How to Conduct a Session Review

Introduction

In this article

• Why are reviews important for your development as a poker player?
  
• Review types and tools
  
• Methodology – How do you approach it and what do you need to know?
  

Why are reviews important for your development as a poker player?

Reviewing describes the process of analysing played hands or hand histories in retrospect. This is a necessary tool for every successful poker player. In the long run, your profit comes from making the best possible decisions at the table. To make such decisions in poker is not easy and requires a lot of knowledge and skill. Exchanging ideas about lines, moves, patterns, bet sizing, hand selection, spot selection, table selection and numerous other topics are things that make you a long term winning player in poker.

That's why you should keep in mind: if you want to increase your win rate, you have to be willing to thoroughly work on yourself and your game. This includes things such as good time management, a great deal of discipline and training opportunities.

PokerStrategy.com's hand evaluation forum gives you the opportunity to have your hands analysed by professional hand evaluators. In addition to that, it is important that you continuously analyse, think through and possibly re-evaluate your hands, your decisions and above all the reasons why you played a certain way.

Especially if you have taken up poker only recently, you should regularly set aside some time for training. How much time you spend playing and how much time you spend training is of course up to you. As far as the learning phase is concerned, a rough division into 60% playing phase and 40% training phase can be recommended. After all, you should also be thinking, learning and making continuous progress while you are playing. You could also play sessions for example and focus your attention on particular things (topic focus) that played an important role during your last training. By doing that, you can apply what you have learned or at least increase your awareness of these topic-specific problems.

Review types and tools

In general, there are the following types of reviews: Hand review, hand history review, (video) session review.

Hand review:

• In-depth discussion of a hand and all its details, especially with regard to the lines played and the bet sizing, taking into account all available information on opponent type, opponent's range and opponent's playing tendencies
• Focus on specific decisions in order to identify structural leaks in Hero's game

Hand history review:

• Thorough analysis of several hands that were played in a row at a particular table, taking into account the short-term history
• Collecting and noting down opponent-specific plays (read-building)

Session review:

• Complete analysis of the development of a particular session
• Focus on decisive hands (key moments)
• Continuous identification of leaks in seemingly unimportant (standard) situations

Video review:

• Thorough analysis (breaks are possible) of all game aspects
• Focus on timing tells (Hero and Villain)
• Identification of insecurities regarding bet sizing and line selection (mouse cursor observation)
• Analysis of multi-table spots (with the same opponent at multiple tables at the same time, possibly while involved in a hand with him)

Even though most of the considerations in this article apply to all review forms, the main focus will be on hand reviews. For such reviews you need a number of tools which you have to become familiar with in order to strategically use them for your analysis. What you need:

• a calculator for the necessary calculations in your hand analysis
• a tracking tool (e.g. PokerStrategy.com Elephant, Hold'em Manager) for statistics on your opponent and hand visualisations (Hold'em Manager Hand Replayer)
• equilator software (e.g. PokerStrategy.com Equilator, PokerStove)
• word processing software (e.g. Editor Notepad, OpenOffice) to document your analysis as well as the range assumptions and working hypotheses
• for video reviews: a desktop recording tool (e.g. Camtasia Studio, Fraps)

Methodology – How do you approach it and what do you need to know?

The most important thing you need for a review (besides the above mentioned tools) is an objective. But where do you find this objective? How do you know what you have to do during the reviewing process? The following section will provide an answer to this question.

As explained further above, you generally have the option to analyse a hand in its entirety. When you do this, you try to shed light on and if possible assess specific aspects (lines, bet sizing, etc.) of the hand from your own perspective, taking into consideration all the information you have available. Since it covers everything related to the topic, this "open reviewing" offers you maximum learning effects, since many different aspects can be brought up in the discussion. There are important bits of information about the opponent(s) in the given hand that you have to take into account:

• player type / opponent's image
• his preflop range
• his general level of aggression postflop (how does he play draws? How does he play bottom or top pairs on draw-heavy boards? Is he able to bluff and if so, what is his bet size?)
• specific reads (estimations about playing tendencies: how often does he float or play check/raise?) which are relevant to the situation
• the board structure
• stack sizes
• your own image
• history-related aspects

Poker is a complex game, each hand is embedded in unique conditions. As a good player however, you have to be able to recognise structural elements in each hand and relate them to these specific conditions as much as you can. Therefore it is important to establish a repertoire of structural elements, which are the pillars of your understanding of the game. This structure of your playing system will continuously be refined and your feel for the structures of other playing systems will steadily improve, so that the way you actually apply them to individual hands will become better and better adjusted. That's why training is essential, especially training away from the poker tables, since you will be able to pay more attention to your opponent's behaviour and the exploitation of leaks here.

