Two Plus Two Publishing LLC
Two Plus Two Publishing LLC

Go Back   Two Plus Two Poker Forums > >


Beginners Questions Poker beginner? Ask your (possibly) naive question here and our community will attempt to help you.

Thread Tools Display Modes
Old 08-30-2013, 12:24 PM   #1
TheDefiniteArticle's Avatar
Join Date: Feb 2012
Location: Bristol, UK
Posts: 14,085
The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Hi Two Plus Two,

Some of you might not know who I am, this post has taken so long to write. I originally aimed to have it out by the end of June, but writing longer pieces about poker is much harder than just quickly tapping out a response to a hand. In case you're unaware, I've been using the account 'TDA2' for the past few months (and accumulated around 2100 posts on that account too - would've been rather embarrassing if I'd reached PB on my gimmick first tbh).

A little bit of background:

I started playing poker, like most people really, in home games with mates. We played no limit hold'em without position, and played 100 antes deep without blinds. There was no preflop action. I liked it a lot, looked up strategy and started winning and enjoying it more. So, the long and short of it is that I started playing online around about when this account was created, being an aggrodonk at Party Poker 2NL full-ring. I haven't had a meteoric rise through the stakes by any means, but I'm currently playing 25NL Zoom and taking occasional (failed so far) shots at 50NL. Two Plus Two has improved my poker so much, both in terms of strategical knowledge and helping me find a stake (cheers Peter) that it would be rude, really, for me not to give back in some way, and I think this post reflects the extent to which Two Plus Two has helped me.

Before I begin, I'd like to link to a couple of incredibly useful posts that aren't linked quite as often as they should be, and also one which might not be as useful but already has minor nostalgic value for me:

Firstly, the legendary Pokey's Unbelievably Long Guide to Hand-Reading. Initially, this post was just an annotated version of that one (and it probably would've been out in about April if I'd taken that route). It has such influence and insight that anything I say here should be taken in the light of that, though I've tried to take a fundamentally different approach to the subject here.

Secondly, Bostik's COTW, Evaluating Board Texture. I haven't gone into incredibly detail here about how to actually decide whether a board is wet or dry in deference to the comprehensive nature of that post. Consider that part of your pre-reading for this post.

Finally, and this is just out of nostalgic value for myself, it's not a particularly incredible post compared to the canon of Two Plus Two, my own 1k post on flop play in 3bet pots at the nanostakes.

Anyway, to business. I hope you enjoy it and I'm happy to answer any/all questions. I also have a pdf version I can post if anyone wants to put this on an e-reader or something (also to remove minor formatting issues - I've had to put this through two converters so I didn't have to retype it).

1: General principles

Here, I outline some of the ideas behind hand reading. Most of the first section isn’t especially relevant to poker per se, and so it could beskipped if one is just looking for immediate improvement in their game, but I feel it important to understand why hand reading works as it doesrather than simply how it works if one wishes to develop skills beyond those which others can teach you (which are probably limited; though I won’thypothesize here as to quite how limited they are).

1.1: The absolute basics – what is a range?

Although most of you will already be very comfortably acquainted with the idea of a range, it is probably good to make this guide accessible to completebeginners, as well as reinforcing some basic concepts for the more experience among you, to start here. One of the most important steps in the developmentof a poker player is the switch from ‘putting you on AK’ to evaluating a range. A range is the group of hands which your opponent could feasibly hold atany point in the hand. Note the word ‘feasibly’ – just because a hand isn’t within their range doesn’t mean that they couldn’t hold it ever. Anotherwise-competent reg could have misread their hand, or be drunk. However, in making decisions, we should tend to discount the chance of this happeningfor two reasons. Firstly, it is impossible at any point to evaluate the chance of being the case. Secondly, although by discounting these hands we mightmake the odd FToP mistake that we wouldn’t otherwise make, if villain is the sort who does this sort of thing frequently enough that it becomes a genuineconcern, they’re going to be making sufficiently many mistakes vs our range that we’ll be rolling in the G-bucks.

I’d also like, at this stage, to distinguish between two ways to evaluate a range. Firstly, we can enumerate every hand within that range. This is mostoften practical towards the end of a hand, or in post-game analysis. However, in standard preflop and flop decisions, it’s simply not possible to considerevery hand that your opponents could hold, especially given that you’re likely to make large mistakes in your estimates. This leads to the second method ofrange evaluation – evaluating the general strength of a range. An example of the difference between the two follows.

6-max cash, 100bb effective stacks. A positionally aware 21/18 with no particular idiosyncrasies opens UTG.

Method 1:

Villain definitely opens AA-88, AJ+. He probably opens some but not all of the following hands: 77-22, AT, KQ, suited broadways, suited connectors, Axs. Heis unlikely to open anything which isn’t within that range.

Of course, this estimate could become refined with more details, like precisely how positionally aware he is, and any hands he’s gone to showdown withafter opening UTG, but it takes a long time for positional stats to converge, we’re unlikely to see many showdowns occur (villain is likely to go toshowdown about 4% of the time he is UTG, or about once every 150 hands overall) and it’s consequently difficult to put villains on precise ranges.

Method 2:

Villain is competent and he’s opened UTG, his range is pretty strong.

This clearly has the disadvantage of not giving us specific hands which he’s going to have in his range, but so long as one is well-acquainted with a coreUTG open range, well-placed notes will do the rest.

1.2: Deductive logic and its application to hand reading

Deductive logic is a process by which one can take certain statements and use them to reach conclusions which are necessarily true given the truth of thosestatements. I’m not going to go into too much depth here about the theory behind it (I’m sure there are many on the forum who could explain it much betterthan I), but the two main branches for our purposes are syllogisms and contrapositives.

1.2.1: The law of syllogism

The law of syllogism is in general the way in which solid arguments are made. In it, a set of premises are used to reach a conclusion using logically soundsteps. In its simplest form, it will in general appear like so:

Premise 1) If P, then Q

Premise 2) If Q, then R

Conclusion) If P, then R

A simple concrete example:

Premise 1) The television requires power to function.

Premise 2) The mains lead is the only way of getting power to the television.

Conclusion) Without the mains lead, the television wouldn’t function.

I should briefly note at this stage (although this is even less immediately relevant to poker) that when people are attempting to make persuasivearguments, they will often use a bastardised form of syllogism with hidden (or implied) premises like the following:

Premise 1) The television requires power to function.

Premise 2) The mains lead is the only way of getting power to the television.

Conclusion) The mains lead shouldn’t be removed from the television.

Hopefully the hidden premise here should be fairly obvious. The full version of the argument is as follows:

Premise 1) The television requires power to function.

Premise 2) The mains lead is the only way of getting power to the television.

Premise 3) It is desirable that the television should continue to function.

Conclusion) The mains lead shouldn’t be removed from the television.

Now, syllogisms can be a lot more complex than the above, often involving many premises and several intermediary conclusions, but given how abstract allthis seems with relation to poker, I feel I should move on fairly quickly. However, I would like to add one more thing to the abstract version. There arejust two ways of disproving a syllogism – one must either disprove one of the premises, or show that the logic is flawed (i.e. show that the conclusiondoesn’t follow from the premises).

So this is all well and good, but how does it apply to poker? Well, hand reading itself is essentially deductive logic. We take premises (I’ll discusswhere we get those from later on), and apply reasoning to deduce villain’s range of hands. Here’s a very simple example:

Premise 1) Mr Weak-Tight Nit never continuation bets the flop without at least top pair.

Premise 2) Mr Weak-Tight Nit has continuation bet the flop.

Conclusion) On the flop, Mr Weak-Tight Nit has at least top pair.

Here’s a multi-street example:

Premise 1) Mr Weak-Tight Nit only open-raises AJ+ and AA-88 UTG.

Premise 2) Mr Weak-Tight Nit has open raised UTG.

Conclusion 1) (derived from P1 and P2) Mr Weak-Tight Nit goes into the flop with a range of AJ+, AA-88.

Premise 3) Mr Weak-Tight Nit never continuation bets the flop without at least top pair.

Premise 4) Mr Weak-Tight Nit has continuation bet the flop.

Conclusion 2) (derived from P3 and P4) On the flop, Mr-Weak Tight Nit has at least top pair.

Premise 5) The flop is J74r.

Conclusion 3) (derived from C1, C2 and P5) Mr Weak-Tight Nit’s range for going into the turn is AJ, JJ+.

Premise 6) Mr Weak-Tight Nit always continuation bets the turn with top pair or better.

Premise 7) Mr Weak-Tight Nit has not continuation bet the turn.

Conclusion 4) (derived from P6 and P7) On the turn, Mr Weak-Tight Nit no longer has top pair or better.

Premise 8) The turn is a K.

Conclusion 5) (derived from C3, C4 and P8) Mr Weak-Tight Nit’s range for going into the river is AJ, QQ.

Premise 9) Mr Weak-Tight Nit always bets the river with two pair or better.

Premise 10) Mr Weak-Tight Nit never bets the river with worse than two pair.

Premise 11) Mr Weak-Tight Nit has bet the river.

Conclusion 6) (derived from P9, P10 and P11) On the river, Mr Weak-Tight Nit has two pair or better.

Premise 12) The river is an A.

Conclusion 7) (derived from C5, C6 and P12) Mr Weak-Tight Nit has AJ.

