• Poker Range Matrix
• Range Matrix Poker Tournaments
• Range Matrix Poker Games

Selecting a range of poker hands from a matrix. Ask Question Asked 1 year, 10 months ago. Active 1 year, 10 months ago. Viewed 290 times 2. I am looking for any.

• We can find a basis for 's range space first by finding a basis for the column space of its reduced row echelon form. Using a calculator or row reduction, we obtain for the reduced row echelon form. The fourth column in this matrix can be seen by inspection to be a linear combination of the other three columns, so it is not included in our basis.
• The Poker Ranges You’ll Need. Here are the ranges that you’ll have to devise for the current stakes and games you play: Opening Ranges – Know what hands you’ll open in various positions (cash and MTT/SNG) as well as at different levels of the MTT/SNG (Early Stages, Mid-Stages, Late Stages).
• I am having some tough time understanding the basic concepts, like range of a matrix A. From what I basically understand, if a set columns in a matrix are linearly independent, i.e. One column in that set can not be derived from linear combination of others, than we can get a bunch of set of vectors by linear combination of the columns of matrix A.

I didn’t consider implementing poker ranges in my first few years of playing poker. One of the problems I used to experience at the tables was what to do with hands that weren’t so obviously strong (AA, AK – raise, raise, raise!) or so obviously weak (27o, J4o – ditch ‘em faster than green grass through a goose). Hands like K9o and 86s always gave me pause when it was folded to me. “Should I open… limp… or just fold?” I’d have to ask myself these questions all the time.

The answer to this problem was to create my own poker ranges. Bringing my off-the-felt analysis to on-the-felt play simplifies the game and ensures I’m making good opening hand decisions.

Finding ranges made by others online can help as a start, but they need to be tweaked and analyzed to fit your games and stakes. You can incorporate your own play style and the population tendencies at your stakes, with your own experiences and hand histories to help guide you in creating them.

The Poker Ranges You’ll Need

Here are the ranges that you’ll have to devise for the current stakes and games you play:

• Opening Ranges – Know what hands you’ll open in various positions (cash and MTT/SNG) as well as at different levels of the MTT/SNG (Early Stages, Mid-Stages, Late Stages).
• 3betting Ranges – You need to know which opponents you’ll 3bet and what you’ll 3bet with, both for value and as semi-bluffs.
• 4betting and 3bet Defending Ranges – Same considerations as your 3bet range.

The Importance of Building Ranges

There are three main reasons why we’d want to build ranges:

1. Simplification – by creating ranges that we drill into our heads, we’ve simplified our game. We’ve put these common spots into our unconscious competence, so we can act without thinking. We’re letting our subconscious mind direct our plays, so our conscious mind has more resources to devote to analyzing more difficult, less common situations. This has the added benefit of allowing for more multi-tabling, which in turn will increase your hourly.
2. Comfort – with your subconscious making decisions for you, you’ll be more comfortable and feel less stress at the tables. You’ll be more likely to avoid tilt and can continue playing longer sessions. Stress at the tables can lead to poor decisions, and making your subconscious work for you will be a great stress reliever.
3. Bringing off-the-felt analysis to on-the-felt play – by spending time off-the-felt, creating a thoughtful range that takes into account your position, blind structure and opponent type, you’ll be able to bring your stress-free analysis of the game onto the felt. How many times have you reviewed a hand history and thought, ‘Why did I fold TT? It’s obvious he’s opening 30%+, and TT dominates him!’ When you’re working on your game off-the-felt, you’re doing so without the stress of in-game play, which allows for more clear and level headed thought. You can spot patterns and weaknesses easier off the felt. Creating your ranges then using them in-game is a way to bring your level-headed, stress-free thoughts from off-the-felt analysis to on-the-felt play.

How to Create Your Poker Ranges

Start by building your own hand table in Excel (or just download this one that I built) like the following example (6-max Mid-level Open Ranges of a micro stakes SNG):

Different colors divide ranges into sub-ranges. For example with Opening Ranges:

• Use one color for your default opening range (dark blue in the example above)
• Utilize another color (green) for an expanded range when there are fish in the blinds
• Use another color (yellow) for an even more expanded range when there are nits in the blinds
• You can use as many colors as you want to differentiate ranges. You can even toss in some bluffs vs regs (red) if you feel it necessary.

Don’t try to memorize the ranges you build. Constant use will help to naturally ingrain them in your Unconscious Competence. Just print, laminate and have at the ready as you play online, and eventually you’ll end up memorizing them (or make flash cards to ensure they get in that noggin quicker).

