Game Analysis (2)
Introduction
In this article Why equity calculations are at the core of your analysis
 How you perform different equity calculations
 What "thinking in ranges" means
The article Game analysis (1) introduced you to the most essential basics of some simple analysis methods. In today's article, we will provide you with some more indepth knowledge about the detail analysis.
As a quick reminder, here are the three fundamental questions for your detail analysis.
 When
Continuously, during the course of your session analysis, ideally after each session.  Why
The goal is to identify mistakes as well as potential profit that you missed out on. The analysis will help you become better and better at evaluating situations during the game and at making the right decisions within a relatively short amount of time.  How
Analyse individual hands from sessions that you were unsure about. Your main analysis tool will be tracking software as well as the Equilab; equity analysis will be your most dangerous weapon.
Equity calculations
Equity calculations are at the core of every detail analysis. To be precise: We will usually calculate the required equity and compare it with the analysis performed by the Equilab to see if it's possible at all to achieve this required amount of equity.
Don't worry, we will not throw any complicated formulas or highly scientific details at you now. In fact, this article is a short and compact guide that will show you how you can perform the required calculations quickly and easily. In order to reach this goal, two definitions are important.
 Equity refers to the probability that your own hand will win against a given hand of the opponent.
Theoretically, you could calculate the equity of every hand manually, provided you have a lot of time on your hands over a very long period of time. As that's probably not the case, we will not list the exact calculation steps here and instead refer you to the Equilab, which is much faster at processing these calculations. However, if you want to learn more about the maths behind the topic, you will find everything you need in the article series Mathematical Concepts for No Limit Hold'em.
 The required equity is the minimum probability of winning that you need to get through the situation under the given conditions (pot size, bet size) without losing any money.
Even during the game, it's relatively easy to calculate the required equity because there are no unknown factors involved.
You know how big the potential profit is and you know the risk. So, how often do you have to win under the given circumstances so that you don't lose any money?
This simple formula gives you the required equity:
Required equity = Risk / (potential profit + risk) * 100
The following brief example will illustrate this further.
0.05/0.10 No Limit Hold'em (9handed)
Preflop: Hero is CO with
3 folds, MP2 calls $0.10, MP3 folds, Hero raises $0.50, 3 folds, MP2 calls $0.40
Flop: ($1.15) (2 players)
MP2 bets $0.85, Hero...
What does the calculation look like now? Well, first of all you have to figure out all the required numbers. The potential profit is $2, i.e. the money that was in the pot at the beginning of the betting round plus the opponent's bet.
To call the bet you would have pay $0.85. This is the money you want to risk for a chance to take home the potential profit.
If we put these numbers into the formula, we get the following:
Required equity = $0.85/($2+$0.85) * 100
You risk $0.85 for a chance to win $2. This means the required equity is around 30%.
To check the result, you can reverse the calculation. You win in around 30% of cases and lose in 70%.
Again you need to fill the formula with figures:
Profit: ($2 * 30) / 100 = $0.60
Loss: ($0.85 * 70) / 100 = $0.595
As you can see, with an equity of around 30% you have reached the point where profit and loss balance each other out. A higher equity would lead to theoretical profit in this situation, a lower amount of equity would mean longterm losses.
However, this calculation does not yet say anything about the actual equity of your hand. The formula only tells you the minimum required amount, which you can then compare with the equity calculations in the Equilab.
Easier than you thought, right? Either way, it's still an additional formula that you need to memorise somehow.
However, you can also calculate the required equity with the help of a concept that you should already be familiar with, i.e. pot odds. Pot odds are also calculated from the risk that you have to take (the amount of money you have to invest) and the potential profit (the pot size).
In our example, the pot odds are $2 : $0.85 or 2.35 : 1. This means that the pot is so big that you can afford losing a little more than two times per one instance of winning.