For open reviews we recommend finding a review partner to discuss the assumptions you make. Your discussion partner usually contributes new ideas about the given hand, which will contribute to your own structural progress. What's important here is that you are open to other opinions on the topic and don't insist on your own understanding of the hand, since otherwise you will miss out on valuable learning opportunities. Poker entails a number of interesting aspects: a constant "what if..." should dominate your training sessions. What's particularly important: You have enough time in this situation to thoroughly analyse everything, so that when you get to the table, you will have an advantage as far as your own preparation is concerned, i.e. an advantage in time and skill.

Your objective in so-called open reviews is not determined from the start, it evolves from the specific circumstances in a given hand. The focus here is on the absolute improvement of your basic poker understanding, i.e. your own overall playing strength. This could include mathematical correlations (How much equity do I have against range x or y? How often does Villain have top pair?), or complex issues such as general dynamics (float or check/raise frequencies) and playing tendencies (which hands does he call, which does he raise? Bet sizing?).

Reviews that deal with a "closed" topic are essentially different. These reviews examine a specific topic and all hands (ideally they were selected for this beforehand) are analysed with respect to this topic. During this process, certain standard arguments (compare the term: "structure elements") are continuously exchanged and then put in relation to each other. The advantage is that when you find yourself in a similar situation at the table, you can evaluate the arguments more quickly since you already know them, and this will usually allow you to make better decisions. Popular topics for such reviews are "blind battle situations", "PFA on paired boards", "pocket pairs on draw-heavy boards with one/two over-cards" "non-PFA against LAGs and maniacs IP", "3-bet pots OOP" and much more. There are no limits to your imagination here. Technically you should choose topics that are relevant in many situations you will encounter at the table, so that you can profit from it as much as possible.

The third review variant is probably the one that you should use the most when you start out. It is a specific question-oriented review. The preparation for it is easy: You highlight a hand in your tracking tool that left you unsure, where you are interested in a particular aspect or that you would simply like to check again. Then you write down the question that you have about this hand and start.

Since this is the main form of specific training, you will learn in the following section how you document your analyses and their results, i.e. how you secure your learning progress so that it sticks to your memory and how you make it applicable to future situations by formulating your progress in a precise manner. Before that, it is essential that you are familiar with certain mathematical basics that are important to reviewing. Only if this is the case can you get correct results in the first place. Above all, you will learn a method that allows you to mathematically estimate the opponent's range. This will help you make as precise estimations as possible about your opponents' ranges and their strengths, which will help you with your decision-making process.

To most questions that you specifically ask about a hand, there is a mathematical answer. Discussing assumptions in poker is something that will rarely lead to safe conclusions. What's decisive in order to ensure maximum reliability are the experiences you have had at a certain limit, ideally with the specific opponent in the hand.

Once you have made an assumption (working hypothesis) however, you can work with it and evaluate the result mathematically. You need to be familiar with a few mathematical basics for this. Learn and improve this basic knowledge by studying the following article series, which illustrates everything you need to know:

Mathematical Concepts for No-Limit Hold'em (1)

Especially the calculation and comparison of the expected values (EVs) of different actions are important factors in a hand review, since the review is the only opportunity you have to do this thoroughly and accurately. You don't have much time for it at the table. As you gain (training) experience, you will become more and more accurate. That's why you should spend a lot of time learning the most relevant concepts, especially as you start out.

What we will do in the following is try to determine hand ranges, i.e. to split them up into their components in order to give you a better, more precise understanding of this topic, which will help you in actual postflop situations. The relevant mathematical foundation is the basic principle of card combinatorics in Hold'em: The game has 52 cards which can form a total of 1326 different hand combinations (abbr. HC) (Mnemonic: "The complete range hits you on Friday, 13th (13), and it does so twice (26)" = 13+26 = 1326.) If you combine every ace with every other ace for example, without allowing any combinations to occur twice, you get precisely 6 hand combinations. When it comes to suited hands, there are exactly 4 possible combinations for each hand category (e.g. AKs), when it comes to offsuit hands there are 12 hand combinations. An overview of this looks as follows:

• 100% = 1326 HC
• of these, 5.88% = 78 HC (6 * 13 HC) are pocket pairs.
• of these, 23.53% = 312 HC (4 * 78 HC) are suited hands.
• of these, 70.59% = 936 HC (12 * 78 HC) are offsuit hands.

