Equity, Tools and Winning Strategies
[POKER HAND ANALYSIS]

The Importance of Hand Analysis for Improving Your Poker Strategy

Hand analysis is one of the most crucial skills for poker players at all levels. It allows you to better understand encountered situations, correct mistakes, adjust your strategy, and make better decisions in future hands.

In poker, players must constantly adjust their strategy based on different factors such as stack sizes, position, opponent profiles, and tournament conditions. Hand analysis is a valuable tool for better understanding how these factors influence the decisions we need to make.

Hand analysis helps you better understand your own limitations and biases. For example, you might discover that you're too aggressive or too passive in certain situations, or that you tend to overvalue certain starting hands. By knowing our weaknesses, we can correct them and improve. This requires time and patience, but it can also be very rewarding. Players who take the time to analyze their hands will have a clear advantage over those who don't.

The Goal: Providing Tools for Effective Poker Hand Analysis

This article will provide tools for effectively analyzing poker hands. We'll examine the various questions to consider when analyzing a hand, address equity calculation, the use of tools (tracker and solver) for poker, as well as the impact of stack size, position, and ICM (Independent Chip Model).

The questions to ask when analyzing a poker hand.

Certain questions can serve as a guide to easily analyze a poker hand. Here are the top 9 questions that will help you:

1. What is the game format and what are its implications?

2. What are the player profiles at the table and their history?

3. What are the stack sizes of each player at the table?

4. What is your position at the table and over which players do you have position?

5. What is the range of the opponent(s)?

6. What is your perceived range for other players at the table?

7. What are the different possible options?

8. What are the possible sizings for these decisions?

9. How will the hand play out based on my decision?

By asking questions 1 to 4 preflop and questions 4 to 9 during each decision (between folding, calling, or betting), the analysis will be simplified.

The first questions (1 to 4) will help you identify the overall game situation of the hand. You can then consider the risk of tournament elimination, power dynamics between different opponents through stack sizes, analysis of positions and player profiles.

The following questions (5 to 9) will help you choose the right decision during the current hand for each betting round. These questions are more complicated to answer and require good technical knowledge and solid strategy fundamentals.

Equity Calculation and Counting Outs

Explanation of Equity and Its Importance in Hand Analysis

Equity is an important concept in poker as it allows you to evaluate the relative strength of a hand. Equity refers to the probability that our hand will be the best at showdown, taking into account the community cards and potential hands of our opponents.

When analyzing a hand, one of the questions we should ask ourselves is: what is my hand's equity? If our equity is high, it means we have a good chance of winning the hand, while if our equity is low, it means we have little chance of winning the hand without bluffing.

We can also estimate the probability that our opponent will fold when we bluff. This is called "Fold Equity".

Equity and Fold Equity are important because they help us determine whether we should continue playing a hand or not. If either equity is high, it can justify a raise or a call, while if both classic equity and fold equity are low, it can justify abandoning the hand by checking and folding.

How to Calculate Poker Hand Equity

Poker equity is the probability of winning a hand expressed as a percentage. If a player has 0% equity, they have lost the hand, and if they have 100% equity, they have won the hand. The sum of all players' equity in a hand equals 100%. To calculate equity precisely, you must divide the number of boards that make the player win by the total number of possible boards. Outs are the cards that allow the poker player to win the hand, and they help quickly calculate equity.

To quickly calculate your equity, you can multiply your number of outs by 4 on the flop and by 2 on the turn. At the river, equity is fixed because all cards have already been dealt. EV (Expected Value) is the mathematical expectation of gain from an action. Being EV0 means that the average gain from an action is zero, and the action will be neither winning nor losing.

To know whether to call for a draw, the equity must be higher than the equity needed to be EV0. If the equity is higher than EV0, mathematically you should call the draw. To calculate EV0 when calling, you need to calculate the average pot gain after the call being equal to the call value. The equity needed to be EV0 corresponds to the bet divided by the sum of the bet, the pot, and the opponent's bet.

How to Count Outs in Poker?

To count outs to adjust equity, you must take into account the cards that are already known (in players' hands or on the board) and those that are still unknown. Based on these cards, you can determine how many remaining cards can help each player win the hand.

For example, suppose you have two cards in your hand and there are three cards on the board. This means there are still 47 cards in the deck that can be dealt on the river. If you have a pair of aces, there are only two other aces left in the deck that can improve your hand. If you have a flush draw, there are 9 cards of the same suit remaining in the deck that can improve your hand. These cards that can improve your hand are called outs.

Based on the number of outs you have and the total number of cards remaining in the entire deck, you can calculate your equity. This allows you to know approximately what your chances are of winning the hand, which can help you make strategic decisions based on pot size, number of players involved, and other factors.

Counting Card Combinations to Estimate Opponent Ranges

When estimating an opponent's range, we try to determine the starting hands they could have received during the preflop distribution. We can identify 3 categories of cards:

• pairs

• suited hands

• offsuit hands

The notations h means hearts, s means spades, c means clubs, and d means diamonds.

Counting Pair Combinations

A pair corresponds to two cards of the same value. In a deck, there are 4 cards of the same value, for example Ace of hearts (Ah), Ace of spades (As), Ace of clubs (Ac), and Ace of diamonds (Ad). To form a pair, it's possible to combine these 4 cards in 6 different ways. For a pair, there are therefore 6 possible combinations (AhAs, AhAd, AhAc, AsAd, AsAc, AdAc)

If you think your opponent might have a pair of Aces but an Ace is already in your hand, then your opponent has half the chance of having a pair of Aces. If the Ace in your hand is the heart (Ah), all combinations containing the Ace of hearts are blocked (AhAs, AhAd, AhAc cannot exist).

