Nah **** that. I'm done cooperating. You're not a nice person and I mean that in the meanest way possible. I don't like you. Please ignore me in the future.

Nah. You were done before you started.

Your opinion of me is irrelevant, as are your instructions.

All I would need to see is a hand range where you go from 90% equity to 60% equity on the basis of card removal effects alone as you drop your Ax hand and turn it into a KK hand. Whether you take up the challenge or not makes no difference. I'm very doubtful that this would happen.

Still talking ****? Leave me alone.

Anyway, to finish the point about card removal effects:

When we step down from A2 to KK, we don't introduce any new hand types. We add extra Ax hands that beat us because of the ace we used to hold is now available to our opponent, and we take away some Kx hands because we now are sitting on kings that our opponent needs.

Let's see what happens in the most minimal of cases. Let's say that the opponent's hand range is exactly A7s and KK and that the board is AQ568. (Yes, it makes no sense at all for KK to be in the hand range. I'm doing this is create the maximal card removal effect. And yes, I changed the 5 to a 6. Why? It's again about maximizing the swings. Since the board is paired, we would be getting chops instead of losing, and that reduces the swing size.)

If we hold A2, there are exactly 2 A7s hands and exactly 6 KK hands. This is 75% equity. If we change our hand to KK, then there are 3 A7s hands and 1 KK hand. This is 12.5% equity (75% lose and 25% split). This is an equity drop of 62.5%. Without artificially restricting villain to exactly one suited ace, I believe this is the largest possible equity drop from card removal effects.

So how does increasing the number of hands in the range impact the equity swing? Let's look at a couple more examples with just a few more hands.

A7 vs KK
-- Hero: A2 -> A7 = 8 hands, KK = 6 hands --> 57% equity
-- Hero: KK -> A7 = 12 hands, KK = 1 hand --> 4% equity
====== 53% equity shift

A7s vs KQ
-- Hero: A2 -> A7s = 2 hands, KQ = 12 hands --> 86% equity
-- Hero: KK -> A7s = 3 hands, KQ = 6 hands --> 67% equity
====== 19% equity shift

A7 vs KQ/QJ
-- Hero: A2 -> A7 = 8 hands, KQ = 12 hands, QJ = 12 hands --> 75% equity
-- Hero: KK -> A7 = 12 hands, KQ = 6 hands, QJ = 12 hands --> 60% equity
====== 15% equity shift

A7s vs KQ/QJ
-- Hero: A2 -> A7s = 2 hands, KQ = 12 hands, QJ = 12 hands --> 92% equity
-- Hero: KK -> A7s = 3 hands, KQ = 6 hands, QJ = 12 hands --> 86% equity
====== 6% equity shift

Notice how just adding in a couple hands kills a lot of the equity shift. This is because the denominator grows quickly relative to the number of hands being added back in. In a full deck, removing a single ace reduces the number of available Ax hands by 28. This means that *AT MOST* you add back 28 hands that beat you when shifting from Ax to KK.

In the switch, you also take away some hands that you beat. The biggest proportional hit you could take from that is to go from 6 KK combos down to 1 KK combo. And that's what you see in the first two cases. Once you get past that, there's not much of a shift. You lose at most half of the Kx hands and there's no impact on hands that don't have a K in them. And in the realm of second-pair hands with a K-kicker, there's really only one combo that you're looking at. So you lose 5 or 6 hands from the "hands you beat" category.

Anything that looks like a more normal hand range will be shifting on the order of a few percent. The shift from A3 to A2 will probably be smaller than the shift from A2 to KK, but it's not anything close to the size that was suggested.

90% equity on the river basically means that for every hand that beats yours, there are 9 that you beat. To get 60% equity, there for every 2 hands that beat you, there are 3 that you beat.

It is helpful to have an intuitive sense of how that ratio looks because when you're sizing up ranges and making actual EV estimates, this is the type of thing that you will need to be able to do. And you build intuition by working through the details of specific cases. By doing that, you can start to get a true "feel" for the percentages and values involved.

Good to see Aaron W. hasn't changed.

Who knew that so many people are afflicted by such pain and resentment simply for being provably wrong?

I'm not mad because you proved me wrong. I openly admit that I overestimated. After playing with stove last night vs a likely calling range, I found KK had about 60% equity and A2o had about 80% equity. So I was off with my estimation.

However the reason I'm mad is because you were a dick about it.

Aaron, I'm sometimes wrong. Heck, I probably set a record for being wrong on this board.