This means only every twentieth hand is a pair, only every fourth hand is suited and around 70% of hands are offsuit. There are three times as many offsuit hands as there are suited hands, and for every fourteen offsuit hands there is one pair. This is very important in order to understand how your opponents' hand ranges are composed. Usually, the tracking tool displays a specific stat (e.g. VPIP, PFR, 3-bet, ATS). As a poker player, you then have to be able to assign specific ranges with the specific hands (i.e. hand combinations) they contain to these values. Some players prefer Ax hands, other prefer suited connectors (SC). It is important here to keep in mind that Ax hands are three times as frequent as SC.

In order to methodically determine (or break down: "hand range break-down") hand ranges, you have to follow these steps:

• 1. You highlight all pocket pairs that you think might be in Villain's range, starting from the top ("which other pockets are included?", in the example this would be all: 78 HC - 22+)



• 2. You highlight all suited hands that you think might be in Villain's range and work your way through one high card after the next, starting with the ace and going from the weakest to the highest kicker for each hand (in the example: 174 HC - 22+, A2s+, KTs+, QTs+, J9s+, T8s+, 98s, 87s, 76s).

• 3. You highlight all offsuit hands that you think might be in Villain's range and again work your way through one high card after another and one kicker after the other (in the example: 306 HC - 22+, A2s+, KTs+, QTs+, J9s+, T8s+, 98s, 87s, 76s, A9o+, KTo+, QJo, JTo, T9o).

We will give stereotypical examples of SH preflop ranges for three common player types (Nit, LAG, TAG). Compare the relations between the hand categories within the ranges. This will allow important conclusions relevant to your postflop game:

• What percentage of the range are pocket pairs?
• What percentage of the range are Ax hands?
• What percentage of the range are exclusively broadway cards?
• What percentage of the range are exclusively suited connectors?
• What percentage of the range are offsuit connectors?

Nit Range
Entire range	6.18% 82HC (TT+, AJs+, KQs, AQo+, KQo)
Pocket pairs	TT+: 30HC
A-high	AJs+, AQo+: 36HC (12HC + 24HC)
K-high	KQs, KQo: 16HC (4HC + 12HC)
Categories
Pocket pairs	37% (30HC/82HC)
Ax	44% (36HC/82HC)
Broadways	100% (82HC/82HC)
Only SCs	0%
Offsuit connectors	0%

LAG Range
Entire range	28.81% 382HC (22+, A2s+, K9s+, Q9s+, J9s+, T8s+, 97s+, 86s+, 75s+, 65s, 54s, A7o+, K9o+, QTo+, JTo, T9o)
Pocket pairs	22+: 78HC
A-high	A2s+, A7o+: 132HC (48HC + 84HC)
K-high	K9s+, K9o+: 64HC (16HC + 48HC)
Q-high	Q9s+, QTo+: 36HC (12HC + 24HC)
J-high	J9s+, JTo+: 20HC (8HC + 12HC)
T-high	T8s+, T9o+: 20HC (8HC + 12HC)
9-high	97s+: 8HC
8-high	86s+: 8HC
7-high	75s+: 8HC
6-high	65s: 4HC
5-high	54s: 4HC
Categories
Pocket pairs	20% (78HC/382HC)
Ax	35% (132HC/382HC)
Broadways	50% (190HC/382HC)
Only SCs	14% (52HC/382HC)
Offsuit connectors	6% (24HC/382HC)

TAG Range
Entire range	16.89% 224HC (55+, A7s+, KTs+, QTs+, JTs, T9s, 98s, 87s, 76s, ATo+, KJo+, QJo, JTo)
Pocket pairs	55+: 60HC
A-high	A7s+, ATo+: 76HC (28HC + 48HC)
K-high	KTs+, KJo+: 36HC (12HC + 24HC)
Q-high	QTs+, QJo+: 20HC (8HC + 12HC)
J-high	JTs, JTo: 16HC (4HC + 12HC)
T-high	T9s: 4HC
9-high	98s: 4HC
8-high	87s: 4HC
7-high	76s: 4HC
Categories
Pocket pairs	26.7% (60HC/224HC)
Ax	33.9% (76HC/224HC)
Broadways	74.1% (166HC/224HC)
Only SCs	7.1% (16HC/224HC)
Offsuit connectors	0%