1.2.2: The law of contrapositives

The law of contrapositive suggests that if P necessarily implies Q, if Q is not true, then P must also necessarily not be true. A simple example of this:

1) If the fridge is open, it is possible to see inside.

2) It is not possible to see inside the fridge.

3) Therefore, the fridge is not open.

The quicker among you will have concluded already that, in its application to poker, this is mostly a way of excluding hands from a villain’s range.Perhaps the easiest way to display this is by using an actual hand example (selected fairly randomly from my database). In this hand, BB is an unexcitingreg:

PokerStars - $0.25 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

Hero (BTN): $33.52
SB (SB): $22.11
BB (BB): $28.41
UTG (UTG): $27.39
MP (MP): $21.24
CO (CO): $32.14

SB posts SB $0.10, BB posts BB $0.25

Dealt to Hero: T7

fold, fold, fold, Hero raises to $0.62, fold, BB calls $0.37

Here, the law of contrapositive tells us that if he had (making some assumptions) AA-TT, AK-AQ, he would’ve 3bet preflop, and as he did not 3betpreflop, those hands are not in his hand range.

Flop ($1.34, 2 players): K98
BB checks, Hero bets $0.84, BB calls $0.84
Again, making some assumptions, we can exclude sets and many draws (the latter to a lesser extent), as well as most 2 pair hands due to his flop flatcall, as well as underpairs and random trash.

Turn ($3.02, 2 players): 7
BB checks, Hero bets $1.90, BB calls $1.90

Further, we can now exclude 65s and JTs, which would’ve raised this wet a board with a turned straight.

River ($6.82, 2 players): 5
BB checks, Hero bets $4.29, fold

So we get to this stage, and villain’s range consists primarily of non-AK Kx, with some missed flush draws that decided not to raise the flop too.Importantly, while villain’s range is capped (more on this later), ours is uncapped, so he’s going to have a very hard time calling with any of hisremaining range on the river.

Hero wins $6.51

You’ve probably noticed that the laws of contrapositives and syllogism act pretty well as complements to each other in this regard – the law ofcontrapositives often formulates part of the reasoning in a syllogism (and indeed, can simply form a negative syllogism), especially with regards to poker.Although many of you probably went through these thought processes already, it’s certainly useful to clarify what exactly you’re doing in your head.

1.3: Inductive logic in hand-reading

1.3.1: How it works

Inductive logic is a probabilistic form of reasoning, which states that given the premises, the conclusion is likely (rather than certain). As a result, ithas strong links to the application of statistics, and indeed, the primary form that we will use is statistical syllogism. A very simple example of howthis works is as follows:

Premise 1) Most people who live in the UK have access to the internet.

Premise 2) Thomas lives in the UK.

Conclusion) Therefore, it is likely that Thomas has access to the internet.

Note that we can also make an inductive use of a technique similar to the law of contrapositive:

Premise 1) Most people who live in the UK have access to the internet.

Premise 2) Thomas does not have access to the internet.

Conclusion) Therefore, Thomas is unlikely to live in the UK.

Some might object that for this to be the case we would need a third premise along the lines of ‘There are many other places in which inhabitants are lesslikely to have internet access’. However, this is unnecessary. With the given data set, we have no reason to consider other possible locations ofinhabitation; we consider the probability that Thomas lives in the UK in isolation rather than with reference to other places. It would, of course, bepossible to construct a statistical syllogism with reference to all of these variables, but it would be rather complex, and will not be touched upon here.

In its application to poker, the most obvious use is the interpretation of HUD stats. For instance:

Premise 1) Most players who have a VPIP of 80 and a PFR of 0 after 10 hands are whales.

Premise 2) I_H8_MONEY has a VPIP of 80 and a PFR of 0 after 10 hands.

Conclusion) Therefore, it is likely that I_H8_MONEY is a whale.

We can add to this, firstly by enumerating ‘most’ and ‘likely’:

Premise 1) 98% of players who have a VPIP of 80 and a PFR of 0 after 10 hands are whales.

Premise 2) I_H8_MONEY has a VPIP of 80 and a PFR of 0 after 10 hands.

Conclusion) Therefore, there is a 98% chance that I_H8_MONEY is a whale.

(Numbers plucked out of thin air; I haven’t actually analysed a data set. However, I think 98% is a reasonable guess)

To a certain extent, we also use analogous reasoning in poker (generally for extremely small sample sizes of particular idiosyncrasies), but as we willgenerally have a decent enough sample to make comparisons to a population rather than an individual datum.

How does this apply to hand-reading? Well, it allows us to make guesses from HUD statistics about hand ranges. In the example above, the definition of a‘whale’ is largely a reference to the hand ranges that the player plays, both preflop and postflop. Similarly, although not all whales will call threestreets with third pair, we can use the fact that many will to make assumptions against someone who is identified as likely to be a whale.

1.3.2: Convergence

The link between inductive logic and convergence may not be immediately apparent. However, too often, poker players (particularly microstakes ones) tend totreat convergence as a binary value – in other words, they treat a statistic as either converged (and therefore reliable) or unconverged (and thereforeunreliable). The flaw with this thinking can be easily discovered by simply considering the point at which a stat becomes converged. Let’s say Bob thinksVPIP is converged after 100 hands. What’s the major difference between VPIP with 99 hands and VPIP with 100 hands? If you’re thinking clearly, the answeris ‘very little’.

The link to inductive logic here is in deciding the level of trust we give a sample size. Naturally, this is linked to the amount by which the statistic inquestion deviates from the norm. For instance, with relation to continuation-betting the flop, we might take relatively little from someone having cbetanywhere between 3 and 5 times out of 5 opportunities (if it were 5, we would probably conclude that their range was highly unlikely to be purely valuehands; if it were 4, we would probably conclude that their range was somewhat unlikely to be purely value hands)… but if someone hadn’t cbet at all overthat sample, that would be quite abnormal. It probably isn’t enough to draw the conclusion that they never cbet, due to the basically non-existentproportion of any given poker-playing population that never cbets at all, but we might assign a reasonable probability to the idea that villain only cbetsfor value. This turns what we might have before considered an insignificant sample size into something quite useful – for instance, if the villain inquestion cbet A22r heads-up next time they had the opportunity, we’d be much more wary about peeling with TT – and even if we’re wrong about villain’scbetting tendencies some percentage of the time (they might have had an exceptionally bad run of cbetting spots), the decent probability that we’re correctmeans that we can already make inherently +EV adjustments. It is suggested here that we can start using more assumptions in EV calculations, but factor inthe probability that they’re wrong as part of the calculation.

1.4: Exercise 1

1) Which of the following is not a valid deduction from the premises given?

Premise 1) Gravity causes things to fall towards the ground if there is not a counter-force preventing it.

Premise 2) Vases are brittle and the slightest contact with the ground causes them to smash.

Premise 3) Thomas is currently holding the vase above the ground.

Option 1) Thomas shouldn’t drop the vase.

Option 2) If Thomas drops the vase, it will fall.

Option 3) If Thomas drops the vase and there isn’t an intervening counter-force, it will smash.


2) xxJokerxx is playing 75/0 after four hands. Which of the following is correct, assuming standard NLHE values for regs and fish in VPIP/PFR?

Option 1) xxJokerxx is a reg.

Option 2) xxJokerxx is not a reg.

Option 3) xxJokerxx is more likely to not be a reg than to be a reg.

Option 4) None of the above.


3) Assume these reads are perfect. A (bad) TAG villain opens UTG. We know the following about him:

1. He has a static UTG open range of {22+, ATs+, AJo+, KJs+, KQo, QJs}.

2. He has a polarised flop cbet range of top pair and better, and no pair hands.

3. He always bets two pair or better on the turn and river, but never bets worse hands.

We call on the BTN with two cards. The flop is AJ3r. Villain checks. We check behind.

The turn is an offsuit King. Villain now bets.

Q: What is villain’s hand range?


2: The preflop part

Every hand starts preflop. This is the first place to begin narrowing ranges, and the place in which most hands will be removed from your assessment of avillain’s range (as obviously there is no need to assess a villain’s range for folding pre). Here, the ‘what’ and ‘how’ of evaluating preflop ranges isdiscussed. Most of the material in this section should apply to any stakes, but if something doesn’t apply to your stake it should be fairly obvious fromthe material (e.g. if you play 2NL it’s highly unlikely that you’ll need to consider light 3bets much).

2.1: The open raise

Much of the available material on considering a range for an open raise is somewhat lacking, merely giving Pokerstove-style tables of what a PFR percentageactually corresponds to. Here, it is sought to remind the reader to consider why an opponent would open a particular hand in a particular spot,rather than just proceeding on pre-conceived ideas of what they might open. However, we shall first look at an important topic.

2.1.1: Enumerating preflop 2bet ranges – largely unnecessary

It should be fairly clear that the point at which a person’s range is widest during a hand is when they have simply raised preflop. It’s probably alsofairly easy to see that it’s difficult to quickly assign a specific range of hands to an opponent’s open raise; indeed, it is suggested that this simplytakes too long, not to mention being too inaccurate without incredible sample sizes and reads on an opponent. Therefore, rather than thinking “villain is apositionally aware 13/10 player who has opened UTG, his range is likely 88+, AK, AQ”, it is just as well to think “villain’s a positionally aware nit whoopened UTG, he’s strong”. Similarly, and perhaps at a point where enumeration reaches an even greater degree of futility, there is no point trying to countout every hand that a 26/22 player might open-raise the button with; simply reaching the conclusion that ‘his range is pretty wide’ is sufficient.

