You're visualizing it as being a binary thing when it isn't.

Imagine you open with TT on the button and the big blind calls and the flop is QJ7

You can bet TT here and you'll deny some equity, but how much exactly are you denying? Some, but not much. You'll still make some ace and king high hands fold and maybe a gutshot like the 98 But you won't be denying much equity here because those hands don't have much equity against you anyways. Likewise, you'll make the pot bigger in case you win by betting here, but how effective is that going to be? You mostly just make your opponent fold weak hands that have very little chance of outdrawing you and if you bet your opponents range of the turn will consist of a higher % of hands that beat you.

Now imagine you open on the button with the T9 and the big blind calls. The flop is once again the QJ7

Now how relevant is making the opponent fold? Hugely relevant, right? Any ace high or king high hand has a tonnnnnnnnnnnn of equity against you and most without a pair are going to muck against your bet. How relevant is making the pot bigger here in case you win? Huggggggggggggggeeeeeeeeelllllllyyyyyyy relevant because you're drawing to the nuts, right? So here both reasons to bet are very clearly and very well satisfied so checking on the flop is likely a mistake.

Yes things can get more complicated than this but at the end of the day this is why you are betting or raising. The better you are the more precise you'll be with betting frequencies and bet sizings, but it's not usually that difficult to tell "Is this hand a reasonable bet here?" once you understand what reasons justify a bet to begin with.

Hope that helps

Good example and it got me thinking that denying equity might have a broader meaning to include inducing your opponent to make calling mistakes ? For example hero betting JJ on a T85 flop will deny Kx and Qx hands their equity when folded but will also induce a mistake when called. Should a Q or K come on the turn hero needs to slow down and not reward villain for making a bad call. Agreed or is this delving off topic ?

I think Matt's given a great example in #1426, but to add to it, using the QJ7 flop he used...

The most obvious value bets would be the top of your range (QQ, JJ, 77, QJ, J7s, AA etc), since these hands get called by tons of worse hands. You want to build a big pot when you have a big hand. You're not too worried about villain folding A9 or 65s or 44, because those hands require runner-runners and aren't going to play the big pot your hand warrants unless you let them hit the backdoors for free. You're focused on getting value from villain's continuance range. Most of your EV with this group of hands comes from villain's calls, not his folds.
The most obvious bluffs would be AT, KT, K9, T9, T8 (straight draws, basically, that are unlikely to win at showdown if every street is checked down). These hands gain a lot of their EV from villain folding hands that are either already ahead or have good equity against you (A9, K5s, 44, 66 etc). They also have robust equity against villain's calling range (they have 4-8 outs vs top pair, plus backdoors, an overcard etc), so are in good shape even when villain continues. An additional point is that the best bluffs often contain a blocker to villain's calling range, which means the bluff is slightly more likely to work. (KT has a blocker to KQ, for example).
The hands that benefit most from 'protection' would be the weaker made hands like T7s, 97s, 87s, 76s, 33, 22. (Some of these hands can also be considered semi-bluffs, since 87s would have 5 immediate outs to two pairs/trips). Bottom pairs are vulnerable to overcards, but are also vulnerable to bluffs on later streets. If you checked back 33 on QJ7, then not only do hands like A9 have 6 outs against you, they could also make a bluff on the turn, forcing you to fold the best hand, as you'd generally have 4th pair at that point. If your EV is maximised by protecting your equity (or preventing villain from realizing his) by betting your weak hand on the flop, you should bet it.

When you build a betting range containing "obvious" value-bets, obvious bluffs, and obvious protection bets, you'll be left with some combos that don't clearly belong in any group. Some of these hands might benefit from protection, or have a bluffing component, but if you have more obvious combos to pick from first, then you can often just check back with the weaker stuff. (I call these hands "give ups", but sometimes they improve on the turn for free or are good candidates for delayed c-bets on some runouts).
Other combos will be hands that clearly don't make sense as bets for value, bluff or protection. These become "obvious" checkbacks. Middling pairs like Q8s, AJ, KJ, JT, TT-88 fit in this group. They have showdown value, and can call at least one street once the flop checks through. Since they don't need much protection from hands they are already beating (they often only need to fade 2 or 3 outs), can't get called by a lot of worse hands, and they won't make better hands fold (by "bluffing"), they should usually be checked, and then often used as bluff-catchers if they don't improve on the turn.

Arty

Thx, appreciate it

LB

Hi Matt,

I'm making my way through your preflop chapter. I am partly an online player, and being able to see the frequencies of my opponents with a hud made me think about pre flop range construction.