But I also try not to be arrogant. I admit lots of mistakes. You, on the other hand, are quite arrogant and never admit lack of knowledge or error. And that's a particularly bad trait to have given your professed religious beliefs (hint, the founder of your religion probably would have found you as insufferable as a number of people here do).

Seriously, dial it back dude. It's a message board, a message board that attracts very smart hard-working people who put a lot of thought into this particular subject matter, and many of whom, honestly, have higher winrates than you do. And yet you seem to be fighting a constant battle for intellectual superiority that the rest of us are mature enough not to engage in.

Or, as they say in the South, you catch more flies with honey.

I would still like to see your ranges.

Then maybe you should take a step back and re-assess the flow of the conversation.

I believe you're wrong on more than just the equity estimates. But for the same reason you got defensive when I pushed you on it, you're defensive about the conversation in general. I have my share of pushing people around and such, but this one looks to be more you than me.

Good morning,

I'm not gonna argue about the definition of "being a dick" because the definition is hazy and subjective. I suppose it's not your fault if you don't realize, nor think, that you were being a dick. I took some time to cool off and I'm feeling much better about the situation.

I'm glad the heat has dissipated.

I would still be interested in seeing the hand ranges. I have not been able to produce anything that comes close to having a significant majority share of the equity with a weak ace and then dropping by close to 20% in equity when taking on KK on the basis of card removal.

Let's take the actual board (AQ558) and give hero A2. In this case, there are tons of chops. If we give villain AJ/AT/A9/A7/A6/A4/A3/A2 as all the ace combos, we have:

AJ/AT/A9/A7/A6/A4/A3/A2 = 25 hands that chop with us

If our initial equity was 90% and that there are x hands weaker than ours, we would have

[(50% * 25) + (100% * x)] /(25 + x) = 90%

After some algebra, you get x = 100. So this means that villain's hand range must consist of about 100 more hands that we beat. To shift the equity by 20%, we need to push through about 25 hands (20% of 125) in order to create the equity shift.

AJ/AT/A9/A7/A6/A4/A3/A2 = 32 hands that beat us

This only a net gain of 7 hands from the Ax hands. This still leaves another 18ish hands, and card removal effects from picking up two kings doesn't do that.

If we start with a more modest 70% equity, we get x = 34 for a total of 66 hands. We would now need to push through only about 13 hands. This is actually kind of close, sort of.

We still gain by the 7 hands from before, which only leaves us about 6 hands to remove. The KQ range drops from 12 hands when we hold Ax to 6 hands when we hold KK. And that would account for those 6 hands.

But in this case, the dominant effect is actually that A2 is chopping with so many hands that it normally loses to, not because card removal is dramatically sinking your equity.

If you make the board unpaired, you should see a significantly different story told by the equity numbers.

---

If you could be specific about what buttons of yours in particular I pushed, I can try to avoid them in the future. But lacking that, the odds are good I'm going to press them again.

Here are my assumptions:

Preflop: I took out the top ~20% because he didn't raise and gave him the other 80% of hands.

Flop: I had the small blind fold no pair no draw. I also had the small blind raise strong hands.

Turn: I had the small blind fold gutshots that didn't have a flush draw and raise any leftover strong hands.

River: I had the small blind check 100%. Then after I bet the river, I assumed that the small blind would fold his busted draws, and call any leftover pair, which left this calling range:

I'm not sure why Qd8d is in there as it's an impossible combo. It shouldn't change the results much though.

vs that range, As2c has 81.16% equity.

KK has 57.24% equity

----
I don't feel like going through the thread and picking out specifics that pissed me off. In a general sense, you're not teaching a class; nobody in this forum owes you anything; you're not in a position of authority.

This really isn't a card removal effect at all. I may be off slightly on my counting here because I'm not paying that close attention to the suits, but that's not the point. The rough numbers are good enough to make the point.

Board = AQ558

Hero holds A2:
-- Hands that beat hero: 15 hands
A8o = 6 hands
Q8o = 9 hands

-- Hands that chop with hero: 39 hands
A4s-A3s = 4 hands
A2s = 1 hand
A9o = 6 hands
A7o-A6o = 12 hands
A4o-A3o = 12 hands
A2o = 4 hands

-- Hands that hero beats: 80 hands
44-33 = 12 hands
22 = 3 hands
Q7s-Q6s = 6 hands
Q4s-Q3s = 6 hands
Q2s = 2 hands
Q9o = 9 hands
Q7o-Q6o = 18 hands
Q4o-Q3o = 18 hands
Q2o = 6 hands

------ Total hands = 134 hands

Hero's equity:
(15/134 * 0%) + (39/134 * 50%) + (81/134 * 100%)
= 0 + 14.6% + 60.4%
= 75.0%

