This is intended to be a discussion thread for the book "Further Limit Holdem" by Phil Newall:

http://www.amazon.com/Further-Limit-.../dp/1880685531

published by 2+2. This is an excellent book for those looking to expand their understanding of limit holdem through rigorous theoretical analysis and examination of the play of bots.

Phil has generously agreed to answer questions about the material. Let me start with one from early in the book.

Pg. 48: This is from the discussion of the [0,100] game with betting capped at 1 raise. You say "when facing aggression your odds of folding should equal your opponent's pot odds of winning the pot". So in a 1BB pot, when player 1 bets, and player 2 raises, player 2's odds when bluff-raising are 1-1 so player 1 needs to fold 50%.

Player 1's strategy according to the table on pg 49 is to bet-fold as a bluff 5.9%, bet-fold for value 2.9% and bet-call 8.9%. Why are bluff bet-folds included in the 50% we need to fold? These hands can't beat player 2's bluff raising range anyway since they are from right at the bottom of our range, so player 2 is really only "targeting" our value range with his bluff raise. So folding 50% of that should be our strategy, correct?

The trouble with folding 50% of the value range is that is gives villain an instant profit on his bluff-raises since you fold 3/4 of the time and he is getting even odds.

Your point about villain's bluff-raises being better than your bluffs is true. But villain can't call instead of bluff-raising since that leads to him losing against your value-bet range (his calling range is already set so that his weakest calls break-even). So his only strategy with those hands is to re-bluff you off your bluff.

I'm interested in page 54, specifically the check folding frequencies of the out of position player. After the out of position player checks, these are the frequencies in question:

1BB pot:

54.9% check fold: a 9.8% increase from bet/pot

3BB pot:

30.5% check fold: a 25% increase from bet/pot

6BB pot:

18.3% check fold: a 28% increase from bet/pot

It seems to me that the smaller the pot, or the smaller the pot in relation to the bet, the closer the out of position player will be to a check folding frequency of bet/pot, while the larger the pot is, the more the out of position player may fold due to the asymmetry of ranges.

I plotted these % increases onto a rough graph, which showed a curve that approaches bet/pot as the potsize decreases, and climbs farther and farther from bet/pot as the potsize increases. The curve seemed to top out as it approached the 30% increase marker, though I'm very unsure of the exact upper limits of the % increase.

I started a thread in the theory forum titled "folding frequency" in the hopes of getting some discussion of asymmetrical ranges and the effect on folding frequency, but it was kind of a mess as I probably tried to fit too much into the original post. Perhaps someone can quantify the effect that pot size and bet size have on folding frequencies for the out of position player, but I'll be damned if I can do it. As of now, I'm simply aware of this effect, which according to the % increases seen on page 54, will affect limit games more than no limit games.

Hi Bob, was just wondering if you could clarify your question a bit? Both players have symmetric distributions in these situations, so the only variable that changes is the pot size. In general as the pot size gets bigger there is a shift towards more bets over checks, more calls over folds, and a higher proportion of hands that are bet being for value (the bluffing ratio goes down as the pot size gets bigger, but the number of hands that bluff might go either up or down as the pot size increases due to these two effects work in opposite directions).

Isn't the situation asymmetrical as soon as the out of position player checks because, if the ranges were symmetrical after the out of position player checks, then the out of position player would be missing value? As the potsize increases, so does the out of position players betting range widen, thus his checking range is weakened as the pot size increases, creating a more asymmetrical situation than in a smaller pot, thus allowing the out of position player to check and fold at a frequency higher than that would make the in position player indifferent to bluffing.

I was mostly just stating theory as fact, something which I love to do. I was hoping you could disprove my final statement in my first post: This effect is greater in limit games than in no limit games because of the relationship between pot size and bet size.

Also, would it follow that since the out of position player builds his strategy around check raising the top of his range for value because it's a two bet capped game, that in a three bet capped game the out of position player would build his strategy around bet 3 betting the top of his range?

Ahh ok, sorry I did not realise that you were talking about the relationship between Player 1's checking range and Player 2's entire range. I wouldn't know enough to confirm your statement about the differences between FL/NL games. A lot of the results from this model games can be dependent on the restrictions involved (e.g. number of bets, also the big difference between one-street and multi-street games) and may not hold in the real game of poker.

I think you're right about the bet-three-betting the top of Player 1's range in a 3-bet max game. So in a four-bet game you might c/r 4-bet the very top of your range. One thing though is that these compound action reasons become very small very quickly (e.g. there are few hands Player 2 would 3-bet for value to Player 1's check-raise, so there are very few hands that Player 1 could take this value line with).

Regarding: checking the flop behind

I couldn't find the passage, but I think I recall you writing something along the lines of, "An effective flop checking strategy may allow for a wider preflop raising range."

