Matrix Poker
2021年2月28日Register here: http://gg.gg/oh3ic
Recently, one of the most popular online poker rooms in the world, Full Tilt Poker, introduced Matrix Sit and Gos.The concept is pretty symbol: battle against eight other online poker players on. 1887 Matrix Blvd, San Jose, CA 95110 (Directions) Phone: (408) 244-3333 ext. 160 Minimum Age: 21 Poker Tables. Card Room Casino M8trix Details. Phone-in list: 1. 1887 Matrix Blvd. San Jose, CA 95110. Report missing or incorrect information. General Game Information Runs Always. All Vegas Poker is now part of PokerAtlas,.
Guest Post by Alex Rousso, May 22, 2014 Part 1 – How to use The MatrixIntroductionMatrix Poker Tournament
Poker has one of the longest learning curves of any game. Trying to learn the game can at first be bewildering. All the talk of odds and strategy seems like alchemy when you only know the basics.
But there’s a simple principle at the heart of the game which will govern 90% of what you need to know. From there, it’s just a question of playing the game, applying that principle and gaining experience.Matrix Poker Tournaments
I’m going to give you a simple tool – a representation of that principle – which will help make the right decisions in a hand of poker. Not just before the flop, but on every street and for pretty much any situation. Believe it or not, even high level pros are enacting an advanced form of what’s presented below; it’s that fundamental.
I’m going to assume you know the very basics of poker – hand values, how betting works, and so on. If you don’t know these things, most poker websites will have a beginners guide explaining them. The matrix below should then serve as your most fundamental learning tool in the game, something that you can keep coming back to. The basic principle of money-making poker
The principle is this:the way to make money in poker is to lose less from the bad situations and gain more from the good situations than your opponents do. That’s it. That’s money-making poker.
This principle is based on a very important observation: in the long run, everyone gets dealt the same mix of cards – you’ll end up having the same situations as everyone else, in the same frequency. You simply make money in the game by playing each situation more profitably than your opponents do. To be explicit: your task when you get Aces and your opponent gets Kings is to make more money than you lose in the reverse situation, i.e. when you get Kings and your opponent gets Aces . . .
. . . and so on through all the possible permutations in poker. As I say, if you play poker for long enough, eventually all possibilities will befall you in roughly equal measures in comparison to your opponents.
Another way to put it is that poker is a game of mistakes, and the key is to make fewer mistakes than your opponents. This is where the poker decision matrix comes in.
The matrix sets your hand against your opponent’s in terms of good hand versus bad hand. This may seem overly simplified, but you can add complexity (e.g. against multiple opponents) as you gain experience. When you start out in poker, the very first distinction you have to make is simply to play the good hands and fold the bad hands.
Before the flop, that’s a question of knowing which are the good hands. Once again, an introductory poker text will explain these.
After the flop, the permutations increase, and that’s where it starts to get more complex. A second distinction arises here. Bad hands (tend to) remain bad hands, but good hands split into two broad categories: those that remain good on their inherent strength (hands like AA, KK, etc.), and those which can improve on the flop. We’ll call these hands “development hands”.
Development hands are usually drawing hands such as suited cards, connected cards and low to medium pairs. They all have the potential to develop into major hands (i.e. flushes, straights and sets respectively). Once again, the simple approach at the beginning is to view these hands in a polarized manner. Either they do develop, in which case they are good hands, or they don’t, in which case they are bad. Play the good hands, fold the bad hands, add complexity as you become more experienced.
As I say, you can extrapolate to most eventualities in poker from the matrix. You may have heard, for example, that drawing hands are “semi-bluffing” hands. This simply means that until you hit them, you can assume it’s likely that your opponent has a better hand. If you bet your hand, it’s a bluff: to try to get your opponent to make a mistake by folding a better hand. However, if you hit your draw, you are subsequently betting for value: now you’re trying to get your opponent to call with a worse hand. Classifying the situations
The key to improving at poker is to get better at knowing whether the hand you hold is better or worse than your opponent’s. It follows that as you get better at the game, more and more of the situations you find yourself in can be pigeonholed as cell B or C in the matrix (see above), and fewer of them will be A and D. All the extra trickery such as reading tells, managing your emotions, understanding table dynamics, categorizing opponent playing styles, and so on, are simply augmentations of that basic approach.