In this example you see how certain ranges are composed. Every player has modified ranges that depend on the given spot. For your analysis you have to try to make estimations about these modifications that are as accurate as possible. Your tracking stats (position-specific PFR / 3-bet stat etc.) along with the overall image that you have of your opponent should be enough to make approximations. If you have precise reads on him, that's even better. What's important with this form of mathematical hand range break-down (compare hand-reading) is that due to methodological principles it is impossible that a hand that is not in Villain's range preflop is in Villain's range postflop. The rule is therefore:

"Over the course of the hand, Villains range will become smaller with every action, but never wider!"

To further analyse the situation mathematically, you can look at how Villain's range has hit the board (the so-called hitting case analysis) in order to determine its relative strength. In a vacuum (without a hand of your own) it is recommended to use a top pair with a good kicker as point of reference. If you have a specific hand, you use that hand as your point of reference of course. The questions that you should ask yourself when it comes to the strength of a hand range are the following:

• What percentage of the range is better than top pair? (Nut part)
• What percentage of the range is paired? (Paired part)
• What percentage of the range has four or more outs in relation to a top pair? (Remaining equity)
• What percentage of the range is taken up by the rest? (Trash part)

Depending on the board structure and the situation, it can be sensible (especially when it comes to making estimations about value bets) to ask more specific questions in your analysis:

• What percentage of the range have a flush draw?
• What percentage of the range have a straight draw (OESDs, gut shots)?
• What percentage of the range consist of each top, middle and bottom pairs?

With these questions, mathematical numbers will help you to quickly develop a feel to figure out which ranges hit which boards, how often someone can continue playing with them and how often he can play for stacks. This is extremely important when it comes to hand-reading. Keep in mind which range your opponent has and specify it further during the course of the hand based on his actions, then use this to justify your decisions at the table.

Generally it is essential to have important specifications (I) about the hand at the start of the documentation, best would be an overview of the entire course of the hand (link to the hand in the PokerStrategy.com hand converter optionally a screenshot of the hand replayer with HUD stats); at least you should have all the information important for the analysis. These are usually: your own hand, table situation details (your own position, Villain's position, stack sizes), HUD stats and notes about Villain's playing tendencies.

On top of that, you should have an objective or at least a specific question for the review before you start your analysis, this is defined as the analysis subject (II). Once you have that, you can start with the actual analysis.

During the course of the analysis (III) it is important that you write down every assumption that you make and, if possible, also express them in mathematical terms, for example by noting down assumptions about ranges  (including the range percentages or hand combinations, which the range contains). Keep in mind that every single action of your opponent provides information. You shouldn't only try to figure out what range he will bet with, but also if you can remove a few hands from his range if he checks, by making use of hand-reading principles. Also, when it comes to bet sizing, you can make assumptions that help you narrow down Villain's range further (in the form of: "with hands xyz Villain would make bigger or smaller bets, that's why I can remove them from his range").

Therefore you need to use every piece of information you have to narrow down your opponent's range as much as possible. Based on these assumptions you can then legitimise, examine and possibly discard your game decisions. Always write down preliminary results as "statements", you can use them later in your analysis conclusion. During the course of the hand you will continuously encounter further analysis assumptions that either narrow down Villain's range or contain information about equity (EQ) and fold equity (FE). When it comes to writing down these analysis components, you should stay consistent. For the required equity or fold equity you could use *EQ and *FE for example (*= required). Along with every assumption you should note down a description (possibly in the form of abbreviated text) and why you are making this assumption.

For example, you do so for the particular ranges on the streets: "PFR range: xyz", "Flop calling range: xyz", "Turn check/raising range"; if you want, you can abbreviate the streets:

• PF (preflop), F (flop), T (turn) and R (river).
• Moreover you should be consistent when it comes to writing down the player's actions: "bet" (b), "call" (c), "raise" (r), "fold" (f), "check behind" (cb), "check/fold" (c/f) "check/raise" (c/r), "check/call" (c/c), "cold call (cc)",
• or for various important analysis abbreviations "all-In" (AI, push), "small/big blind" (sb/bb), the positions (UTG, MP, CO, BU, SB, BB).