I think this is true, as I came to the same conclusion last winter after discussions in this thread:

http://forumserver.twoplustwo.com/35...posts-1299310/

which may be a bit tl;dr, but the argument of one poster who suggested tightening up your preflop range if you're going to cbet 100% led me on graph trip, which I made into a post in the theory forum:

http://forumserver.twoplustwo.com/15...-cbet-1357289/

Sorry for seemingly pimping my conversations into this thread, but I'm interested in the topic of playing a wider range for a higher profit thanks in part to the added ev of these hands.

My hypothesis is that we can add both showdownable hands and drawing hands while trying to maximize equity and playability of these preflop semibluffs.

Yeah I think the idea of having a checking back strategy allowing you to raise more hands preflop is sound. Or, perhaps more accurate would be that tightening up so that you can c-bet 100% is wrong.

Yes, raising fewer hands preflop will increase your average flop equity (assuming the blind doesn't change preflop range in response to you tightening), but that average flop equity will still be distributed in a way that is known to both players. Having a tighter range will not necessarily increase your equity on the flops that should be checked behind the most (assuming the blind doesn't donk), because a tight range won't connect with low and connected flops very often.

I've thought about this and have concluded that these diminishing returns will result in bet 3 betting the top of our range in 3+ bet cap games, and that planning to check raise 4 bet would be an exploitive adjustment against a player who both cbets too much and 3 bets our check raise too much.

Hi, do you recomend this book to someone who wants to learn LHE almost from 0? (if not what?) Since I study mathematics and already did a course in GT I think Im gonna get what's in this book.

I've been mostly a NLHE player so i may have some biases about hand ranges, implied odds and other situations that cant get most of LHE advice without a decent proof

I was reminded of something from Further Limit Holdem while posting the other day. It sounded something like: "If you check and fold a hand that you value bet on the previous street, then that means your value bet on the previous street was in effect a bluff."

I agree with the general statement, but couldn't it be that sometimes the value bet wasn't a bluff, but a bet that had positive expectation which happened to catch a bad card on the next street?

First off, thanks for doing this Phil. This will be my first 2p2 post, as I haven't had much desire to make an account before now. I've gotten a lot out of your book, but am left with some questions.

On page 120 there is a chart with Rockhopper's hu 3 bet range. For fun and science I've used this some lately. A hand came up where I 3 bet Jh8h (hu),flop came Qs9h2s, I bet and villain called. Turn 5d. What happened in the hand is not important; but it got me thinking, what should we be trying to do here in structuring our turn bet bluff range? We have many potential bluffs/semibluffs that we could continue with here, depending on how many value bets we have.

1) Do we want to structure our bluffs in direct proportion to our value bet range, adjusting the number upward for the chance of hitting these draws (whether gutshot or open ended or whatever)? In this case it seems that would be a bit more than 1 bluff for every 5 value bets. Or are we able to actually bluff more than this given that we are not yet at the final round of betting?

2) If we have so many potential bluffs here that we have to pick and choose, do we need to start checking some hands like JTo that seem like an "obvious" hand to bet again on the turn? King high flush draws and most ace high fd's are already hands I'd be inclined to check rather than bet, but as we can check call hands like JT and Js3s and not so much with J8s w/o spades, might we want to change what is the norm for JT and maybe some other middling flush draws by putting them in our turn check range? The fact that we can safely fold our J8s and lower gutshots on the turn when raised, same for complete air hands like T6s w/o spades makes it seem like there may be some merit to rethinking what is optimal for our turn ranges in this and similar spots. It's not fun being raised in this spot with a draw when you have to call.

I'm obviously biased but think it could be helpful, I think having a GT underpinning can make it much easier to learn other games. FLH does go into a lot of detail on a few spots that are most relevant to HUHU play though, so my first book might be a better introduction.

Yeah I can't remember the quote exactly, but what you're saying makes sense and I obviously think it depends a lot on board texture. This would be fine to do on very dynamic boards, but on a static board there will be a very low probability of cards changing the equity shares between the players that much.

It's really hard to say what the right bluffing ratio would be here: your draws might well be quite strong, all else equal allowing you to bluff a bit more, but you are also out of position. Instead of focusing too much on the right GTO ratio I'd try and think more about possible exploitations of your opponent.

I'd say one of the biggest problems people get into here is not balancing their checking range enough. Most people are just too easily read after 3-betting pre, betting flop, and checking turn. The bots do tend to be extremely balanced here with almost all kinds of hands making it into the turn check range with some probability.

Constructing a very balanced turn c/r range, with some strong value, some good semi-bluffs, and also some weak draws, will help you in so many ways as it prevents your opponent from betting the turn too much and putting you in these awkward spots with weak draws. If a hand has just enough drawing potential to get to the river then try to avoid putting in too many bets with it!

Thanks for this. It makes a lot of sense.