Of course, there are situations in which you’ll want to evaluate individual portions of a preflop range specifically – if a particular villain alwayslimp-reraises AA-KK and nothing else UTG, when they open-raise UTG you can conclude that they do not have AA or KK (and the corollary is obviously thatwhen they do limp-reraise their range is precisely AA-KK, which is pretty useful to know and not difficult to remember). However, the general point stands.

2.1.2: Position

Nearly everyone now knows the importance of position in a poker game, and the purpose of this section isn’t to reiterate that. Rather, it’s to considerwhat impact a villain’s position will have on their opening range. It’s always useful to consider whether or not an opponent is positionally aware and theextent to which that’s the case. The main way to do this is HUD stats. Although some swear by reads and notes rather than HUD stats, this is one area thatI’m fairly confident the HUD prevails. After all, although you might be able to quickly take a note that a particular villain happened to open 73s on theBTN and get some quick guidance that they are positionally aware from that, if your note-taking is this specific in every aspect of the game then yournotes on an opponent will quickly become too numerous and individually unimportant to be of particular use. You can’t read an essay on an opponent everytime you encounter them.

Furthermore, a HUD is quite quick to provide an idea of whether a villain is positionally aware. Some complain that positional VPIP/PFR stats take a longtime to begin to converge, and therefore it takes a long time to know whether a particular villain is positionally aware. These people are right in theirformer point, but not the latter. The Attempt to Steal (ATS) stat, which provides a combined percentage of the time that a villain open-raised from the CO,BTN, and SB, converges reasonably quickly; in general in a 6max game, it begins to give a decent idea after about twice the number of hands for VPIP andPFR (I’d argue that this is about 40 hands; some people want more for certainty – but see above on inductive logic and convergence). Naturally, if an ATSstat is significantly larger than a PFR stat from a decent sample, you can be fairly confident that the villain in question is positionally aware; it takesa little longer to be certain that they’re not positionally aware (and to a certain extent small sample sizes must play a secondary role to population baserates – those who are familiar with Bayesian statistics will be comfortable with this idea), but certainly after 100 hands on a villain I’d be beginning todraw pretty firm conclusions.

N.B. Some also like the ‘preflop positional awareness’ stat, available in PokerTracker 4 – I’ve only used this a limited amount but it seems to doroughly the same job as ATS but be less useful over small sample sizes. However, over larger samples it could probably be more specific, so thoseplaying on smaller networks may prefer it.

So what’s the effect of knowledge of a villain’s positional awareness on our perception of their opening range? The obvious thing is that the morepositionally aware a villain is, the wider they’re going to be opening from late position. It is unfortunate that this is where the conclusions of manycease. The other important thing to draw from it is that a villain who is positionally aware is going to be opening fewer hands from early position thanone who is not (or is so, but to a lesser extent), assuming ceteris paribus.

We can also use positional awareness to gauge villain’s ranges dependent on your, or someone else’s opening position, assuming they are a second-levelthinker (which is generally a reasonable assumption for a positionally aware villain; likewise, it is generally safe to assume that a villain who is notpositionally aware isn’t really looking beyond their own cards). This will generally happen whenever you’ve opened and villain doesn’t fold, but there aretwo key situations to note. Firstly, when villain 3bets, his range and balance is likely highly influenced by the opener’s position (and almost certainlyto a greater extent than his own position) – when UTG opens and villain 3bets MP, his range is very likely to be both tight and value-oriented (it would berare to see someone 3betting JJ here, and also to see someone 3betting light more than very occasionally). When CO opens and villain 3bets the BTN, hisrange is both wide and probably heavier weighted toward bluffs. If villain is not positionally aware however, these ranges probably look fairly similar. Ofcourse, this might change if villain is aware that the original raiser is not positionally aware.

The other example, and one which in general makes much less effect, is villain’s calling range based on an open raiser’s position. The wider anopen-raiser’s range is likely to be (i.e. the later the position in which they opened), the more likely villain is to have made two adjustments – firstly,to widen a calling range slightly, and secondly, to shift the focus from speculative hands to broadway-type hands, or other hands that can hit a decent toppair frequently. Remember, this isn’t the only piece of evidence you should take into account – if villain flats a 3x UTG open in MP, and effective stacksare 30bb, he’s still much more likely to have AQ than 33!

The final thing to mention on this topic is that from time to time you will get a villain who repeatedly does something decidedly non-standard in preflopspots with regards to ranges from different positions. This is best discovered by note-taking, as in general it requires very large samples to discoverthrough the use of HUD stats (for at least the first 1k hands for instance, you’d be probably a little premature to deviate from the strong base assumptionthat people open more hands in late position to decide that one villain in particular plays more hands from MP than the CO, but otherwise conforms to thecorrelation). However, there is one common deviation from standard thinking that I will mention – and naturally, it is most common among fish and bad regs– that is to call raises with a very wide range from the blinds, using a vague ‘pot odds’ rationale. I don’t plan to talk about exploitation of particularflaws much in here, but I will briefly say that the best way to counter one of these people is simply to open wider ranges when they’re in the blinds andown them postflop using your positional advantage (and potential newfound hand-reading ability).

2.1.3: The table

Before diving into this section whole-heartedly, I feel it necessary to add a qualification (which also applies, but to a lesser extent, to the lastsection). It’s tough to know whether one villain will adjust to other people who aren’t you at a table as it’s tough to know how much history they havewith each other. Detailed note-taking is the best way to resolve this – if you see preflop wars in which two nits get 200bb in with AJ v 33, it’s probablyworth taking a note of that (but make sure to note WHO this occurred between – generalising reg wars to a player’s whole game will often result in yourmaking decidedly –EV preflop plays). Furthermore, you won’t even know if villain 1 knows that villain 2 is actually a humongous whale (this will be evenmore of a problem in Zoom-esque poker variants in which you have no way of being certain whether they’ve ever been at a table together before). Thesolution to this is unfortunately just to make assumptions based on how regularly they play (although at higher stakes with smaller player pools it wouldactually be feasible to go through your own database through the eyes of another player to check out the history you’re aware of, at that stage theassumptions that two players have played together before will become sufficiently strong to render this rather unnecessary). It is generally advised toassume that a villain is not deviating much from a play they would make based on population assumptions alone, though if you’re aware of specific historythis may change.

Moving on to the crux of this section, the table might change an opponent’s preflop ranges in several ways. The most common of these is table dynamics, butI’m afraid as I’m predominantly a Zoom player I struggle to talk with any great expertise about the matter. I will say, however, that different playersrespond in different ways to different table dynamics, varying from changing with the dynamic, to changing against the dynamic, to not changing at all. Thebest way to assess an individual’s response is to simply watch them in particular rather than making generalisations.

It’s important to note as well that we can generally use a very small number of pieces of data to make often-accurate assumptions about the rest of theirresponses to table dynamics, to a much greater extent than we can make wide-reaching assumptions in other areas – for instance, making assumptions aboutpostflop play based on preflop play. This is generally because with table dynamics, a player’s actions show whether they’re conscious of what’s going on ornot. The most obvious example of this is actually with a forced table dynamic – in an MTT with the bubble approaching. Some, who respond with the tabledynamics, will tighten up preflop, and it is safe to assume they’re not going to be too happy to call off postflop either. Some, who respond (appropriatelyin this case) against the table dynamics, will broaden their preflop ranges, stealing a lot from the first group, and it’s probably safe to assume they’recomfortable enough with ICM that their shoving range postflop is also going to be much wider than their calling range. This sort of example will alsoextend to cash games, though the examples are perhaps less obvious.

The second primary way in which a table will change a villain’s hand ranges is the players left to act, and particularly the players in the blinds. Thefishier the players in the blinds, in general the less positionally adjusted and the more high-card heavy villain’s ranges will be. This is becausevillains will want to isolate the fish from any position at the table, and they don’t have as much fold equity for late position steals. Similarly, if theblinds are both huge nits it’s likely that villain will open wider ranges from the BTN and CO (although this is much less likely to affect early and midposition ranges). Of course, not all villains will make these adjustments, and it’s worth taking notes when you discover villains who will and won’t (butas a general guide for today’s games, the crossing point tends to be that good 25NL regs and better players will make these adjustments, others won’t).

2.1.4: Examples of preflop 2bets

1) Villain is a positionally aware 21/18. Which of the following is almost certainly true about his UTG opening range?

Option 1) It is >18%.

Option 2) It is 18%.

Option 3) It is <18%.


2) Villain, a 50NL player, is 25/21 over 200 hands. His attempt to steal % is 46 over that sample, and he has opened the BTN 8 times out of 22opportunities. Which of the following is a valid conclusion?

Option 1) Villain is very likely to be positionally aware.

Option 2) Villain almost certainly opens the CO and SB more often than the BTN.

Option 3) We can’t draw any meaningful inferences from the data.


3) Villain, a competent regular, flats an UTG open of a boring TAG reg in the CO, then backraises when BB, a hyper-aggressive (but not terrible) player,squeezes and UTG folds. Which of the following hands is most likely in this spot?