Consider your opponent’s ranges

When creating your Opening Ranges, you’ll have to have a good idea of what your opponents will likely call or re-raise with. For 3betting Ranges, you’ll have to be aware of what your opponents are likely opening with and what they’ll continue with. And for your 4betting and 3bet Defending Ranges, you’ll have to have a good sense of what your opponents 3bet with and what they’re likely to continue in the hand with. This exercise takes plenty of experience at your stakes. You’ll want to devote a week to creating your ranges, putting them to the test in your sessions and assessing the effectiveness of your ranges through hand history reviews. Then go back and adjust your ranges based on what you’ve found.

Using well thought out, strategic ranges like this won’t turn you into a robot; it will enable you to have an effective game plan to use vs. your opponent’s ranges. You will be bringing your off-the-felt intellect, problem solving skills and controlled emotions to your on-the-felt play.

How do I know my ranges are good?

You can do a few different things to test the precision of your ranges at your stakes and game type:

1. Use Flopzilla

This program gauges the effectiveness of each hand in your range vs. an expected opponent’s range. For example, how well does ATs on the BTN fair vs. a BB cold call range of 30%? “Oh, it has 62% equity? Yep, it’s an open.”

2. Review the Profitability of Specific Hands

Don’t know if A9s should be in your Cut-off open range? Run a filter in your poker tracking software for this hand (I use PokerTracker 4), and specifically when you Raised First-In with it in the CO. Review at least 20 hands in your history and ask yourself if this is an overall profitable hand to open with. Did you lose or win an unexpected amount with it? Do you often wind up with a kicker issue when called, or terrible equity when you call an opponent’s 3bet? Do the players at your stakes call with hands much weaker, allowing you to extract value from them post-flop?

3. Get Help from a Study Group or Forum

Post your ranges in the appropriate threads and solicit feedback. This is a more subjective way to check your ranges, but it could give you insights into aspects of your range that you never considered.

4. Get Feedback on Your Poker Ranges

Your coach (or respected friends) will have plenty of thoughts on how your ranges would fare vs. your opponents, so use his feedback to adjust your ranges, test them on-the-felt, and make adjustments as necessary.

After going through these four modes of feedback, put them into play. Once you’re confident in your ranges, laminate them and use them all the time. *Remember: When you move up in stakes, move to a new site or game format you’ll need to adjust your ranges.

It’s a time consuming process if you do it correctly, but well worth it. Try to enjoy the process, because as your skills increase and you progress through the levels, you’ll be revising your ranges over and over to account for the population tendencies of your new stakes. I hope this first time creating ranges leads to two, three, four, even five or more times for you!

Please share with me your own poker ranges by emailing them to sky@smartpokerstudy.com. I’d love to review them for you and offer you some feedback.

Until next time, study smart, play hard and make your next session the best one yet!

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It’s incredibly difficult to put your opponent on an exact hand. Therefore, most of the time, you have to think in terms of poker hand ranges. Even though you don’t have a specific idea of what cards are in your opponent’s hand, a hand range gives you something to work with.

Beginners may not have thought of this, but winning players make almost all their decisions based on poker hand ranges and knowing the different types of poker hands you might get is extremely important. Your every action changes an opponent’s idea of your hand range and vice-versa. You can have anything when cards are dealt but every fold, call or raise tells something about the range of hands you can have.

Most players fail to make the effort to figure out a hand range. However, every player who intends to be a long-term winner needs to know how to analyze and weight hand ranges.

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Poker Hand Combinations

How to use a poker range calculator? In order to be able to calculate a range of hands, the first thing you need to keep in mind is how many possible hand combinations there are for different types of hands:

So what does the table tell you?

• There are more variations of non-paired hands than pocket pairs.
  For example, if you think an opponent’s hand range is 44 and 87, it’s more likely for the opponent to have 87 (16 combinations) than 44 (six combinations).
• There are four combinations of suited non-paired hands and 12 combinations of off-suited non-paired hands. Knowing this makes it easier to calculate the likelihood of an opponent having a suited hand.

Using Hand Ranges in Poker

Here’s a scenario: you raise with AK-offsuit pre-flop and the opponent calls. You know the opponent calls in this situation 15% of the time. According to Equilab, here’s the top 15% of poker hands (although someone’s 15% can include different hands–for example, one might play 66 rather than KT-offsuit):

You have AK-offsuit, and you’d like to figure out how your hand matches up against the opponent’s hand range. So you use Equilab to calculate it and you see that AK-offsuit has 61.36% equity while the opponent has 38.64%. Sounds like a good deal for you.