What can you do with that? Easy: You take the first part of the pot odds (2.35), add the latter part (2.35 + 1), divide 1 by the result and multiply this by 100 in order to get a percentage. Sounds more complicated than it really is, as you will see from the following calculation:
Pot size: ($1.15 + $0.85) = $2
Bet: $0.85
Pot odds: 2 : 0.85, equals around 2.35 : 1
1/(2.35 + 1) *100 = 29.85
Again we are getting the 30% required equity.
Want to play some "Find the advantage"?
First of all, you will calculate/have calculated the pot odds anyway. They play a more or less important role in every hand. Calculating the pot odds should therefore be an integral part of every hand that you play.
That way, you can even skip calculating the required equities altogether, if you memorise or print out the following table for example:
Pot odds 
Required equity 
1:1  50% 
2:1 
33% 
3:1 
25% 
4:1 
20% 
5:1 
17% 
6:1 
14% 
7:1 
12.5% 
8:1 
10% 
You can already do a lot with this result. You can compare the required equity with the actual equity of your hand against the opponent's hand. If the required equity is smaller, the play was profitable. If it's the other way around, you "unnecessarily" lost money.
These approximations are definitely sufficient to give you a good first impression. So you don't necessarily need to calculate the equity of each hand to ten thousand decimal places. Instead, you can just round the number.
If the comparison with the actual equity shows that it's a very marginal situation, you can always perform more detailed calculations.
Unfortunately, there are some complicating factors. There are other aspect that come into play, such as the fold equity (how often will your opponent give up?) or the implied pot odds (will the opponent keep investing money, even if you hit a premium hand?).
That's why it is possible that every now and then the calculated equity is smaller than the required equity, while the play itself was indeed profitable. As your experience grows, you will learn to evaluate these situations accurately and make correct decisions.
Fold equity and implied pot odds play a more or less important role in certain situations. Besides the equity calculations, you should also keep in mind fold equity when you bet or raise for example.
If you plan to call a bet however, the focus is on the implied pot odds as well as the required equity. They shouldn't be the main basis for your decision making however. Only in situations where your equity is only slightly below the required equity, a more detailed analysis would be worthwhile.
Thinking in ranges
Unfortunately it is rather rare that your opponent's playing style allows you to put him on the one, correct hand. Usually your hand will be up against an array of possible hands. This array of hands is called a "range".
For the analysis it is essential that you estimate the opponents' ranges as accurately as possible.
How do you go about that? First off: It will be hard to do against entirely unknown opponents. They are unknown for a reason  you know nothing about them and therefore cannot make reliable assumptions about their ranges.
When you put your opponents on a range, all stats that you have on them are important clues. A range is usually determined with the help of the preflop stats VP$IP and PFR and then narrowed down further during each betting round. The postflop stats are again indicators that help you figure out which hands the opponent could be playing like he is.
Let's complete the example we introduced at the beginning of the article by including some stats.
0.05/0.10 No Limit Hold'em (9handed)
Stacks & Stats
MP2: 35/3/0.2 (VP$IP / PFR / AF)
Preflop: Hero is CO with
3 folds, MP2 calls $0.10, MP3 folds, Hero raises $0.50, 3 folds, MP2 calls $0.40
Flop: ($1.15) (2 players)
MP2 bets $0.85, Hero...
Assume for example that a loose passive player is in the hand with you.
Looking at the available stats, you can put him on a relatively wide range on the flop. Your equity should easily meet or even exceed the required 30%.
Something that you should definitely notice here is the extremely low aggression factor.If you see the player suddenly make a hyperaggressive play on the flop, you know that the roof is on fire. The loose preflop range is no longer applicable at all, he will only play aggressively with premium hands.
Which hand combinations are possible here? Possible would be small pocket pairs for example, which turned into a set on the flop. It could also be two pairs, but that's rather unlikely. Which starting hand would give him two pairs here and is playable for this type of player? Not many. That's why you should concentrate on the "set hit" scenario.