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

Hero holds KK

-- Hands that beat hero: 81 hands
A8o = 9 hands
Q8o = 9 hands

A4s-A2s = 9 hands
A9o = 9 hands
A7o-A6o = 18 hands
A4o-A2o = 27 hands

-- Hands that hero beats: 81 hands
44-22 = 18 hands
Q7s-Q6s = 6 hands
Q4s-Q2s = 9 hands
Q9o = 9 hands
Q7o-Q6o = 18 hands
Q4o-Q2o = 24 hands

------ Total hands = 162 hands

Hero's equity:
(81/162 * 0%) + (81/162 * 100%)
= 0% + 50%
= 50.0%

--

So what you're seeing is (at least in my calculations, which again are probably off a little bit because they're manual calculations) is that you lose 15% of the equity due to losing all the chops and only 10% due to stepping down in the range.

Also, for a hand range of about 160 hands, a 10% shift is requires stepping through approximately 16 hands, which is pretty much just stepping through a couple hands, depending on suits and such.

So this really isn't about card removal effects, it's about losing all of that equity from chops.

I'm really not sure how to respond to this. That you perceive me as being in a position of authority is just a perception. If I think I'm right about something, I'm going to put forward my argument for it. If I think someone is wrong, I'm going to challenge the things I think are wrong. And then ideas will rise or fall based on their merit.

You ought to be doing the same. Without that, there's not actually an advancement of ideas.

That's the thing. I don't perceive you as being in a position of authority. Despite the fact that you're smarter than me, we are equal. If you don't want to believe the stuff I say about poker because of this or that, that's fine. However, when you say stuff like this:

This is just plain old **** talking and I don't appreciate it. Maybe this type of stuff gets respect from you peers, but not from me.

So you wanna **** on my contributions? I've shared information with you and the forum. To say that I'm uncooperative is just more **** talking. Typically, I don't respond well when people talk **** to me. You may brush it aside and claim that I'm being "defensive" which I fully admit that I am. However, dismissing peoples feelings and blaming someone for getting offended at things you say is just a tool used by those that don't want to take responsibility for things they say or do. Much like telling someone that is pissed off that they're "over reacting," blaming my defensiveness is just your problem with denying that you're a dick sometimes.
This is fine if you don't want to take the strategic implications of what I've said seriously. I can't fully describe what gto poker is. Nobody in the whole world can. However, if you dismiss what I've said about fret's post because of the entirely separate argument that we're having about card removal, that's being voluntarily ignorant. Surely, someone that values knowledge so much as I know you do shouldn't dismiss ideas. I'll say it again: Fret's range construction system is neither descriptive of gto poker, nor exploitive poker. Using the term "gto style" is just a cop out at best and seriously misguiding to the rest of the forum.

You're rewriting history. That came at the end *after* you declared that you had no interest in conversation and *after* you've already brought crap (crap = contention) to the table.

It's also true. It was hard to get any useful information out of you to begin with. Short one sentence answers that provide no insight is extremely uncooperative.

I recall a conversation in which the other person kept saying "my calculations give me XXX." But when pressed to explain those calculations, the response was "I'm not going to show my work." This interaction had a very similar feel.

At what point have I even denied this? And sometimes, people do overreact. Pretending like they don't doesn't help because it turns into an unaddressed cycle of behavior.

I gave opportunities to explain further. Your initial rejection of the post was literally one sentence long with no explanation:

Be honest with yourself. Do you think that this statement by itself should be read by someone and the response will be "Oh, yes! It's totally outdated!" I even offered you a chance to try to show where it's outdated and present a more modern argument. You didn't do that either.

There were no ideas to dismiss. Just an unsupported assertion. If you have ideas about modern GTO poker, you haven't really shared them.

You're free to characterize it however you want. But until there's substance, it's not useful. The characterization you're giving here is basically saying that nobody should ever even utter GTO except in the case of HU limit because nobody knows what it is. I find that unnecessarily limiting, and I expect that most people do as well.

We know that GTO poker will have certain types of characteristics based on deep analysis of model games. So implementing those things, especially with the idea of having balanced ranges and such, it moving towards that (even if we don't know exactly what "that" is). This type of analysis stands in contrast to basically everything that was done in the early 2000s and before.

The hand ranging analysis you presented (for example), is something that we were basically doing way back then. You have an extra computational tool to help you crank them out faster and with fewer errors (and more decision points), but this type of hand ranging business is really the old school stuff (not that it's bad) and not something that I would be surprised if anyone thought was a modern GTO-style analysis.