Counting Suited Combinations

A suited hand corresponds to 2 cards of the same suit. For example, Ace-King suited is written as AKs and corresponds to AK of hearts, AK of diamonds, AK of clubs, and AK of spades. There are only 4 combinations of AKs.

If the King of spades is present in the community cards on the table, your opponent can only have 3 combinations of AKs because the one corresponding to AK of spades can no longer exist.

Counting Offsuit Combinations

An offsuit hand corresponds to 2 cards of different suits, for example Ace of hearts and King of spades. To encompass all combinations of AK of different suits, we write AKo. This corresponds to 12 combinations (AhKs, AhKd, AhKc, AsKh, AsKd, AsKc, AdKs, AdKh, AdKc, AcKs, AcKd, AcKh).

If the Ace of hearts is present in the community cards on the table, your opponent can only have 9 combinations of AKo in play because 3 combinations can no longer exist (AhKs, AhKd, AhKc).

Tools for Analyzing Poker Hands

Sharing Your Hand with Other Players Using Poker Toolkit

While playing poker, you may encounter hands that can cause difficulties during a session. It can be wise to set them aside to take time to examine them in detail and find solutions to the problems they raise.

When analyzing a poker hand, it's important to examine all aspects of the hand from every possible angle. You can consider the ranges of hands that your opponents might have, as well as the range you represent. It's essential to explore different options for each possible action and evaluate the consequences of each choice.

It's possible to perform poker hand analysis alone or in a group. The Poker Toolkit tool allows you to share hands to study with friends, so each person can provide comments at their own pace. This allows for a group poker hand review without all participants needing to be available simultaneously.

Poker Tracker for Gathering Information on Past Hands

Poker trackers are software tools that gather information on past hands to help improve your game. These software tools can be used to track your own play, but also to analyze your opponents' habits.

For example, PokerCopilot is a tracker that allows you to track your play on many online poker rooms whether you're on Windows or MacOS. It records all sessions, the hands you play, and allows you to analyze them in detail, providing statistics on your actions, position, wins and losses, etc.

Poker trackers can also be used to collect information about your opponents. They record hands played by other players at the table and provide statistics on their playing style, aggression, raise frequency, etc. This information can be very useful for adjusting your own game based on your opponents' tendencies. They can be visible directly on the table via the HUD.

The Solver for Obtaining Optimal Solutions

A solver is software that helps solve complex problems using mathematical algorithms to find the optimal solution. In poker, solvers can be used to analyze hands and find the best possible strategy for a given player.

To use a solver, you first need to import the hands to analyze and define the model parameters. The solver will then simulate thousands of possible hands using different scenarios and strategies to determine what is the best action to take in each situation.

Once the solver has completed the analysis, it will provide detailed results, advice such as optimal ranges for each position at the table, best actions to take in each situation, and expected gains for each hand.

It's important to note that using a solver can be very complex and require certain expertise in mathematics and poker. It's also important to consider that solver results should not be followed blindly, as each situation is unique and it's important to adapt your strategy based on table dynamics and your opponents.

Considering Position and ICM in Hand Analysis

The Importance of Position in Poker

Position is a key element in poker, as it determines the order in which players act at the table. Position can have a significant impact on the game and the strategy to adopt for each hand.

Generally, the closer you are to the button, the more advantageous your position. This means you're one of the last to act and can therefore observe your opponents' actions before making a decision. Thus, you have more information about the strength of their hand and can adapt your strategy accordingly.

Position affects the ranges of hands you play. Players in late position can afford to play weaker hands, as they have more information about other players' actions and can therefore adjust their play accordingly. Players in early position, on the other hand, must be more selective in their hand choice, as they have less information about other players' actions and can get raised by players after them.

How to Use ICM for Tournament Decision Making?

ICM (Independent Chip Model) is a method used to evaluate the value of a player's chips in a poker tournament. ICM takes into account the distribution of chips in the tournament among players and the paid places.

The simplified interpretation of ICM is that losing a chip has more value than winning a chip when significant price gaps are present, such as on the bubble or at the final table. When you lose chips and are eliminated, you can't win more money. When you win chips, it doesn't guarantee a better place in the tournament as there are still many hands to play.

If during a final table with 5 players with the following prize structure:

1. €1,000

2. €700

3. €500

4. €350

5. €275

And the following chip distribution:

1. 50,000 chips

2. 15,000 chips

3. 5,000 chips

4. 5,000 chips

5. 5,000 chips

The player with 15,000 chips should avoid playing against the first player with 50,000 chips to avoid elimination. For example, if they have AK and face an all-in raise, they should fold because if they're eliminated, they only win €275, and even if they double up, they're not guaranteed to win the €1,000.

Players with 5,000 chips will try to wait for other players to be eliminated before playing to climb the pay ladder without taking risks.

We find ourselves in a situation where the player with the dominant stack of 50,000 chips can be aggressive with all hands because other players must mathematically fold to optimize their earnings.

When to Call a Draw

How to Calculate the Probability of Completing a Draw?

To calculate the probability of completing a draw, you just need to know the number of cards that complete the draw (the outs) and multiply this number by 4 if both the turn and river are remaining, or by 2 if only the river is left. This gives an approximation of the probability that the draw will complete when the board is finished.

How to Make a Good Decision on a Draw?

To know whether to call a draw, simply calculate the pot odds: required bet / (pot + required bet). We know the probability of the draw completing. The probability of the draw completing needs to be higher than the pot odds.

In some cases, implied odds can exist if you estimate that your opponent will definitely add more chips even if the draw completes. It's then possible to add these to the pot odds calculation: required bet / (pot + required bet + chips from future streets)