Option 1) AQo

Option 2) AA

Option 3) 54s


2.2: The 3bet

When it comes to 3bets, you can generally take all your assumptions about a villain and throw them out of the window. Of course, you can still draw alittle from general understandings of villain’s ability and preflop aggression, but there are many different styles when it comes to 3betting which don’tnecessarily correlate with other elements of a player’s style. This is the reason it has been decided to consider 3betting as an entirely separate matterfrom 2bets.

2.2.1: Polarisation and merging

The first thing to consider is the difference between polarised and merged 3bet ranges. To briefly describe them, a polarised range is where a rangecontains both nutted hands (for the situation; a range may be both polarised and capped at the same time – more on that later) and bluff/semi-bluff hands,but not SDV hands[1]. A quick example of this in a 3bet range could be {JJ+,AQ+,A5s-A2s}. The thing to noteabout polarised ranges is that although the value component of a polarised range stays fairly constant in any given situation between players, differentplayers choose different types and amounts of hands for the bluff component, and even for any given player it will differ based on the situation. However,a few general guidelines are that when the 3bettor is in position, their bluff range is more likely to be mostly trash with blockers than when they’re OOP(when they’ll likely want more playable hands like suited connectors), and as you get higher in stakes ranges are more likely to be appropriately balanced(at 10NL people may just have discovered 3betting light, be 3betting an 18% range and only continuing with a 3% range vs a 4bet, whereas at 100NLadjustments will be made so that players can’t be exploited simply by 4betting ATC). Note also that a polarised range is unlikely to contain the very worsthands – hands like 42o and J3o might turn out to be +EV to 3bet in a vacuum, but most players think enough about their own ranges, either consciously orotherwise that they pick other hands to do it with.

As for merged ranges, a range is merged when there is no gap between ‘value’ hands and ‘bluff’ hands. This tends to have a much wider value component thana polarised range as a result, though you will sometimes get someone who 3bets {AA-QQ, AK} and nothing else – this range is technically merged but itdoesn’t really need thinking about. A fairly standard merged range might look like this: {88+,ATs+,KQs,AJo+,KQo}, though obviously the exact range will beplayer- and situation-dependent.

So the question arises – when can we expect to see a polarised range, and when will we see a merged one? There are some players who only ever use one orthe other, and if you find one of these players, it is more than worth taking a note to that effect (in general, you can assume this if you find them usingone when the other would’ve been substantially more appropriate). Well, in general, you should assume a polarised range as a default. However, there aresome things which should influence this assumption and maybe cause it to be changed:

· Effective stacks are short. Because of how shortstack play functions[2], a player who understands this willbe much more likely to 3bet with a merged range (this becomes more true as stacks get shorter – 20bb deep 3betting polarised is likely going to be a verybad decision).

· The 3bet is likely to be called. Within this section there are a number of factors, the following not being an exhaustive list:

o Effective stacks are deep.

o The 3bettor is out of position.

o The original raiser is bad.

o There are bad players left to act.

Again, these factors are more likely to affect villain’s range when he’s actually thinking – a mass-tabling robot is likely to have fairly static (andtight) ranges. Most of the time it just comes down to an individual assessment, but these are definitely things to think about.

2.2.2: The interpretation of stats and notes

Naturally, the most important HUD statistic when it comes to assessing a 3bet range is villain’s 3bet %. However, it must be noted that this stat takesquite a while to properly converge, due both to the rarity of opportunity and the fact that P(player 3bets) is fairly low. However, you can certainly usethe techniques of inference mentioned above to begin drawing conclusions fairly early on. Notes can well be an interim measure, but as with preflop 2betranges, they shouldn’t be relied too heavily upon in this context (unless villain does something wholly out of the ordinary). The other particularly usefulstat in my book is the ‘3bet vs steal attempt’ one. Naturally, this takes even longer to converge, but it is to the 3bet stat as ATS is to VPIP/PFR. Thereason for this is just because someone is positionally aware in an open raising context doesn’t mean we can assume they are in other contexts. Manyplayers have read hand charts and assumed that’s all there is to being positionally aware. Further, some people go absolutely ape**** against stealattempts, and it’s good to know who these people are so we can exploit the living hell out of them.

The other point is to remind readers to be careful with notes in 3bet spots. People are likely to vary their play, so the fact that we’ve seen villain flata 3bet with AA before doesn’t mean we should assume his range contains every AA combo (though we should certainly not exclude it entirely). This pointcould really go in any section, but it’s a recurring theme; utilise small sample sizes, but don’t abuse them.

2.2.3: Position

Although we briefly touched upon this in the previous section, position can make as much of an effect on 3betting as it does on open raises. However, theoriginal raiser’s position makes more of an effect than the 3bettor’s position (though both matter). This is because how tight or wide the originalraiser’s range is makes a huge effect on both which hands can feasibly be 3bet for value and on how often people feel they can profitably 3bet light. Forinstance, when V1 raises UTG, it probably doesn’t make too much of a difference for V2’s 3bet range whether V2 is in MP or on the BTN. In fact, the onlymajor difference which preflop position can make is whether V2 is going to be in position or out of position postflop – for both the effect on V1’scontinuance range, and the chance that the 3bet becomes +EV (or –EV) due to the presence of a positional edge one way or another. Naturally, this normallytakes effect when V2 is in the blinds, unless he is the type to limp-reraise (in which case, it is best to assume he is a bad player and assess his rangeby note-taking; however, traditionally limp-reraises have been almost exclusively AA and KK).

There’s also consequently some effect on a calling, and therefore backraising range. When V1 opens UTG and V2 calls in MP, V2 probably thinks that he isless likely to face a squeeze than if V1 opens CO and V2 calls on the BTN. The effect of this is twofold; firstly, in the first scenario V2 is much lesslikely to flat super-premium hands (AA, KK etc) with the hope of inducing a squeeze and then 4betting. Secondly, V2 is more likely to be happy to flatthings like suited connectors, not only because he’s facing a stronger range and thus has greater implied odds, but also because of the reduced chance ofbeing squeezed out of the pot.

2.2.4: Examples of preflop 3bets.

In all hands, think of an appropriate range for V1, using all the information above. No answers are given here because it’s more of a point for discussionthan a strict right answer/wrong answer dichotomy.

1) V1 is a positionally unaware aggrodonk, playing 73/64, with a 3bet % of 47 after 120 hands. The rest of the table are TAG regs. Effective stacks 100bb.

UTG opens 3x

MP folds

V1 (CO) 3bets to 7bb…

2) V1 is a good, thinking reg. CO is a TAG reg who has folded to 78% of 3bets over a very decent sample. SB and BB are both aggressive squeezers, who oftenplay the same games as CO and V1. 100bb effective stacks.

UTG, MP fold

CO opens 3x

V1 (BTN) calls

SB folds

BB 3bets to 13bb

CO folds

V1 4bets to 28bb…

3) Same scenario as above.

UTG, MP fold

CO opens 3x

V1 (BTN) 3bets to 9bb…

4) V1 is a professional shortstacker with a stack size of 20bb. BTN is a bad reg with 94bb, all other players are TAG regs, except UTG, who is a fish.

UTG, MP, CO fold

BTN opens 2.5x

SB folds

V1 (BB) shoves for 20bb…

5) All players are TAG regs. 100bb effective stacks.

UTG opens 3x

V1 (MP) 3bets to 9bb…

6) As above.

UTG, MP fold

CO opens 3x

BTN 3bets to 9bb…

7) As above.

UTG, MP fold

CO opens 3x

BTN folds

SB 3bets to 10bb…

2.3: 4bets and beyond

In general, once a player knows their stuff about 3bets it’s safe to assume that they’re capable of applying the same logic to 4bets and 5bets (that is notto say that they will 4bet light or wide – particularly if population tendencies make it generally unprofitable to do so). However, we must still observethem to gauge how they respond to certain factors. The fact that it takes such a long time for 4bet+ stats to converge means that in larger player poolsour greatest aid for being aware of non-standard tendencies will be notes. If you see someone 3bet/5bet A2s, that is well worth a note, at lower stakes inparticular, despite the fact that it’s one of the best hands to do so with as a bluff. Again, the general rule applies – if something deviates frompopulation expectations, it’s worth noting if it will significantly change your play against them.

Again, mostly the same logic applies for whether 4bet and 5bet ranges are polarised or merged, but where reference is made in 3bet ranges to an openingrange, replace that with 3bet and 4bet ranges respectively. In fact, there’s very little more to say on the subject of 4bets and 5bets in terms of handreading that hasn’t already been covered in the 3bet section. The only thing that was brushed upon earlier that wasn’t fully expanded upon was backraising.For those not in the know, a backraise is when a player flat-calls an open raise, then 4bets over a 3bet (or 5bets over a 4bet). Simply put, there are twotypes of backraise, which I’m going to call the planned backraise and the off-the-bat backraise.

The planned backraise is when a player flats an open raise in a spot they’d normally 3bet it because they have spotted an aggressive 3bettor/squeezerbehind them, and they hope to induce a squeeze play. Here’s an example (you may recognise a similar situation from the 3bet quizzes above):

Effective stacks 100bb, SB is squeezing 27%.

CO opens 3x.

Hero flats the BTN with AA.

SB squeezes to 13bb.

BB, CO fold.

Hero 4bets to 28bb…

The planned backraise is a lot less common, at microstakes at least, than the off-the-bat backraise, because it requires a player to be particularly awareof what’s going on around them.