Of course you don't have to stick to these abbreviations, what's important though is that you keep a clear overview and that you always know what the abbreviations stand for. It would be ideal if every person from the outside will immediately know what your abbreviations mean. That's why it may be best to use these established abbreviations.

At the end of your documentation, you come up with a conclusion (IV) about the hand based on the assumptions you have made and on the mathematical analyses. This conclusion refers to the initial question for the analysis. The more complex the assumption about the hand, the more complex the conclusion will be, for example in the form of "If Villain xyz, then xyz. However, if Villain yxz, then yxz etc." This means you formulate results for the various assumptions. If assumptions are unclear, you should write down here how they influence a decision in the hand and how big the potential influence (IV-A) on the EV of these decisions is.

It may happen that after you write down your analysis conclusion, you realise that you are interested in an alternative assumption and you want to calculate what influence this assumption has. Instead of starting an entirely new anaysis, you simply add assumption B to your analysis and start calculating from scratch. This analysis branch can be added to your conclusion as part B.

Another general characteristic of the analysis conclusion is that it fixes important things you have learned (IV-B) during the review. You note down all the new things here that you noticed during the analysis (enhancing of your game understanding). There is an infinite number of details that could be included in this. For example that a certain range contains Ax hands more often than you had previously assumed; that this range therefore hits certain boards less frequently. On top of that, you might now see here how this influences his postflop ranges etc.

Don't underestimate the documentation of the things you have learned. It's very easy to forget information that you noticed during the analysis; they might not be essential to the decision in the given hand, but extremely important for your own development as a poker player. That's why it's so important to take your time and write down everything that struck you as new and that might affect your future game decisions.

Hand review - Examples

In section 4, we will now give two examples of such a documentation, which will show you what an overall analysis may look like. There is an infinite number of analysis examples and of course we cannot discuss all of them. Instead we will look at two rather mathematically-oriented examples, the second of which works with somewhat more complex assumptions in order to illustrate analysis branches.

Texas Hold'em No Limit, Big Blind $0.50 (NL50)

Hero (CO) $54.83
Villain (BB) $9.25 VPIP 18, PFR 18, ATS 30, 3-bet 12.8, AF inf, Hands 2.4k, no notes

Preflop: Hero is CO with AJo
Hero raises to $1.50, 2 folds, BB raises to $9.25

Relevant questions for this hand are:

• 1. Is the call with AJo against the short stack's all-in correct?
• 2. Can you already call with ATo here?
• 3. What is the lowest pair you can call here?

1. Determine Villain's preflop pushing range:

• Since he 3-bets against a CO raiser, we will 3-bet slightly tighter than he would against a BU raise, but considerably looser than against a UTG or MP raiser. His range is estimated to be "12.22% - 162 HC" (22+, ATs+, KJs+, ATo+, KQo).

2. Determine the required equity for the planned call:

• Pot = "Open-raise:" 3bb + "SB:" 0.5bb + "Push" 18.5bb = 22bb
• Amount to call = "Push" 18.5bb - "Open-raise" 3bb = 15.5bb; End pot: "Pot" 22bb + "amount to call" 15.5bb - "Rake" 1.8bb = 35.7bb
• Required equity (*EQ) = 15.5bb / 35.7bb = 0.4342

You need an equity of 43.42% for the call.

3. Determine the equity of AJo against Villain's pushing range:

• EQ(AJo, [22+, ATs+, KJs+, ATo+, KQo]) = 44.14%

AJo has enough equity for the call, since 44.14% > 43.42%

4. Determine the equity of ATo against Villain's pushing range:

• EQ(ATo, [22+, ATs+, KJs+, ATo+, KQo]) = 39.53%

ATo doesn't have enough equity for the call, since 39.53% < 43.42%)

5. Determine the lowest pair you could call here:

• EQ(55, [22+, ATs+, KJs+, ATo+, KQo]) = 44.64% 55 can still be called, since 44.64% > 43.42%
• EQ(33, [22+, ATs+, KJs+, ATo+, KQo]) = 38.96% 33 cannot be called, since 38.96% < 43.42%
• EQ(44, [22+, ATs+, KJs+, ATo+, KQo]) = 41.8% 44 cannot be called, since 41.8% < 44.42%

Statement: The lowest pair you can call here is 55.

