of a paradox in this example. It's fairly simple:

The only place we make money is from his flop call when he's the one with the gutshot. But, we don't make ALL of his flop call, because sometimes he will complete his gutshot allowing him a discount on his loss. The smaller the pot is at that point, the smaller the discount he gets. When he makes less the times he hits, we make more.