The off-the-bat backraise, however, is generally done when the squeezer’s range is weaker than the open-raiser’s range (hence not 3betting a marginal handin the first place), and so the backraiser feels that they can profitably 4bet in their spot. An example:

Effective stacks 100bb, CO is an 11/8 nit folding to 78% of 3bets. SB is a LAGtard squeezing 27% and stacking off with most of that.

CO opens 3x.

Hero flats the BTN with TT/AQ.

SB squeezes to 13bb.

BB, CO fold.

Hero 4bets to 28bb…

It’s generally pretty difficult to find out which type of backraise is more likely without history, but a guideline is that you should probably assume it’san off-the-bat backraise without reason to think otherwise. Another brief point to be made is that backraising is rarely done as a bluff. This is becausethe sort of person who might consider it (i.e. a player competent enough to realise that a squeeze range might be weak) is also likely to realise that abackraise range generally appears capped so is more likely to face a light 5bet. That said, with levelling and history, it’s not impossible.

The very last thing to mention about 4bet/5bet hand reading is bet sizing. When people realise they can 4bet light, they in general also realise that4betting 3x (which is advocated in some older strat threads) is going to make light 4betting very tough to make profitable. From this, you can makeassumptions about someone’s 4bet range from their sizing. For instance, at a limit where the population is in general capable of 4betting light in goodspots (say, 50NL), JJ in the SB facing a BTN 4bet is probably a jam vs a 2.2x 4bet, and a fold vs a 3x 4bet. Of course, this isn’t to be taken asaxiomatically strong evidence, but it’s a good assumption to proceed with.

2.4: Using PokerStove to learn more about ranges

This will be a brief section. A new player could do well to mess around a fair bit with Pokerstove/Equilab or some other equivalent program to understandwhat sort of range each percentage correlates to. However, it’s best not to drag and drop or just enter a percentage, as those will retrieve likelyinaccurate ranges – Pokerstove ranges are based (I believe) on hot-and-cold equity without taking factors like playability into account, so will be a poorguide. For instance, QTs and A9s are included in a Pokerstove range before a hand like 77, and 98s is rated at the same tier as K5s. For that reason, ifyou’re just looking for numbers to match to ranges, it’s probably best to go the other way around and match ranges to numbers, picking hands in the orderyou think they’d be played.

With this, however, it’s best to remember the danger of assigning static preflop ranges for a player in any given situations. Many invisible factors canaffect a player; drunkenness, a change of mood, having read strat recently, etc., and naturally, these will begin to affect a villain (and arguably havethe most significant effect) preflop. Therefore, just because Mr Nitty-Nithead has opened UTG, don’t assume you can automatically exclude 98s from hisrange. Certainly, you can weight assumptions against it, but never say never.

2.5: Concluding quiz on preflop

In each hand, assign a range (or merely strength and weighting) to each player who enters the pot. Stacks are 100bb unless otherwise stated. Assume goodsample sizes.


UTG (VPIP 22, PFR 18, 3bet 4, fold to 3bet 66, ATS 33) – boring reg

MP (VPIP 74, PFR 6, 3bet 0, fold to 3bet 32, ATS 7) – calling station fish

CO (VPIP 11, PFR 9, 3bet 2, fold to 3bet 73, ATS 16) – nitbox

BTN (VPIP 26, PFR 22, 3bet 8, fold to 3bet 70, ATS 48) – good, perceptive regular

SB (VPIP 18, PFR 16, 3bet 4, fold to 3bet 88, ATS 28) – nitty regular

BB (VPIP 60, PFR 59, 3bet 55, fold to 3bet 0, ATS 73) – complete maniac

UTG raises to 3bb, MP calls 3bb, CO raises to 12bb, BTN raises to 26bb, SB folds, BB calls 26bb,UTG folds, MP folds, CO raises to 100bb and is all-in, BTN calls 74bb and is all-in,BB calls 74bb and is all-in


UTG (VPIP 22, PFR 18, 3bet 4, fold to 3bet 66, ATS 33) – boring reg

MP (VPIP 74, PFR 6, 3bet 0, fold to 3bet 32, ATS 7) – calling station fish

CO (VPIP 11, PFR 9, 3bet 2, fold to 3bet 73, ATS 16) – nitbox

BTN (VPIP 26, PFR 22, 3bet 8, fold to 3bet 70, ATS 48) – good, perceptive regular

SB (VPIP 18, PFR 16, 3bet 4, fold to 3bet 88, ATS 28) – nitty regular

BB (VPIP 60, PFR 59, 3bet 55, fold to 3bet 0, ATS 73) – complete maniac

UTG raises to 3bb, MP calls 3bb, CO folds, BTN raises to 12bb, SB folds, BB folds, UTG folds,MP calls 9bb


UTG (VPIP 22, PFR 18, 3bet 4, fold to 3bet 66, ATS 33) – boring reg

MP (VPIP 74, PFR 6, 3bet 0, fold to 3bet 32, ATS 7) – calling station fish

CO (VPIP 11, PFR 9, 3bet 2, fold to 3bet 73, ATS 16) – nitbox

BTN (VPIP 26, PFR 22, 3bet 8, fold to 3bet 70, ATS 48) – good, perceptive regular

SB (VPIP 18, PFR 16, 3bet 4, fold to 3bet 88, ATS 28) – nitty regular


UTG raises to 3bb, MP folds, CO calls 3bb, BTN raises to 12bb…


UTG (VPIP 22, PFR 18, 3bet 4, fold to 3bet 66, ATS 33) – boring reg

MP (VPIP 74, PFR 6, 3bet 0, fold to 3bet 32, ATS 7) – calling station fish

CO (VPIP 22, PFR 19, 3bet 3, fold to 3bet 79, ATS 30) – boring reg

BTN (VPIP 20, PFR 18, 3bet 11, fold to 3bet 72, ATS 40) – TAG

SB (VPIP 26, PFR 22, 3bet 8, fold to 3bet 70, ATS 48) – good, perceptive regular

BB (VPIP 13, PFR 10, 3bet 3, fold to 3bet 77, ATS 22) – nit

UTG folds, MP folds, CO raises to 3bb, BTN folds, SB raises to 10bb…


UTG (VPIP 22, PFR 18, 3bet 4, fold to 3bet 66, ATS 33) – boring reg

MP (VPIP 74, PFR 6, 3bet 0, fold to 3bet 32, ATS 7) – calling station fish

CO (VPIP 22, PFR 19, 3bet 3, fold to 3bet 48, ATS 30) – reg who struggles to fold to 3bets

BTN (VPIP 20, PFR 18, 3bet 11, fold to 3bet 72, ATS 40) – TAG

SB (VPIP 26, PFR 22, 3bet 8, fold to 3bet 70, ATS 48) – good, perceptive regular

BB (VPIP 13, PFR 10, 3bet 3, fold to 3bet 77, ATS 22) – nit

UTG folds, MP folds, CO raises to 3bb, BTN folds, SB raises to 10bb…

3: The postflop part

This is going to have to be much vaguer than that which came before, for the reason that once a hand goes postflop, the variable of the board isintroduced, which is the biggest complexity in any poker hand. It is proposed to cover in adequate, but not excruciating detail several topics which arelinked to a degree, but to a much lesser extent than most of the above (also, writing this has taken a couple of months longer than I wanted so at thisstage I’d quite like to get it out).

3.1: Principles

There is much less cohesion to the ‘principles’ of hand-reading postflop as a whole, and as a result I’m not quite sure it’s the right word to use in thecontext. Nonetheless, I can’t think of a better word. Here, it is proposed to revisit polarisation and merging as they manifest themselves after the flop,cover the idea of a perceived range, and how it should affect our perceptions of an opponent’s range in more detail than above, briefly discussfourth-level thinking, and indeed, how to discover which level of thinking is appropriate. Hand reading based on bet size will also be discussed, thoughthis is less fundamental and much more player/population-dependent. Finally in terms of actual principles, interpreting board texture will be discussed.

Then, a few more specific scenarios will be discussed – it’s likely impossible to cover all of them, but hopefully the fact that some of the more commonones (capped ranges, donk bets and the likelihood of a bluff) will be discussed, along with the principles given will enable the reader to effectivelyinterpret more obscure situations.

3.1.1: Postflop polarisation

It was explained above (in the 3betting section) what polarisation is, so I’ll move on to a general rule that will hold true for 95% of postflopsituations: an aggressor’s range is polarised, a passive player’s range is merged. Naturally, there are some exceptions to this – the most obviousare when a player intends to float (to call one street with the intention of bluffing at the pot on another) – and in general isn’t thinking about theirrange as a whole, as with streets to come, it is nearly always better to use hands with some equity even for bluff lines. Similarly, people will sometimesbet with a merged range, especially in situations where a large amount of an opponent’s range will be able to play perfectly against a check (for instance,when the bettor is OOP on a wet flop, or on Axxr flops). There are also some history-based spots in which a range will be merged, though this will usuallybe only a slight merge of a player going for incredibly thin value or turning a made hand into a bluff. However, the general principles given above (and Irecommend going back and reading the other section on polarisation if any of this is unclear) will hold true in most situations in which there is not aclear reason for them not being the case.