Assuming that Villain pushes the following range (22+, ATs+, KJs+, ATo+, KQo)...

• 1. ...the call with AJo is correct.
• 2. ...the call with ATo is not correct.
• 3. ...the lowest pair you can call is 55.

Texas Hold'em No Limit 9-max, Big blind $0.50 (NL50)

 
MP2: VPIP 54, PFR 14, ATS 17, AF 3.7, fewer than 150 hands;
Note: has caught your attention with two A-high bluffs

Preflop: Hero is SB with , Villain is MP2 with
MP2 calls, 2 folds, BU calls, Hero calls, BB checks

Flop: ($2) (4 players)
Hero checks, BB checks, MP2 bets $1,50, BU calls, Hero calls, BB folds

Turn: ($6,50) (3 players)
Hero checks, MP2 bets $5,50, BU folds, Hero raises $26,50 (All-In), MP2 calls

River: ($59,50) (2 players)
MP2 wins

The questions in this hand are the following:

• 1. Is the semi-bluff check/raise all-in on the turn profitable?
• 2. If so, is the semi-bluff also profitable if Hero and Villain are 5bb deeper?

1. Determine Villain's open-limping range preflop:

• So far, Villain has appeared to be a donkey who loves to see flops and is able to bluff postflop.
• However, since Villain is able to open-raise a certain part of his range, you assume that you can remove top parts of the range.
• Since he probably plays wide parts of his range but not the maximum range from MP, parts of the bottom range will also be excluded.
• That's why you assume his range to be "36.95% - 490HC" (TT-22, AJs-A2s, K2s+, Q8s+, J8s+, T7s+, 97s+, 86s+, 76s, 65s, AJo-A2o, K7o+, Q9o+, J9o+, T8o+, 98o).

2. Determine Villain's betting range on the flop:

• Since he has shown that he is able to bluff, he will probably not only bluff a lot, but also bet many marginal hands.
• Therefore, in comparison to the preflop range you can only limit his betting range by those hands that didn't hit at all, i.e. all medium cards that have not hit and have no flush draw.
• You cannot be sure whether or not he bets any pair. For methodical reasons however it is reasonable to only exclude hands from the range if it is very plausible to do so. In this case Villain is very aggressive to donkey-like. That's why it would not be plausible to exclude pairs.
• In addition to that, you assume that he will bet most high card hands (A-high and K-high) as well as hands that have an OESD or a gutshot.
• Villain's estimated betting range on the flop is therefore "29.79% - 395HC" (TT-22, AJs-ATs, As9s, As8s, As7s, A6s-A2s, K9s+, K4s-K3s, Q8s+, JsTs, Js9s, Js8s, Ts9s, Ts8s, Ts7s, 9s8s, 9s7s, 8s7s, 8s6s, 76s, 65s, AJo-A2o, K9o+, Q9o+, Jto).

3. Determine Villain's betting range on the turn:

• After the turn doesn't complete the flush draw, you assume that Villain will keep betting with large parts of his range.
• You assume that HERO folds most FDs as well as many weaker pairs on the turn.
• Villain is also likely to value bet/protection bet again against many draws and weak made hands.
• It is possible that the only hands Villain will not bet are those that have only marginal showdown value and take a free card with his draws.
• Of his draws, he will only bet the stronger flush draws and combo hands such as 65s, which have a pair and a flush draw or OESD.
• His estimated range is therefore "17.19% - 228HC" (TT-33, AJs-ATs, As9s, As8s, As7s, A6s-A2s, KQs, Q8s+, JsTs, Js9s, Js8s, Ts9s, Ts8s, Ts7s, 9s8s, 9s7s, 8s7s, 8s6s, 76s, 65s, A6o-A5o, KQo, Q9o+).

