Hi Matt,

I found this article very interesting and wanted to start a thread in this forum rather than reply in the thread about your book. I'll post a link there as well, but I just think it's a shame the only activity this forum sees is complainspam.

I like your concept of "robust equity" that seems to appear in your book as well. Is this an original term or was it in use before? Also, how does it differ from implied odds?

Hi,

I've heard the term robust equity used before, but don't think I've ever seen it defined anywhere.

It's related to pot odds but quite a bit different. Robust equity basically just means it's equity that remains even as the opponent's range gets stronger. So, my gutshot might have 20% equity even if my opponent's range is weak (lots of high cards and single pairs) or has become very strong after a lot of betting (so it's now lots of two pairs and overpairs).

Pot odds more of just focuses how much you expect to win, which will also depend heavily on each player's range, streets left remaining, and stack depth. I would say hands with very robust equity usually have more implied odds than their equity alone would indicate, but it again depends a lot on the variables I just listed.

Where to find this?

http://www.twoplustwo.com/magazine/i...ker-ranges.php

Ok, thanks for that explanation, much clearer now. My question was more about implied odds (meaning future pot odds), but I can see how robust equity gives hands better implied odds. In other words, hands with 37% equity that is robust have much more value than other hands with 37% equity.

I'm still wondering about your argument for denying your opponent the chance to realize his equity. Clearly it's an important concept, but in the examples you give you imply that Villain folding to a 3-bet preflop with 37% equity is more valuable to Hero than a flop raise forcing a fold by hands with 16% equity. Setting aside implied odds for the moment, and assuming opening sizes of 3bb and c-bet sizes of 5bb (which would be 2/3 pot in example 2), Hero actually gets more value out of the flop raise.

In the first example, Hero wins a 6bb pot in which Villain had 37% equity, netting Hero 2.2bb. In the second example hand, Hero wins a pot of 17.5bb in which Villain had 16% equity, netting him 2.8bb. Of course, implied odds can add or subtract value from Hero's line, but hands like a gutshot or BD nut flush draw seem to me to have more robust equity than a preflop hand like 76o (which gets a lot of its equity vs AQo by making one pair and holding on for dear life).

you feature great articles

Sorry it took me a while to respond to this, I was away for about 2 weeks and forgot about this thread.

I'm unfortunately a bit confused by this post. Is your main point that denying equity matters more when the pot is bigger? If that's the case then I of course agree, but often times your "bluff" will have less equity when the pot is bigger and your bluff will be more expensive as well. If that's not your point then you'll have to clarify what you mean.

That's ok, was just intrigued by your article and wanted to try to wrap my brain around the concepts. My point was in fact that it seems denying equity matters more when the pot is bigger, but also good point by you that the risk associated with that bet is usually bigger in a bigger pot.

I have a different concern with the article. I'm wondering about your explanation for your weaker range. You say that by getting rid of dominating hands, certain cards like Q2s become relatively better, but I'm not sure that's enough to mitigate the effect of bringing more knives to gunfights. I mean, think about this:

T9s has 41.2% equity vs top 35% of hands (propokertools). It has 45.45% equity vs. top 53% of hands.

Q2s has 37.2% equity vs top 35% of hands and 41.6% vs top 52%.

The equity delta is about the same 3betting vs calling the Q2s as the T9s, but it has lower equity overall.

However, the average pot size in a 3bet pot is going to go up, and the overall equity matters. Say the average pot size for a 3bet pot is 2.5x as big as the average pot size for a standard pot (I'm sure you could empirically answer this one.) Now by 3betting with Q2s instead of T9s you're playing pots that are 2.5x as big with a hand that has 4% less equity....

Call with T9s -> .45 equity x 1 = .45
3bet with Q2s -> .37 equity x 2.5 = .925

weighted equity = 1.375/3.5 = 39.3%

Call with Q2s -> .41 equity x 1 pot size = .41
Raise with T9s -> .41 equity x 2.5 pot size = 1.025

weighted equity = 1.435/3.5 = 41%

What is an equity delta?

I'm of course not just concerned about maximizing my equity in a 3-bet pot. If I was I'd 3-bet a more linear range. I care a lot about keeping dominated hands in my opponent's range and making hands that dominate me fold (3-betting Q2s is much better at this than 3-betting T9s).

I'm not sure Q2s is a 3-bet and T9s isn't either, FWIW, and probably wouldn't trust someone who says they are certain.