3.1.2: Perceived ranges

To start this section, I would like to clear up a common misconception – that a perceived range has more importance than merely as a tool to be used inhand reading. One’s actual range certainly has more than a little relevance when attempting to bring balance and/or game theory into one’s game,but the perceived range is merely assessing how our opponent’s ranges will change in response to what our range looks like, given our line, which is theembodiment of hand reading. This extends further to all higher ‘levels’ of thinking.

Beginning anew, a brief definition of a perceived range for those who are unaware would be our opponent’s assessment of our range. As a result, the factorswhich ought to be considered in discovering our perceived range are:

· Our line (including bet sizing, responses to differing board textures etc)

· Our opponent (including any hands we may have played with them, how they perceive us, their ability in particular spots, or for relative unknowns,population assumptions of the above)

The mistake people often make when assessing their perceived range is forgetting the latter of those two factors. For a start, if villain isn’t lookingbeyond their own cards, their ranges are wholly unaffected by the ‘credibility’ of our lines – in other words, we don’t have a perceived range. Secondly,different villains will interpret different lines differently. Some will always interpret a raise on a paired board as strong, others will interpret asweak. Unfortunately, the only real way to keep track of this is meticulous note-taking.

In this way, it’s good to be consciously aware of how you differ from the population at the stake you are playing, so you don’t assign your own perceptionsof ranges onto villains’ perceptions of your own (this also applies to second-level thinking – you shouldn’t exclude hands from a villain’s range justbecause you wouldn’t have played those hands that way).

That said, the core of discovering a perceived range is still fundamentally the same hand-reading process, just with your axioms being dependent ondifferent things.

3.1.3: A brief introduction to fourth-level thinking and beyond

Before going into this with gusto, it is worth recapping what is meant by first-, second- and third-level thinking:

· First level thinking: ‘What do I have?’ (what are my cards and how do they connect with the board?)

· Second level thinking: ‘What does my opponent have?’ (this can either be the naïve player putting his opponent on a single hand or the experienced oneassessing a range)

· Third level thinking: ‘What does my opponent think I have?’ (what is my perceived range?)

From this progression, it should hopefully spring to mind that fourth-level thinking is understanding what an opponent believes their perceived range tobe. Naturally, this is where we start to get into the realm of levelling wars, but early on after identifying that an opponent is capable of thinking inthat way, and does in hands against the hero (more on how to do this later), it can be particularly useful in situations when an unusual line is taken – ifa villain understands their perceived range to be weak in a spot, they are generally more likely to take razor-thin value lines in that spot than make bigbluffs. Conversely, if a villain understands their perceived range to be strong, they are more likely to make big bluffs than go for thin value.

Of course, this effect won’t last for long. Soon we get into mere levelling wars (‘He knows that I know that my perceived range is weak, so he’s going tothink I’m more likely to go for thin value than bluff here, so he’s going to fold more of his marginal hands, so I should actually start bluffing in thisspot more often’ – and this is towards the simple end of levelling wars), which I really can’t advise the reader about much, as they tend to be toogameflow-dependent to offer generalised advice on.

3.1.4: Discovering what level an opponent is thinking at

Naturally, all of the above is practically useless if we are completely incapable of assessing how villain is thinking. In general, we do this bycollecting evidence as to which level a villain is thinking on and continually re-assessing (as a villain may change as they get better or change theirperception of us), but we would naturally start from population assumptions (at the moment, a 10NL Zoom reg is normally a 2nd-level thinker andno more, about half of the 25NL Zoom regs are capable of 3rd-level thinking and basically all of the 50NL Zoom regs are thus capable). As usual,we must be sure not to over-value individual pieces of evidence. When we get called on the river in a spot where our perceived range is weak by a relativeunknown with a weak-ish hand, it could equally mean that said opponent is capable of reading hands, or that they are a bit of a calling station. The moreevidence you gain towards one conclusion, the more certain you can be, but the most helpful piece of evidence is naturally going to be disproving thealternative. Unfortunately, proving someone not to be a calling station is going to be harder than proving them to be one, as the former necessarilyinvolves them folding.

Discovering that someone understands their perceived range is going to be much more inductive in the associated thought process. It tends to be evidencedby someone making thin plays which are appropriate to their range, or what they might reasonably believe it to be perceived as. Again, unfortunately, thesame pieces of evidence could often produce the alternative conclusion that they’re just a bit bad, and would be performing the same thin plays even whenthey were completely inappropriate based on their perceived range.

Fourth-level and further thinking tend to be discovered just as one descends into dick-swinging reg wars, and it’s fairly obvious when it happens providedboth hero and villain are competent. A general point to make is the structure of the levels of thinking exists for a reason – if someone is incapable of 2nd-level thinking, they are necessarily incapable of 3rd-level thinking and so on.

3.1.5: Interpreting bet size

At the lowest limits, bet sizing is an incredibly useful tool in reading hands and should often be preferred over basically any other indication because ofhow many dumb lines you will see. At higher limits, many more people use standardised (if sometimes creative) bet sizes with their entire ranges inparticular spots, and it becomes much less useful as a result. However, a few things will remain consistent, if not necessarily exploitable.

At the lowest limits, you will find in general that bet sizing is proportionate to hand strength; this remains consistent among weaker players higher up(although extremely large bets often tend to be tilt-induced pot-buying attempts; treat a pot size bet as stronger in most scenarios than a 3x pot overbet,especially on dry boards). Naturally, this is not going to be true for the entire nanostakes population, especially those who have found 2+2, but those whodon’t size their bets in this way tend to be the exception rather than the rule, and 2NL players would do better to take notes on those who usestandardised bet sizes rather than the other way around.

At higher limits (in general in 2013, this is anything at 10NL or above), most people won’t make such an obvious mistake. In fact, the poor players areoften the ones who will give away the least information with their bet sizing – they won’t think about it at all and will simply hammer the 2/3 pot buttonmost of the time. However, despite the fact that you will likely be able to discover a more accurate range for the players who actually put thought intotheir bet sizes, it’s not easily exploitable (that said, the goal for this is not to talk about exploitability). It’s certainly good to identify one typefrom the other; in this context, like many others, notes are the best way to do it.

In general among strong players, a larger bet represents a more polarised range (note that this is also true for many weaker players, but the weakerplayers will have few to no bluffs with which they balance their range), while a smaller bet is often a medium-strength value hand which is looking to getthin value by keeping calling ranges wider. Only those who are acutely aware of their perceived range will tend to include bluffs in a range for bettingsmaller when realising they represent a stronger range in general by betting small (this is possible; see below).

This is also true among some players who are distinctly unaware of their perceived range. However, they will often have very value-heavy or bluff-heavyranges for betting large in particular spots, unlike the better players who will tend to play more balanced ranges (but understanding that they’repolarised may nonetheless be helpful). Note that this is dependent on their perception of the hero – if hero is perceived as a calling station or a nit,ranges might be constructed in different ways for maximal perceived exploitation.

There are also spots in which a bet size makes no sense for value (for instance, a river overbet in a spot where villain will know that hero is capped).This is nearly always a bluff from a semi-competent player, though as an opponent gets worse it becomes more and more likely to represent a butcheredmonster desperately trying to get the value that the player feels they ‘should’ have had. It should be fairly clear where this line can be drawn – andthere should be a gap in between the two extremes, as the former tends to be an average player and the other an extremely bad one.

3.2: Specific but common postflop scenarios

Here, the focus will be on a few specific postflop scenarios mentioned above – the first extremely common, later ones not so much.

3.2.1: Capping of ranges

Simply put, a range is capped when it cannot (or will very rarely) include a sub-range of hands at the top end of possible hands including the nuts. Sayinga range is ‘capped to x’, therefore, means that the best hand within that range is x. Knowing when a villain’s range is capped, and to a lesser extent,knowing when your own range is capped are very powerful tools in any poker game, but especially no-limit varieties. A range becomes capped when a playerwould have taken a different line for value to the one taken with the nutted sub-range in question. Note that evaluating whether this is true becomesharder as more history develops, and also with worse opponents, due to the unpredictability of how they play the top of their range. There are threescenarios to discuss.

Scenario 1: Villain is capped while hero is uncapped

The first thing to note is that hero being uncapped is only remotely relevant in the case where villain is able to read hands to a decent degree.Certainly, when villain isn’t looking beyond his own cards, he might be the sort of person against whom it is tougher to exploit a capped range (in otherwords, a calling station), but certainly on dry boards it tends to allow us to profitably bet 100% of our range regardless of whether we are capped. When aperson with a capped range is aware of their perceived range, we are more likely to see continuance with a wider range than someone who is just a level 2thinker, especially in river spots where they’re going to be capable of taking an approach of calling with the top x% of their range. Regardless, I don’twish to talk too much about exploitation here.

With capped ranges, the most useful thing for evaluating precise ranges is notes and reads. A preflop spot where there has been a backraise – often, the4bettor is capped when he flats, so it would be helpful to know if he is capable of flatting monsters in this spot. On a similar note, sometimes poorplayers miss extremely obvious value bets to any competent player – and this is a more common situation. The thing about capped ranges is that one has tohave a good grasp on villain’s ability to be able to properly appreciate the extent to which villain is capped. If people often take weird valuelines, that’s a further reason to not give too much credence to a seemingly capped range, as it can be extrapolated generally accurately from having seenone weird line that villain will wish to take unorthodox lines in general. Furthermore - at lower stakes to a greater extent than higher ones – you have tobalance general ideas about turn and river raises being strong with a seemingly capped range, often with the former consideration winning out readless.