4. Formulate the EV formula for the check/raise push "EV=Pot*Pfold + (1-Pfold) * (Equity*Win – (1-Equity)*Loss)":

• "Win" represents the pot after Villain's bet plus the amount he still has to call when HERO has pushed, i.e. WIN = $12 + $21 = $33
• "Loss" represents the amount that Hero invests with his check/raise and wouldn't get back if he loses, i.e. = $26.5
• EV(push) = Pfold * $12 + (1-Pfold) * (EQ*$33 - (1-EQ)* $26.5)

5. Determine Villain's calling range against the push in order to determine "Pfold" and "EQ":

• Since Villain will probably go to the showdown very loosely, he will still call a couple of hands, besides sets these are particularly top pair and most pairs with a draw.
• He will most likely only call flush draws if he has a pair on top of that or he will call randomised, which is why you have to discount some of them.
• Therefore, the estimated range with which he calls HERO's all-in is "11.76% - 156 HC" (TT-33, As9s, As8s, As7s, A6s-A5s, KQs, Q8s+, JsTs, 9s7s, 8s7s, 8s6s, 65s, KQo, Q9o+).
• Calculate fold equity: Pfold = (228HC - 156 HC) / 228 HC = 0.3158 Hero has 31.58% fold equity
• Calculate equity with Ks5s against Villain's calling range to the push: EQ = 0.3866 If Villain calls, Hero has 38.66% equity

6. EV Calculation: EV(push) = Pfold * $12 + (1-Pfold) * (EQ*$33 – (1-EQ)*$26.5)

• Put in the values Pfold and EQEV(push) = 0.3158 * $12 + (1-0.3158) * (0.3866*$33 – (1-0.3866)*$26.5)
• Summary:

  EV(push) = $3.7896 + 0.6842 * ($12.7578 – 0.5394*$26.5)
  EV(push) = $3.7896 + 0.6842 * ($12.7578 - $14.2941)
  EV(push) = $3.7896 + 0.6842 * (-1.5363)
  EV(push) = $3.7896 - $1.0511
  EV(push) = $2.74 The check/raise has a positive expected value of about $2.74

7. EV calculation if Villain is 5bb deeper (assuming that the ranges stay the same):

• Modified course of the hand:

  Turn: ($6.50) (3 players)
  Hero checks, MP2 bets $5,50, BU folds, Hero raises $29 (All-In), MP2 calls

  River: ($64,50) (2 Players)
  MP2 wins pot $64.5

• Calculation of modified WIN and LOSS:
  Win = $12 + $23.5 = 35.5
  Loss = $29
• Formulating modified EV formula: EV(push) = Pfold * $12 + (1-Pfold) * (EQ*$35.5 – (1-EQ)*$29)
• Put in Pfold and EQ: EV(push) = 0.3158 * $12 + (1-0.3158) * (0.3866*$35.5 – (1-0.3866)*$29)
• Summary:
  EV(push) = $3.7896 + 0.6842 * (13.7243 – 0.6134*$29)
  EV(push) = $3.7896 + 0.6842 * (13.7243 - 17.7866)
  EV(push) = $3.7896 + 0.6842 * (-$4.0623)
  EV(push) = $3.7896 + (-$2.7794)
  EV(push) = $1.0102 (  Although the effective stack is bigger by 5bb, the play has a positive expected value of $1.01)

Provided that the assumptions about Villain's ranges are correct, the check/raise on the turn is correct and has a very high expected value. Even increasing the effective stack by 5bb didn't change much about that, which is due to the fact that the equity against Villain's calling range on the turn is still very high. If his ranges becomes much tighter there, the expected value will probably drop considerably. Until the hand is actually played, you can only speculate about Villain's hands. Due to the high equity of K5s on the turn, the EV will most likely never be really bad.

Conclusion

In this article you learned about the different review types and which advantages each of them has and which tools you need in order to employ them. The last section with the hand analysis examples showed you how to approach these reviews. Since you do not always have enough time to document everything in detail, it makes sense to only make quick notes about the range calculations. However, it is important to know how you should generally conduct a review whenever you have specific questions about a hand. This may be a mathematical analysis or a comprehensive discussion of assumptions.

What's important when studying poker is that you always take enough time to conduct reviews - whether on your own, with friends, coaches or a group of other poker players - or that you have your game reviewed by the great number of hand evaluators you can find at PokerStrategy.com. Use these resources to improve your game in the long run. During or after your sessions, highlight the hands that you want to know more about, that need clarifying or discussing, and note them down for a review session or put them up for discussion on the forum. You can also use these reviews for training, by focusing on certain game-theoretical questions and using specific hand material for illustration purposes.

Independent of the review type you choose, it is always important to work on your game, to continuously implement new ideas and impulses into your game, i.e. to internalise the structure of the thought processes involved in the decision making process at the table. This is like water to fish. Keep that in mind.

LINKS
Discussion forum: Discuss this article in the forum