Do you suggest constructing preflop ranges based on your Villains calling freq, 3bet freq, and position?

Or is it better to have a static ranges preflop for every position and every villain?

Is the worth the time to create these ranges based on Villian types even though they gain equity when they see a flop?

This is probably the most important poker thing theory-wise I've learned in years.

A term used a lot in the book is "to realize equity". Does this refer just to pot equity, to pot + fold equity, or something else? Every time I pass it I am left a bit uncertain.

Thanks very much in advance!!

What is WCGRider's coaching site? I couldn't find anything online


re: the pokersnowie ranges

One thing that I find really odd is there isn't much in there for 4bet bluffs.

For example, when we raise on button and get 3bet by SB, it says:
A4s - AQs is simply a call, A3s is 4bet 8% of the time, & A2s is a 4bet 32% of the time. Similarly, K7s-KQs are a call while K3s-K5s is a fold and K2s is 4bet 63% of the time. The only other hands that are 4bets in this spot over 10% are A5o and A4o (20% & 21% respectively). This can't be correct can it? This range will have us 4bet bluffing far too infrequently when in a Btn vs SB situation...

Its upswing poker. Not sure about pokersbowie ranges, but seems very hard to have a frequency of 63%

Hi. I apologize if this question has already been asked but there's over 1000 posts on here which I can't read. I was wondering if this book took a "this is how to work it out for yourself" approach, or a "here, do this" approach, or maybe somewhere in between.

Reason I ask is I'm only just thinking about poker from a game theory perspective. One thing I've learnt so far is (correct me if I'm wrong) your unexloitable strategy you work out heavily depends on how the game is being played (eg common 3 bet percentages from the small blind), hence my first two concerns are what happens when the games start changing and this book is 3 years old and took 2 years to write so a "here, do this" approach would be out of date. Now, I am aware that if the book gave a perfect nash equilibrium solution to poker then this wouldn't matter, but it obviously doesn't.

So if anyone could let me know which approach this book takes that'd be awesome. Or maybe I have no idea what I'm talking about which is certainly possible

Page.47:
2nd part of the equation: "-9.325 = (0.45)(201.5) - 100"

Why is it "-100" and not "-96.5"?

Can someone explain it to me pls.

This book is more math heavy than most and is more of "here is a big book of solutions". It's not as math heavy as Mathematics of Poker but still not a great book for beginners to dive into. I'd suggest starting off with Poker's 1% by Ed Miller, which is more of a "how to work it out yourself".

I thought it was a "this is how you work it out approach" This book made me start thinking about poker a completely different way. It is by far my favorite book. I also like poker's 1%, both these books read well together. For me The Mathematics of Poker by Bill Chen is a good starter book. I am a math major, so take my advice accordingly.

"Induce a mistake when called" just falls into the "betting make the pot bigger in case we win" category for me. So sure, if you play against opponents who don't fold as much as they should you aren't denying as much equity as you'd like, but you're coming out way ahead in making the pot bigger in case you win (and you'll win a lot, since they're calling with bad hands that should be folded).

I think I'm pretty good at taking the correct line on a given street, but I'm not good enough to know what I'm doing on every possible turn and/or river when I'm playing the flop. Sure, I need to have some idea of how to throw down on different board run outs or else I can't play the current street well, but I'm not fretting about future streets right now if I know the right line. So if I had JJ on a T85 flop as per your example, I'd just make the right play right now (which is probably to bet decently-ish big, but it depends on more factors than just the exact board) and then if I get called and the turn comes a T/Q/K/A or something tricky I'll just deal with it when I get there.

Agree with this guy, thanks for taking the time Arty.

It basically just means "how effectively can you actually get this hand to showdown when you want to?"

A mistake people make is they think "Oh wow, I have 35% equity against my opponents betting range, so on average I'll win 35% of what's in the pot when I call!" when this isn't close to how poker works. In other words, you cannot convert equity into EV. In fact, it's even possible to have 60% equity against the opponents betting range on the flop and it still be correct to fold just because of how equity is distributed** (i.e. villains range is very polarized and your range is just filled with bluff catchers).

Another way to look at it might be like this. "Hey, I have a pretty crappy hand right now, it only has 20% equity. But overall, my range is pretty damn strong, so it's unlikely my opponent will be able to make big bets or raises against me, so I'll probably actually be able to see turn and river cards with my hand and get to showdown if I really want to. In contrast, if my range was very weak, my opponent would bet and raise a lot and I probably wouldn't get to see many turn or river cards with my crappy hand, or in other words I wouldn't get to realize my equity."