Finally, just because this sentence needs repeating in this section: a range becomes capped when a player would have taken a different line for value tothe one taken with the nutted sub-range in question.

Scenario 2: Villain is uncapped while hero is capped

This situation will not come up at all unless villain is a reasonably competent hand reader, as otherwise hero’s perceived range doesn’t matter. The firstthing is to realise that hero’s perceived range is actually capped, which is a simple hand-reading exercise using the main guideline mentioned above. Thesecond is to realise how villain’s range changes in response to this capping. Some relatively oblivious players won’t change their ranges at all, whilesome will go bananas and barrel off whenever somebody caps their range. Again, the best way to assess this is meticulous note-taking, and once again, it isnext to impossible to assess using HUD stats alone, the closest indication being barrelling stats vs missed cbets (but due to the tendency of most playersto flat preflop rarely and cbet often, these will take a long time to converge).

A brief word on strategy, therefore, as it is a spot that is rarely discussed in the general form – it seems that the best way to play when one’s range iscapped facing aggression from an uncapped range readless is to take a game theory-oriented approach to calling ranges – in other words, trying to berelatively unexploitable by calling with the top x% of one’s range, because responses to capped ranges vary so vastly it tends to be futile to attempt totake a population exploitative approach in these spots.

Scenario 3: Both hero and villain’s ranges are capped

In this spot, it’s best to pretend the hands that neither player can hold simply don’t exist. Polarisation still exists – after all, there’s no reason whysomeone who can’t hold top pair or better (but their opponent can’t either) can’t value bet second pair, check third pair and bluff no pair. Furthermore, arange can still be relatively capped (you heard the term here first, folks) in the case where both ranges are capped by being capped to a weakerhand than its opponent. For instance, in the case where one player cannot hold better than top pair, but their opponent cannot hold better than secondpair, their opponent is relatively capped. This ought to be treated in much the same way as standard capped range scenarios, again, by forgetting that thebetter hands exist.

3.2.2: Facing donk bets

Many problems come up when people face a donk bet and simply don’t know what to do. For those who are unaware, a donk bet is a bet into the person who hadthe initiative on the previous street before they have acted on the current street (i.e. if the flop checks through it is impossible for there to be a donkbet on the turn). These can be split into a few general categories.

If a decent regular donk bets the flop, it is almost always the case that they felt that a continuation bet was unlikely in the specific spot (in general,this is when a pot is multiway or a flop is devoid of high cards and wet). In this case, their range for donk betting will roughly align to a standardcbetting range in that spot – in other words, a wide value range with made hands (often including both sets and second pair type hands), and a wide rangeof hands with some equity (sometimes as little as a gutshot or two overcards). It is very unlikely that they will have any hands with no equity at all –take that into account when evaluating c-ranges against a raise.

Turn and river donk bets from decent regulars are much rarer, and can best be evaluated by considering their reasoning for it and their perception of thehero – remember, they have elected to lead rather than check-calling, check-folding or check-raising, and so they must feel that leading has a higherexpectation than any of the other options. This leaves the situation very vague, but these kind of bets come rarely enough that it is tough to set out ageneral rule for evaluating them, and they can best be dealt with through specific notes (though over larger samples, donking stats for those streets canbe utilised to evaluate the breadth of a range – and a range for doing this is fairly likely to be merged and perhaps capped due to the decision tocheck-call the previous street).

Donk bets from fish and other weak players tend to be divided into three categories, based on bet sizing – minbets (or other very small bets), standardsized bets, and overbets (note that a pot-sized donk tends to have very different implications to an overbet!). The minbet tends to be the hardest to finda precise range for, but it is very rare that a typical mindonking range contains nutted hands, and rather any given player’s mindonking range tends toinclude one or more of the following categories: complete air, weak made hands and drawing hands trying to ‘set their own price’. Fortunately, players thatmindonk tend to do it frequently so you should be able to discover a specific tendency fairly quickly (and even if you don’t see a showdown, use yourhand-reading ability and draw inferences – for instance, a player that mindonks and calls a raise is very unlikely to have had complete air, and if they dothe same on the turn then check-fold to a smallish river bet when all draws missed it is likely that they had a drawing hand).

Standard sized donk bets from weak players can represent any hand so I’m not going to go into it in depth. The one thing I’ll say is that it isn’t soair-heavy that you can auto-raise any normal sized donk and expect to be +EV in doing so. Furthermore, your best aids for discovering a range for doingthis are going to be board texture and notes – if a fish donks for close to pot when a flush card hits, expect them to have a large number of flushes intheir range – similarly, I would rarely be raising TPTK for thin value against a x/c-donk line even on the most innocuous of turns, as a standard range fordoing that (for greater than half pot, a smaller donk is often a draw) includes a lot of turned 2P hands that we can’t exclude from a fish’s preflop range.

As for overbets, again, I can only really speak from experience as there doesn’t seem to be much logic which goes into this kind of play, but donkoverbetting ranges tend to differ between single raised pots and 3bet pots, in that a range in the latter is much stronger. In saying that, I shouldbriefly cover a situation which isn’t a donk bet but doesn’t fit anywhere else – if a fish min 3bets pre (obviously we’re never folding any of our raisingrange) then shoves the flop for about 8x pot, this is nearly always an overpair, and most often AA or KK. I can only assume that they reason that they’vedisguised their hand with their preflop sizing (or maybe they’re just ‘checking’ they have an overpair before they shove).

Other donk overbets in 3bet pots tend to represent extremely strong ranges. Even fish tend to have some understanding of SPR, if not necessarily aconscious one, and they understand they want money in the pot quickly. In single raised pots, this is not so much the case, and they tend to representfrustration more than anything else, or a draw trying to ‘maximise fold equity’ (before the river at least – river donk overbetting ranges are muchstronger). I wouldn’t be folding top pair often without a specific note which suggested I should do otherwise.

3.2.3: Is villain bluffing?

It’s a common situation – villain does something which polarises his range (we’ll talk about river spots here as polarisation is more common, but ingeneral you should be folding bluffcatchers slightly more often on earlier streets if they don’t have draws to better hands), and we have a bluffcatcher.We want to know if we can call. The first thing to do is make sure you are comfortable with pot odds and the effect on how often you need to be right (’re getting 2:1 against a pot-sized bet so you need to be ahead one-third of the time to call profitably, assuming rake is already capped). Sort of as afollow-on from that, you should remember that just because you called and happened to be behind, it isn’t necessarily a bad call (and this is one of thespots where more people than normal forget ‘range’ over ‘hand’).

Anyway, there are two main components to evaluating the likelihood of a bluff – whether they can have got to the river with bluff hands, and, given therange with which they got to the river, how often they’re likely to bluff with the air sub-range (again, these also apply earlier but far more of villain’s‘bluffs’ are likely to be semibluffs instead).

Knowing whether or not villain can have bluff hands in his range for reaching the river is a simple hand-reading task, and one which focuses heavily onpolarisation. Somebody who was the preflop raiser and cbet flop and turn is likely polarised, and thus far more likely to have bluff hands in their rangeon the river than the person who, in that hand, called the flop and turn (who is likely doing that with a more merged range). Of course, this is dependentto a degree on board texture. On a dry board, someone who calls twice (especially OOP) is likely very strong, and on a wet board where most draws hit, thepassive player is very unlikely to have air hands by the river (but the aggressor is also less likely due to standard barrelling ranges on differenttextures), whereas on a wet flop with blank turn and river cards, it is entirely possible for the caller to have air hands (busted draws).

Of course, the tendencies of an opponent also come into this – someone who never double barrels without top pair or better will not have air hands afterdouble barrelling, and likewise, somebody who is capable of turning made hands into bluffs can have an ‘air’ range (that part of their range is effectivelyair because it is behind their opponent’s bluffcatchers) even after taking a passive line in the hand. Another major factor is how they play draws –someone who raises most draws on the flop likely has more made hands after calling twice on a busted-draw type board than someone who likes playing thempassively.

Also linked to tendencies is the second element – given that the person can have air hands in their range, how many of them they would bluff with. This canlargely be linked to generally how aggressive and/or spewy a player is, but of course, people will depart from their normal tendencies from time to time(however, we should probably factor that into our general decision making process subconsciously and only overtly include it in EV calculations doneoff-table). The hero’s perceived range is also relevant – the stronger our perceived range, the less often we can expect a bluff from competent opposition.In general, in a standard bluffcatcher vs polarised range situation, we don’t really need to consider which specific combos would be used to bluff, justconsider how many can be used to bluff and use a general percentage of the time that villain will bluff the spot in question (and remember, value handswill be bet near 100% of the time unless a mistake is made by our opponent).