Also, I'm pretty ok with bringing "knives to a gun fight" in general. I used to not be, but after spending years doing math/pot-odds/etc it seems like it's unavoidable and the most +EV to play hands a lot. I'm constantly unhappy when I'm calling bets or when I'm bluffing, but still think it's the most +EV line.

Don't you think 3-betting T9s gives us knives in a gun fight frequently as well?

For "equity delta" I was looking at the difference in EV between a hand vs opponent's range in a 3-bet pot and vs opponent's entire opening range. 54s has pretty close to the same EV, for instance, and thus has a lower delta.

Do you think domination plays out in a fashion that's not accounted for by hot-and-cold equity?

Yeah, but it's a bigger knife. Clearly has more equity.

I'm spoiled by your books. I want to see some diagrams of postflop play here to convince me that pushing out hypothetical dominating hands is more important than hot and cold equity.

Just in terms of ranges, let's say opponent folds Q9-Q8, Q5s-Q2s to the 3bet and overall goes from 53% open to 35% play on vs 3bet. By my rough count Qx used to be about .15 of his range, and now it's about .14 of his range, and that's ignoring card removal effects from the queen in your hand, which cuts his chances of holding a queen by 1/4. So like .11 of his range down to .105 or so. And even then you're only getting dominated when you are both holding a queen and see a third queen flop, which is even less likely. It all nets out to a really small reduction in the chance of domination, unless you expect your opponent to be mucking things like QTo and Q6s-Q7s, in which case it'll be measurable but still seemingly super minor.

That's realistically unlikely to happen as that seems like a lot of work for not a pretty small pay out. I think I could literally spend all day on this and still wouldn't be convinced QXs is a clear 3-bet or T9s is or is not.

I also just think T9s is a lot more +EV in a single raised pot than Q2s is in a single raised pot. That's the main reason why T9s is called. I of course agree post-flop I'd much rather have T9s in a 3-bet pot than Q2s too, I just think it's a lot better in a single raised pot (and if we call the single raised pot happens 100% of the time, whereas playing in a 3-bet pot may only occur 45% or so of the time).

FWIW, I just checked pokersnowie out of curiosity, and Snowie is using a mixed strat of 3-betting and calling with nearly all weak KXs/QXs/JXs in this spot. It is 3-betting T9s 100% of the time though, so that may be correct ot 3-bet as well. But I also think Snowie 4-bets at too low of a frequency and I think against players who 4-bet more aggressively T9s makes a better call (because if we 3-bet it we'll have to call the 4-bet).

Well, if your Q2s sees a flop in a 3bet pot 45% of the time, but the pots where you do see a flop are 3x as big (go from a starting pot size of 6 to 18, say), I don't think that's a net gain. You're putting your weak equity at risk more often. 3 x .45 > 1 x 100

Going back to the main point, the main thing you're passing up with the Q2s is the value from your kicker pairing. The chance of (you and opponent both pair your kickers) + chance of (you pair your kicker and your opponent has an unimproved pocket pair) is significantly higher than the chance of (you pair your top card and your opponent also makes that pair). Granted, the pots are bigger when you both hit top pair, but as you describe your strategy you're already in loss-minimization mode when you pair the queen, so I don't think it'll make up for it.

Anyway, quibbles aside, it's great to see you writing for the 2+2 magazine, and engaging with us in the peanut gallery. I hope to see more.

Yes. But if this were always the biggest concern, every raising range would be linear. There are times when using a non-linear range is justified and I think this is one.

Glad to see you're happy I'm writing and I enjoyed the discussion.

Hello,

where can i find the article from july 2014 because I can't find this on the two plus two site anymore.

You'll have to contact the author, Matthew Janda, to get a copy. I've already e-mailed him to inform him of this thread request.

Thank you, I'll try to send him a message.

Yikes. I had parts 1 and 2 bookmarked, but of course when I just looked for them the bookmark goes to current issue. Ooops.

PM Matthew Janda and give him your e-mail address.

He'll definitely send you Part 1.

Part 2 is here.

hi

where could I find part 1 of this amazing article?

thanks in advance

where can I access the 1st part of the article?

http://www.twoplustwo.com/magazine/i...ker-ranges.php
seems not to be online anymore

Thanks

Matt, your book is amazing. I am very interested to also have a look at the three (I think) articles you wrote on SB vs. BB ranges for the 2+2 magazine. I actually joined the forum specifically to PM you to ask for these, since none of them are still posted online. Unfortunately, there is some unknown post threshold I have to reach before the PM feature is activated...

Yes I would like to get my hand on this article as well. Coudlnt find it tho.
Some help would be appreciated