In an ideal world, you’d like it to be clear whether you have the worse or better hand in all the situations you find yourself. That way, you know how you can get your opponent to make a mistake, which is how you make money from the game.
Cells A and D are essentially where you’re in the dark about your hand in comparison with your opponent’s. Those are the tough decisions. The key when you’re a beginner is to simplify your decisions by choosing hands which make it much more likely that you can identify the situation as either a “B” or a “C” rather than an “A” or a “D”. Getting to intermediate
That covers basic strategy for the beginner. To become an intermediate player, you have to learn how to make more profit, more frequently from the times you find yourself in cells B and C. For the record, advanced players not only excel at these two basic strategies (getting to cells B or C and playing them profitably when you get there), they also excel at determining what to do in cells A and D. In part two, I’ll explain the intermediate strategy in more detail.The Poker Decision Matrix – Part 2
The fundamental lesson from part 1 was this: beginners get better at poker by pushing more decisions away from cells A and D in the Matrix and towards cells B and C. The distinction we want to make is not between a good hand and a bad hand, but between knowing where we are in a hand versus not knowing where we are (regardless of whether we are ahead of or behind our opponent). Not knowing can be very costly.
So let’s reform the poker decision matrix to study which situations we are more likely to know where we are. This time, we’ll consider each situation in terms of how sensitive it is to information you have about your opponent’s hand:Matrix 3: Sensitivity to information about your opponent’s hand
As you can see, I’ve discounted situations where we have a bad hand. Yes, for many people the appeal of poker is playing a big pot where their opponent finally folds and they get to show 7-3 offsuit proudly, but you rarely see how much money they blow trying to chase that glory. If you want to make money from the game as a beginner, best to keep it simple at first, and deny yourself this conceit.
How to make money on roulette table top. I’ve also now split the hands we play into development and premium. Let’s consider the six relevant cells in turn, and the kind of things you need to look for to increase your chances of making a profit:Premium Hand (You) v Premium Hand (Opponent) – Medium/High Sensitivity
This cell is quite high on information sensitivity. But don’t beat yourself up if you lose the lot with your KK against AA. The primary thing here is that by playing tighter, you’ll increase your wins in this cell because your opponents will be more likely to think that weaker hands are premium. For example, more often in a tournament they will go all in with AQ than you do. So you’ll find yourself in more AK v AQ match-ups than the reverse AQ v AK.
As time goes on, you will become more sensitive to the information that’s out there. Some players will only ever four-bet preflop with Aces. To them, you can fold your Kings. Some players will think that all sorts of rubbish is worth gambling with. Against them, you can happily call it all off with Jacks.Premium Hand (You) v Development Hand (Opponent) – High Sensitivity
To the beginner, and indeed the seasoned pro, this can be one of the trickiest situations to deal with. Is your opponent stubbornly calling with a great made hand, or a draw? When the draw hits and they start betting, are they bluffing or do they have it? This is why this cell is the most highly information sensitive. You can lose your stack here and feel justified in doing so, but will always wonder after the fact whether it was “obvious” that they had it.