**I used to be more into nerdy stuff like this and I do think it's helpful when you're really trying to understand how things work, but now I'm more of just in the camp where I'm always reminding myself:

1) Bet and raise to deny equity
2) Bet and raise to make the pot bigger in case you win

And more or less just going from there. The tricky theory stuff is more or less just in the background for me when thinking about a hand unless it's a particularly tricky spot.

Snowie is not an answer key and is just making it's best guess.

If it gives you a mixed strategy, it just means it thinks the EV of both lines is the same. So with A2s, you can call or 4-bet and Snowie thinks it's all good in the hood as the EV is the same.

Unless you are playing pretty high, I really don't think you need to worry about balancing your mixed strats. If both calling and 4-betting have the same EV, then as long as you take one of the two correct lines you should be good to go.

Don't have the book in front of me, but if it's -100 it probably just means that's how much money you can overall lose with the hand.

Sometimes calculations are easier to show by saying "How much money can I win or lose from this point on, treating all money previously invested as dead money?" and other times they're easier to show by showing "How much money can I win or lose overall for the hand by taking these different actions?"

On a side note, I'll be the first person to admit when I started writing Applications I wasn't a particularly good writer (Mason and the rest of TwoPlusTwo did a great job with it), but honestly a lot of the stuff in the book is an absolute pain in the ass to write. The best and clearest way to write something often isn't technically correct, so you end up having to write something in the technically correct way which will realistically just be less clear and more confusing to 95% of readers who wouldn't have even noticed the technicality to begin with. So I apologize for this ahead of time and I wouldn't let it bother you if something seems slightly off or confusing, the general ideas behind the book (defend your checks well and don't recklessly CB, be willing to use multiple bet sizes and overbet when villain's range is capped, bluff a lot more on the flop than the river when you have a polarized range, etc) are much much more important. Get that stuff down then just keep building on it.

^^^^^
This is interesting. I'm a live player and when I first approached your book I had a difficult time seeing the big picture.

I later bought Miller's 1% book and after working through that found Applications much more approachable. Miller of course recommends your work in his book.

I think perhaps this speaks to your point about balancing technical perfection and ease of understanding. To his credit Miller (at the risk of over simplifying) is pretty good at making complex idea understandable.

Big thumbs up to you Matt for your continued follow up itt. For every one poasting I'd bet there are many more like me who read your valuable responses to questions.

I assume equity refers to winning the hand. You don’t get to showdown if either you or your opponent(s) fold. Only a bad fold by you – folding a hand you would have won -- reduces your equity (For the particular game situation, you don’t win as often as the theoretical showdown equity says.) Folds by villain will not reduce equity but could negatively affect potential EV.

Does this make sense to you?.

When villain folds, you don’t get to showdown but your equity value is not negatively affected (if will increase with a "bad" fold), but by your statement, you are not realizing your equity.


Am I being too nerdy?

I'm just starting the book, searched the thread and couldn't find an answer. Page 71 gives an example where "the button should defend 27.5 percent of his opening range by calling against the big blind’s 3-bet. This comes out to be 12.4 percent of all hands the button is dealt preflop." However the preflop chart has the BTN total defending range as 21.4 percent of all hands. Why the big difference?

I'm currently halfway through a degree in mathematics, so complicated maths isn't an issue, in fact I'd probably prefer it. I'm not a beginner to poker either, I've been playing sometime, but I'm just trying to improve my game and take it to the next level. Perhaps a better question would be, do I have to worry about the book being outdated? Or can I apply what I learn from this book to different games that play very differently?

Yeah, I just bought the mathematics of poker. Hopefully it helps my game. Do I need to worry about "Applications of No-Limit Hold 'em" book being outdated though?

+1 to all of this. I think Miller's book complements yours nicely, and thanks for taking the time to answer questions itt!

Matt,

A question came up over in LLSNL in this thread

http://forumserver.twoplustwo.com/17...-pots-1628317/

Basically the question is: do theoretical bluff to value ratios still apply in multiway pots?

Your section on multiway pots doesn't specifically address this although it discusses the shared defending burden.

It would seem the tree between flop and river would have too many branches to effectively work backwards flop to river.

And on the river itself if we are still multiway on most boards we should be facing strong ranges rather than bluff catchers.

So in multiway pots is a balanced bluff to value ratio something that can be calculated?

Hi Mathew,

What things do you think PokerSnowie is good for?

What Snowie features do you pay little attention to?