Most players assume they’d do well but they have never thought their opponent’s hand range through and evaluated it against their own hand. Once you get the habit of using an equity calculator, you’ll be surprised by how much or little equity certain hands have against certain hand ranges.

Your idea of an opponent’s hand range changes with every decision the opponent makes. So let’s say, instead of calling your raise, the opponent decides to raise, which he does 3.75% of the time. Here’s the hand range:

Based on the opponent’s hand range, he’d now have ~57% equity. When he just calls, you’re still ahead of his hand range; when he re-raises, your AK-offsuit is in trouble.

Poker Range Matrix

Weighted Hand Ranges

But an opponent may play certain hands out of his hand range more often than others. For example, instead of re-raising 100% of the time with 99, he may only do so 50% of the time. Based on your reads, you assign more or less weight to a certain hand in a range of hands and, just like before, calculate how your hand does against it.

And it can make a big difference. For example, an opponent’s hand range is AA and QQ while you have KK. In case the opponent plays both AA and QQ 100% of the time in that situation, you might consider your chances of winning poker around 50%, but if the opponent plays AA 100% of the time and only plays QQ some other % of the time, your chances of winning take a hit. You’d be going against AA the majority of the time.

How to Calculate a Weighted Hand Range

So let’s say you have JJ pre-flop and you’re up against an all-in raise. You think the opponent could do this with AA, KK, QQ, AK, and AQ. How many hand combinations do you beat and how many beat you?

Hand combinations that beat you:

Hand combinations that you beat:

Range Matrix Poker Tournaments

You beat 32 of your opponent’s hand combinations and the opponent beats you with 18 combinations. By using Equilab, we can see that your equity is 42.60%. If, however, the opponent only has AK and AQ 50% of the time (which is a relatively realistic scenario), here’s what happens:

Hand combinations that beat you v2:

Hand combinations that you beat v2:

And by using Equilab, we can see that our equity drops to about 36%. That’s a dramatic difference in the long run. which can make the difference between whether you should call or fold, which obviously depends on pot and bet sizes and how much money you and your opponent have left.

Learning to weight poker hand ranges is worth your while. Weighting hand ranges gives you more accurate information about your chances in different poker situations as long as you determine the hand combinations right. Like in almost every skill game in the world, the more complicated a theory is, the harder it is to execute and the more profitable it is when executed perfectly. With a little bit of work and thinking you’ll get more accurate calculations.

How to Manipulate Hand Ranges

The basic idea of manipulating hand ranges is To make strong hands look weak and the other way around. This way we can get the most out of our hands because either the opponent likes to call when we’ve got a tight range of hands – meaning we can get the money in with a strong hand – or the opponent likes to fold when we’ve got a loose range, meaning we can get the opponent to fold when we have a weak hand.

One of the biggest problems is to recognize what strong and weak play is in an opponent’s opinion. Obviously Lisa and Bart are going to read situations differently and they’re going to end up having different ideas of who’s weak and who isn’t. Another problem is to know who’s been paying attention to the game and who has other things to focus on. You have to rely on the idea that the opponent follows the game at least semi-closely and adjusts his play optimally against your range of hands. Usually it’s easy to tell who’s following the game, though.

The third problem would be to understand how an opponent reacts to the way you play. There are different ways for players to react, obviously, since otherwise all the players would play the same way. Some make logical decisions, some don’t.

Range Matrix Poker Games

All of these points must be taken into consideration when manipulating hand ranges in poker. It’s of no use to build an image for yourself if the opponent pays no attention to the game. It might be counterproductive to build an image if the opponent reacts unlike you expected. You’ll always have to consider these points when building a player image and manipulating your range.

Common Mistakes – Being Optimistic

The biggest mistake when figuring out a hand range is to have too much optimism when making decisions. For example, always believing the best and creating hand ranges that are convenient for you is a huge mistake and misses the whole idea. It’s not just about winning; it’s also about losing the least possible. By realizing your hand range is unprofitable against an opponent’s hand range, you avoid losing money.

Giving Up

Losing is a part of poker and beating most of an opponent’s range doesn’t mean you’ll win all of the pots. You’ll lose a certain percentage of them, and you may even have an extremely unlikely run of losses but such is variance.

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