Some tips: give more credit to tight players – if they bet, and keep betting, they probably do have it. Loose players come in different shapes and sizes. Some love drawing hands, some love any old trash and just try to represent that they’ve hit. Keep an eye on playing styles throughout the game. Sticking with your hand can be a risk, make sure it’s an informed one.Premium Hand (You) v Bad Hand (Opponent) – Low sensitivity
This is one of the few areas in poker where ceding control of the hand to your opponent might be more profitable. Dan Harrington called it “rope a dope” because you’re trying to give the impression that you will let your hand go if only you are pushed enough. Sure, occasionally their 8-5 offsuit will hit two pair on the river and you’ll lose a big one, but overall, you’ll make more than you lose, and that’s the name of the game.(Good) Development Hand (You) v Premium Hand (Opponent) – Low sensitivity
As mentioned in part 1, this is a relatively easy one. Of course, you won’t know that you’re up against a premium hand, but in some cases you can have a good idea. Tight players play premium hands straightforwardly, almost broadcasting how anxious they are not to get their Aces busted AGAIN. It’ll be hard to bluff any kind of opponent with this class of hand, but you can certainly get value from most of them if you hit.(Good) Development Hand (You) v Development Hand (Opponent) – Medium/Low Sensitivity
This is a funny situation, reminiscent of the Seventies cartoon “Spy vs Spy” where two opponents try ever more to outgun each other. The key here is that your selection of these hands will be tighter than your opponents’. You are more likely to bet nut flush draws (i.e. A-6 suited rather than Q-6 suited) and high straight draws (J-T makes more nut straights than 7-6). If both you and your opponent hit a flush, you’ll have a big pay day.
The reason for the medium element of information sensitivity is because you’ll have a tough decision if you miss. Is your Ace high good anyway so you don’t need to bluff the river? If your opponent has hit, will they let go based on the betting line you’ve taken? Be sensitive to how you’ve bet during the hand and make sure a river bet makes sense to your opponent (as a value bet, I mean!). Players who look like they’ve been drawing for the whole hand and then suddenly bet on the river when the draw hasn’t come in are easy to pick off.(Good) Development Hand (You) v Bad Hand (Opponent) – Medium Sensitivity
The fact that your opponent could have anything won’t help with your marginal hands. Of course, if you hit your draw, that’s the easy part. But if you miss it’s tough to know whether a bluff will get through in this situation. I think this is the most appropriate spot for a so-called “three barrel bluff” – i.e. if you’ve semi-bluffed the flop and the turn with your draw and you think your opponent has nothing brilliant, it’s probably profitable to fire the third barrel on the river. After all, they know you’re tight and probably wouldn’t go this far with nothing. However, at this point in the hand, you should be satisfied that your opponent does not hold a monster and is practising his own “rope-a-dope”.
Alex Rousso is a food importer, journalist, poker player and coach with a PhD in Memetics - the study of cultural evolution. He has written extensively about winning psychology and risk in everyday life, on topics including financial risk management, game theory, statistical analysis, emotional discipline, and risk psychology. He has a BA from Nottingham University and MSc and PhD from the University of East Anglia. Alex is an Omaha/Omaha-8 specialist and a columnist for Bluff Europe and Titan Poker.Further Reading:
Get Amazing Benefits by Signing Up
Poker and the Bible
Texas Hold’em Poker Guide
Why Poker Is Better than Sex
What do you think about the Poker Matrix? Comment below and let us know! View the discussion thread. We will abbreviate the types of Texas Hold’em formations as follows: 1p – one pair; 2p – two pairs, 3k – three of a kind; st – straight; fl – flush; fh – full house; and 4k – four of a kind. By hand we mean the card configuration of the entire board (community board and your own hole cards), along with the number of your opponents in play at the moment of analysis. This holds for any poker variation.For any type of formation F , we denote by the probability of F being achieved by river by your own hand and by the probability that at least one opponent will achieve something higher than F, if you will achieve F.
For any hand and type of formation F, we call the pair the strength vector of that hand with respect to F.Example: Community cards: (8♦ 5♠ 2♣) (flop stage) Your own hole cards: (2♥ J♦) 4 opponentsFor full house (fh), we have and (For computing we must consider all possible reconstitutions of the community board in the river stage, in the assumption you achieve a full house by river, then calculate the q probability for each case, and then using some probability formulas for obtaining the overall probability. This process of calculation is described in detail in the chapter Evaluating the strength of a hand of the book Texas Hold’em Poker Odds for Your Strategy, with Probability-Based Hand Analyses). The strength vector of this hand with respect to full house is (2%, 41%) and reads as follows: You have about 2% chance for achieving a full house by river; in case you do achieve it, your opponents have about 41% chance of beating it.Definitely, it is a weak hand with respect to full house: only 2% chance of achieving it and then 41% chance of loosing (59% of winning) with it. Thus, you might consider other inferior formations to analyze.