The shift from "my hand vs your range" to "my range vs your range" is one of the big steps forward in moving towards something that looks more GTO-ish.

Not at all. I think you should maybe think for yourself about why it's outdated. My disinterest in explaining myself had to do with non 2+2 stress that has nothing to do with poker. If you wanted to make me sorry for posting in this thread, then consider your mission accomplished.

My problem is that I don't think it is outdated. It's a system for helping to think through hand ranges and a non-trivial range vs. range exercise.

If "outdated" simply means "incomplete" then I'd agree with you 100%. But I don't immediately see that there's something "new" in the world of poker strategy that makes the information wrong.

And this is also the type of response that's completely uncooperative and unhelpful.

I'm sorry that things aren't going well for you right now.

That's fine with me. You can keep on clinging to the old view of indifference for as long as you like. Doesn't make it any less incorrect.
That's your opinion and you're entitled to it. However, it's not my fault that you can't figure it out without being taught. Nobody took me aside and spoon fed me the ins and outs of poker theory and I'm not about to do that for you. You'll have to investigate on your own to figure it out just like I did. That, or you can continue to be complacent with your current incorrect understanding of poker theory.

Nobody saying that it's 100% correct. I don't know where you're coming to that conclusion unless you're misreading something that someone wrote. Do you think that there's a belief that indifference on a street-by-street basis is the way to attain a GTO solution? There was *NEVER* such a belief. But if you're learning to build hand ranges, starting by thinking through something like this to get some intuition about hand ranges and equity is not a bad place to start.

So I maintain my initial criticism of your post: "I think you have not understood it." And until you present something that suggests otherwise, I will maintain that belief.

LOL -- I don't mind you talking like this to me, but if you choose that route then you really ought not to be whining as much.

If you think that the sharing of information comes down to the assertion of an opinion, you're welcome to that. I'll remain in my criticism that you've failed to present any useful information.

So now standing up for yourself = whining? You're really good at taking shots at people without crossing the line. Maybe that has served you well in your life. I don't know because I'm not in your shoes. Where I'm from it's a good way to make enemies.

Just as you're free to present an unsupported assertion as if it's a meaningful discussion, you're free to believe what you want about your behaviors.

If the way you've presented yourself in this thread what you think "standing up for yourself" means, then so be it.

what do you mean by "13 aces in the deck"?
so the only hand that villain limps preflop and calls down is A7o?
but in the next post you used A2s etc. Shift is a shift but if we have less than 50% equity it's not nice

But A2 beats Q8
------------------
Never seen Bob behaving like this... sad to see he's so angry

In the midst of two nice guys having some frustration, there has been some good poker discussion, imo.
Aaron is counting combos and I believe he means "there are 13 combos with an A" in the range. I haven't done the work to be sure. If you download equilab, you can enter ranges and it will show you combos. It will even do card removal (or not) based on board cards, just select via an option button. It is a really good way to look at hands.

LOL -- I literally have no clue what I'm saying there. I done screwed that up real good.

In that spot, I'm literally just making up hands to show that card removal effects don't do tons of work for you. Way back when, there was a lot of debate over card removal effects. The card removal people argued that if you had an ace with a weak kicker, that you didn't have to worry about being dominated because you're blocking the other Ax combinations. Others argued that this was overly optimistic.

I can't remember the exact details anymore, but someone did some sort of simulation of preflop holdings at a 10-handed table to determine the probability someone else had an ace preflop if you held an ace compared to the probability that someone else had an ace preflop when you didn't hold an ace, and it was basically at the level of noise.

After a while, the consensus moved towards saying that it's just not that big of a thing, which isn't to say that it's completely not a thing. It's just not a big thing in limit.

You see talk about holding blocker cards a lot more in NL and PLO (I think) because hand ranges tend to be narrower and more sharply defined. In limit games, you can draw to a weak flush and feel good about the value you're getting. In no limit, it can be quite expensive to draw to a weak flush because the bet sizes are so much larger and the pain is much worse when you lose to flush-over-flush. So holding the A of flush draw puts quite a severe restriction on the sorts of draws your opponent has and would be willing to draw to.

More clumsiness. Doing these things by hand is very error-prone. I actually don't have functioning software for this anymore.

Don't waste your time. It's definitely wrong.

I would actually like to see someone take on Fret's post if there's something specific that needs to be updated about it. Granting that it's known to be more of an exercise and approximation than a literal GTO strategy, the idea of trying to break out different groups of hands to create lines with balanced ranges (I think) is something that's in line with the general GTO thinking.