Against the made set your hand has a phenomenal equity of 4.34%. That's not quite the required 30%, is it? And you won't reach that amount here, even if you put all your hope in the hand.
Determining the range is the most critical aspect about the analysis process, since you have to base your decisions on mere speculation. However, you don't take into considering for example that the opponent might be on tilt, doing the most unthinkable things. If he has been playing a rational game up until now, you can assume that he will continue playing like that and therefore put him on a smaller range than you would if you knew that he is tilting, going crazy with his chips. Another important aspect here is the overinterpretation of stats.
Let's suppose the following starting situation:
0.05/0.10 No Limit Hold'em (9handed)
Stacks & Stats
BU: 25/10 (VP$IP / PFR)
Preflop: Hero is CO with
5 folds, Hero raises $0.40, BU raises $1.50, 2 folds, Hero...
At first glance you see the PFR of 10%. Against a 10% range you have an equity of 53%.
If you suspect that the 3betting range is a bit more narrow, around 5% for example, the equity changes to 46.56%.
Imagine you take a closer look at the stats and realise that the BU has a 3bet stat of 2%. Okay, no one could anticipate that. Your equity hits the bottom with 19%.
You can see how a few small changes in a range can change the situation from slightly profitable to outrageously negative.
We can't stress often enough how important it is that you define the ranges as accurately as possible. Sometimes, even the smallest changes can decide whether an action leads to profit or loss.
So far we have analysed the ranges of individual opponents. But what if you want to analyse several opponents?
The process itself does not change much. Again you define a range for each remaining player  and you try to do that as accurately as possible  and then calculate the equity. After each action you try to reasonably narrow down the individual ranges and reevaluate the situation afterwards.
A final thing to remember about the topic:
IMPORTANT  
The range of an opponent can only get smaller during the course of a hand. Once you have excluded certain hand combinations from his range, you cannot include them again at a later point. 
When you sit at the table, you won't have much time for your decisions. What counts here is the experience that you have. If you regularly perform detail analyses, you will soon be able to make reliable estimations even during the game, and act accordingly.
Summary
You now have all the information that you need to carry out thorough detail analyses yourself. Try and use this analysis method to improve your understanding of the game. You will soon realise that internalising this process can be a valuable advantage at the tables. In the future, you will then be able to make correct decisions and assess situations more quickly.
The most important aspect about the analysis  and something you can of course do while you are at the tables  is the accurate definition of ranges. Pay attention to the different stats of your opponent, even during the sessions, and try to put them on possible ranges. The more you practice, the better your results will be.
If you are still not sure about certain hands, the professional as well as voluntary hand evaluators at PokerStrategy.com are always happy to help!
LINKS  

#1 adamrothwell, 15 Feb 14 16:51
for the below can we just calculate0.85/(2+0.85) * 100 = 29.8% also could you let me know what technique you used to round 2 : 0.85 to 2.35 : 1 ? cheers :)
"Pot size: ($1.15 + $0.85) = $2
Bet: $0.85
Pot odds: 2 : 0.85, equals around 2.35 : 1
1/(2.35 + 1) *100 = 29.85 "
#2 coperneeque, 15 Oct 14 11:33
adamrothwell,like this:
What ever odds you are calculating they are in fact a ratio of X:Y.
If your Y is not 1 and you want it 1, then just go ahead and use a calculator to make the division of X:Y.
That's how they do it:
2 : 0.85 = 2/0.85 = 2.35 = 2.35/1 = 2.35 : 1
Basic maths dude!
#3 toske1, 13 Mar 15 18:35
ok#4 mirth, 28 Mar 15 14:19
learning to quickly do these approximate calculations during hands will take bit of practice.#5 LyToLV, 11 Jun 15 16:14
i like calcualiting but dont like to do it. :(#6 bubamarasr, 22 Jan 16 22:00
Read it. Thank you.#7 hassux, 25 Jan 16 21:32
k#8 CroZoZo, 26 Apr 16 13:24
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