[1]For more on the classification of hands, see Sweeney, ‘Dynamic Full-Ring Poker’ (2010, DailyVariance), chapter 10 (‘Understanding Showdown Value’)

[2]See Bakker, ‘Analytical No Limit Hold’em’, (2010, 2+2 Publishing), pp 50-67.
TheDefiniteArticle is offline   Reply With Quote
Old 08-30-2013, 12:32 PM   #2
Tarkyo's Avatar
Join Date: Mar 2012
Location: Fish Pond
Posts: 849
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)


Time to start reading this and thanks for posting it!
Tarkyo is offline   Reply With Quote
Old 08-30-2013, 12:57 PM   #3
Join Date: Jul 2013
Posts: 4,543
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Looks awesome
Now to read it
tomj is offline   Reply With Quote
Old 08-30-2013, 01:09 PM   #4
bob2222's Avatar
Join Date: Nov 2012
Location: everleaf poker #1
Posts: 721
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Lot of effort put into that hope to get it read by next month

jk will read and thanks.
bob2222 is offline   Reply With Quote
Old 08-30-2013, 01:22 PM   #5
Accept No Substitute
Dunna100's Avatar
Join Date: Nov 2011
Posts: 6,168
Wp Sir, will read
Dunna100 is offline   Reply With Quote
Old 08-30-2013, 01:58 PM   #6
Badugi Ninja
bumblebee99's Avatar
Join Date: Apr 2008
Location: FUBT
Posts: 10,998
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Not finished it yet but very good, helpful stuff so far.

bumblebee99 is offline   Reply With Quote
Old 08-30-2013, 02:49 PM   #7
I need a hug
TensRUs's Avatar
Join Date: Jan 2011
Location: still 3x'ing
Posts: 5,578
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Oh s***, you're TDA2?

Very solid, you are. I'll be reading this in chunks
TensRUs is offline   Reply With Quote
Old 08-30-2013, 03:10 PM   #8
asriva's Avatar
Join Date: Jun 2012
Posts: 982
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

In on epic post.

Will take time to chew and digest, pretty sure it'll be solid TDA.
asriva is offline   Reply With Quote
Old 08-30-2013, 03:36 PM   #9
Carpal \'Tunnel
DiamondDog's Avatar
Join Date: Jul 2007
Location: on top of Manhattan Chase
Posts: 7,475
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Holy Moly.

This looks super-good.

Thanks for posting.
DiamondDog is offline   Reply With Quote
Old 08-30-2013, 05:31 PM   #10
BubbRubb4Real's Avatar
Join Date: Apr 2012
Location: Houston, TX
Posts: 105
Subscribed and reading. Looks great!
BubbRubb4Real is offline   Reply With Quote
Old 08-31-2013, 06:06 AM   #11
sheeprustler's Avatar
Join Date: Jun 2009
Location: @sheeprustler
Posts: 3,263
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

It's been added to my study list, looking forward to reading it.

Round about time you got to writing the pooh bah for your gimmick now amirite?
sheeprustler is offline   Reply With Quote
Old 08-31-2013, 06:37 AM   #12
MMSS's Avatar
Join Date: Jul 2013
Posts: 4,584
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Part 1 - I think this is very good, in fact probably one of the better thought out introductions to this type of thing I've seen. I'd argue some of the examples you gave could have been a bit better, but all in all very very good.

Note - There are also quite a few spots throughout where you've missed a space between words, in case you want to edit them out.

I also think "2.1.4 Example 2" is wrong. That sample size isn't enough to conclude that villain more opens more from the CO & SB than he does from the BTN. He attempts to steal 46%.

8/22 = 36%, then we don't take into consideration how many times he's actually had the chance to steal. Even if we conclude that he's had the chance to open 22 hands in each position (which is a false assumption) this still isn't enough to conclude anything when he is likely opening a large % from each position. It'd be a much more logical conclusion to assume that he opens more from the BTN than he does from the CO he's just been running hot in the CO/cold OTB.

Especially when we take into account villain is playing 50nl and is therefore quite likely to be positionally aware from the start, but I think the argument is strong enough without even taking this into account.

(Will finish the rest later, up to start of 2.2)

Last edited by MMSS; 08-31-2013 at 06:50 AM.
MMSS is offline   Reply With Quote
Old 08-31-2013, 07:56 AM   #13
dillchips's Avatar
Join Date: Sep 2011
Posts: 2,167
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

In, gonna read it asap. Rated 5* just cause TDA.

dillchips is offline   Reply With Quote
Old 08-31-2013, 08:23 AM   #14
Join Date: May 2010
Posts: 3,056
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Wow, looks amazing.
subcon1 is offline   Reply With Quote
Old 08-31-2013, 08:58 AM   #15
NoSkill20's Avatar
Join Date: Jun 2012
Location: White Magic Quad 8 Power Fold
Posts: 576
Got burned out solely from reading Pokey's article...this glorious post is right after the pre-reading that follow...glad you finally finished your Pooh-Bah! Should be a good read!
NoSkill20 is offline   Reply With Quote
Old 08-31-2013, 11:01 AM   #16
gamma001's Avatar
Join Date: Dec 2011
Posts: 4,145
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Took me 3 sessions but great read Got me thinking a lot about parts of my game I'm not so sure about. WP TDA
gamma001 is offline   Reply With Quote
Old 08-31-2013, 08:27 PM   #17
TheDefiniteArticle's Avatar
Join Date: Feb 2012
Location: Bristol, UK
Posts: 14,085
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Originally Posted by MMSS View Post
Part 1 - I think this is very good, in fact probably one of the better thought out introductions to this type of thing I've seen. I'd argue some of the examples you gave could have been a bit better, but all in all very very good.

Note - There are also quite a few spots throughout where you've missed a space between words, in case you want to edit them out.

I also think "2.1.4 Example 2" is wrong. That sample size isn't enough to conclude that villain more opens more from the CO & SB than he does from the BTN. He attempts to steal 46%.

8/22 = 36%, then we don't take into consideration how many times he's actually had the chance to steal. Even if we conclude that he's had the chance to open 22 hands in each position (which is a false assumption) this still isn't enough to conclude anything when he is likely opening a large % from each position. It'd be a much more logical conclusion to assume that he opens more from the BTN than he does from the CO he's just been running hot in the CO/cold OTB.

Especially when we take into account villain is playing 50nl and is therefore quite likely to be positionally aware from the start, but I think the argument is strong enough without even taking this into account.

(Will finish the rest later, up to start of 2.2)
With respect to this, you're absolutely right, I don't know what I was thinking. I wrote that section about 2 months ago so I can't even tell you what was going through my head.

Even if we could conclude that villain opened the BTN less from that sample, we can't necessarily conclude that he opens both the CO and the SB more than the BTN.

As for the missing spaces between words, that happened as I put it through the (Word to HTML, HTML to BBCode) converters. I can make a .pdf available which is formatted correctly (will probably post it tomorrow).

Thanks everyone for your comments, you're making me blush.
TheDefiniteArticle is offline   Reply With Quote
Old 09-01-2013, 05:31 AM   #18
Boomeranda's Avatar
Join Date: May 2009
Location: Brisbane, Australia
Posts: 116
Thanks TDA! I'm going to read this thoroughly and then again 100 times. I appreciate the effort you put into this.
Boomeranda is offline   Reply With Quote
Old 09-01-2013, 10:23 AM   #19
Join Date: May 2010
Posts: 3,056
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Read the whole thing and enjoyed it immensely. I learned a lot, some of which helped me in my last session, and it was also great for reviewing concepts I already knew.
subcon1 is offline   Reply With Quote
Old 09-01-2013, 10:27 AM   #20
TiftCountyHick's Avatar
Join Date: Jun 2012
Location: Buford
Posts: 299
Will read. Thanks!
TiftCountyHick is offline   Reply With Quote
Old 09-01-2013, 10:46 AM   #21
outatime's Avatar
Join Date: May 2013
Posts: 202
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Thanks for posting this TDA, this an area that I would like to work on!
outatime is offline   Reply With Quote
Old 09-02-2013, 06:56 AM   #22
TheDefiniteArticle's Avatar
Join Date: Feb 2012
Location: Bristol, UK
Posts: 14,085
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

If anyone wants the pdf, it's here:
TheDefiniteArticle is offline   Reply With Quote
Old 09-02-2013, 07:48 AM   #23
MMSS's Avatar
Join Date: Jul 2013
Posts: 4,584
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Originally Posted by TheDefiniteArticle View Post
If anyone wants the pdf, it's here:
Two questions.

1) Do you mind if I link people to this outside of 2+2?

2) You still haven't edited that part which was wrong in the OP. Why? (more a reminder but I had to make it a question)
MMSS is offline   Reply With Quote
Old 09-02-2013, 09:05 AM   #24
Studebaker Hawk
old hand
Studebaker Hawk's Avatar
Join Date: Jan 2012
Location: Yorkshire
Posts: 1,783
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Thanks TDA, looks awesome.
Have sent it to my kindle to read and study at leisure!

Now if only the mrs hadn't pinched the kindle...
Studebaker Hawk is offline   Reply With Quote
Old 09-02-2013, 09:09 AM   #25
TheDefiniteArticle's Avatar
Join Date: Feb 2012
Location: Bristol, UK
Posts: 14,085
Re: The long-in-the-making TDA Pooh-Bah: On hand-reading (warning: MEGA tl;dr)

Originally Posted by MMSS View Post
Two questions.

1) Do you mind if I link people to this outside of 2+2?

2) You still haven't edited that part which was wrong in the OP. Why? (more a reminder but I had to make it a question)
1) Of course, that's fine.
2) Pdf was made before the OP was posted. I should revise it though, you're right.
TheDefiniteArticle is offline   Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump

All times are GMT -4. The time now is 08:43 PM.

Powered by vBulletin®
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.
Copyright © 2008-2020, Two Plus Two Interactive
Poker Players - Streaming Live Online