Regarding checking back the flop heads up:

I tried to combine elements from the section you dedicated to this topic, hopefully without plagiarizing anything, with some ideas of my own in a thread in the micro forum:

http://forumserver.twoplustwo.com/35...ition-1420368/

I'd be happy if you just read it, but I'd be very happy to hear any comments or criticizm from you either here or there.

Have the limit holdem games gotten tougher to beat like no limit?

Bob I skimmed it and it looks good to me. Anything specific you wanted to discuss?

Much harder. In fact I went back to uni instead of continuing to play pro.

Thanks for checking it out. No pun intended.

A debate has been sparked over the selection of which hands to bluff on the flop and turn. I contend that we should construct our bluffing range on the flop and turn in a way that maximizes equity when called, as this will maximize our bluffing profits and the number of hands we can bluff without bluffing too much thanks to draw equity. It has been argued that we should bluff with the absolute bottom of our range on the flop and turn as if we were playing a static game where bluffs don't have the benefit of draw equity.

I gave this example:

Imagine, if you will, a hand that has 49% draw equity and zero showdown equity on the flop against an opponent who calls just the right amount, thus making your threshold bluffs indifferent to bluffing or checking. Would you rather bluff the hand with 49% draw equity or napkins? I choose the hand with 49% draw equity because it will show a profit where the napkins will be breakeven.

bob, seem to me the problem with this is when you check you will always fold or have 0 c/r range on the next street ( or raise if you are IP)?

it is probably good vs a calling station or a guy who calls a lot and his passif but now you are not playing unexploitably.

I've got a discussion on which hands to bluff vs. which hands to check starting on page 62. Do you mean the case with/without position or both? Being with position is the simpler case. I think the presence of draws really does complicate things in real poker. When I'm with position, however, I do prefer to bluff with the very bottom of my range. That's because these hands gain the least amount from a check, steal the most equity if opponent folds, and because there's little penalty from bet/folding them compared to slightly stronger hands.

Of course your example is also valid, and it does make a lot of sense to bet the strong draw since it's getting such a discount on the bluff from its equity. The reality of the situation in poker is that there will be lots of different bluffing/checking regions in the distribution, with various hands bluffing for different reasons.

The discussion pertains to in position bluffing, but I'm all for going on tangents. I'm always open to speculation.

If you're bluffing the absolute bottom of your range, then I think you're value heavy when you call a check raise because your bluffs can't stand a raise.

The last paragraph sounds good on the surface, but I think it boils down to the premise that, if the game is in an equilibrium state, then all hands across a range will be maximizing their expectation. I think that it's not impossible for a strong draw to have a higher ev by checking instead of bluffing, thanks to implied odds and equity realized for free, but I think this will be a rare exception and not the rule.

My check back range has bluffcatchers that can call down, so no, I'm not folding all the time.

If I check back the flop, then I should have a weaker range than the big blind. Agreed? If I have the weaker range, then it should follow that I'm rarely, or never raising on certain turn and river cards. Ever play against neo or Sartre? When they check back, they're rarely or never doing so as a slowplay, thus their ranges on the turn and river are weak and should rarely or never raise depending on the turn and river cards.

If the example is valid, then wouldn't it follow that we should pack our bluffing range with the strongest bluffing hands, as these will maximize the ev of the bluffing range as a whole? I think this happens in two ways:

1) since our bluffs have equity, they are more profitable than bluffs without equity.

2) by bluffing more frequently, we maximize profits across the entire bluffing range precisely because those bluffs are more numerous.

Yes this would maximise the equity of the bluffing range but at a cost to the equity of the checking range. Which effect dominates, therefore leading to the maximisation of overall EV, is something that seems hard to answer. I'm agnostic and think that both effects will see some representation in the full solution (until I see evidence otherwise).

This is fair. As long as one has reasons for doing what they do, I can't say it's wrong. However, I do think it's much more complicated than: I'm at the bottom of my range therefore I bluff on the flop or turn. This is overly simplistic; it ignores the most fundamentals of bluffing, those being that fold equity and draw equity combine to make a bluff profitable. By ignoring these fundamentals, we end up bluffing hands at the bottom of our range without the requisite profit which is the reason for bluffing.

This will only be true if the equity of the checking range is less than the equity of the draw. If my checking range has 35% equity, and I add a draw with 40% equity to my checking range, then the equity of that checking range will be increased, but at a cost to the bluffing range. If my checking range has 35% equity, and I add a draw with 20% equity to my checking range, then the equity of that range has been decreased, also at a cost to my bluffing range.

I think this points us in a direction:

In an effort to maximize the expectation of our strategy as a whole, we must maximize expectation with both our checking and betting ranges. If a draw can increase the expectation of our checking range more than it costs our bluffing range by removing said draw, then we must check that draw. It should be pointed out that the addition of a previously unused bluffing hand to our bluffing range will also increase the ev of that bluffing range, which must be accounted for in the calculation.