If is the strength vector of a hand with respect to F, we call the number the strength indicator of that hand with respect to F.
In our previous example, the strength indicator of the hand with respect to full house is .
is also a probability, namely the probability that you will achieve a formation of type F by river and none of your opponents will achieve something higher, if you achieve it.
If we were to consider all types of formations (from one pair to four of a kind) and do the same calculations for each of them, we would end up with seven strength vectors, one for each type of formation. These seven vectors would give us the whole image of the strength of that hand. In fact, they form a 2 x 7 matrix of probabilities.
For each hand, we call the matrix the strength matrix of that hand.
On the first row of the strength matrix are the probabilities of the own hand achieving the various types of formations by river. On the second row are the corresponding probabilities that your opponents (at least one) will achieve something higher than you by river, if you will achieve that expected type of formation. Each column corresponds to a type of formation (1p, 2p, 3k, s, fl, fh, 4k). Each hand has an unique associated strength matrix, whose elements are calculable manually or by software program.
Conventions. The following conventions were established in order to compute a strength matrix more easily:
- Straight flush has not been included on the last column as the highest type of formation. In fact, it is included in the flush type. When you hit a straight flush, there is nothing to analyze - you should put all in.
- We replace by 0 the elements of any column of a type of formation that is included at the moment of analysis or will be included – should it occur – by river in a superior type of formation. By this convention, the ignored type of formation F gets a null probability of being achieved and consequently a null probability for the opponents to beat it if it occurs . Thus, it practically comes out of the hand analysis. For instance, the strength matrix associated to a hand in turn stage where you have a full house, has the form .
In this case, one pair, two pairs, and three of a kind cannot be achieved as the full house includes and cancels them, and straight is impossible since you have at maximum two cards of it. Thus full house and four of a kind remain to be dealt with.
Interpretation. As the strength of a poker hand can only be expressed through mathematical probabilities of final events, the strength matrix is the most adequate object to picture such strength. When we evaluate the strength of a hand by interpreting its strength matrix, we actually assume a scale on which to place that strength, and implicitly a relation order over all possible hands. This is what “how strong is it” means in mathematical terms. Assuming we have the strength matrix of a hand we want to analyze, how will we actually interpret it? The rough rule is: The higher the p-probabilities and the lower the q-probabilities, the stronger the hand. However, if we consider the p row, it is better for the p-probabilities to be higher in the second part than in the first, as the second part corresponds to the most valuable achievements. In fact, a high value of a p-probability for only one type of formation of the second part (s, fl, fh, or 4k) may be sufficient for considering the hand strong enough for aggressive raising, as example. Having high values of the p-probabilities in the first part (for 1p, 2p, or 3k) is not a positive factor in the hand’s strength, since consequently we will have lower values in the second part, which means that the most valuable formations are unlikely to be achieved. This happens because the sum of the p-probabilities has an upper bound. The strength matrix cannot be interpreted only by the p-row. The q-probabilities are also important, as they can raise or temper the trust one may have in the corresponding p-probabilities with respect to the outcome of the decision made basing on them. For example, if a strength vector for a type of formation shows (0.55, 0.73), one may not rely on that good p-probability of over 50%, as long as the opponents may beat him/h
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Recently, one of the most popular online poker rooms in the world, Full Tilt Poker, introduced Matrix Sit and Gos.The concept is pretty symbol: battle against eight other online poker players on. 1887 Matrix Blvd, San Jose, CA 95110 (Directions) Phone: (408) 244-3333 ext. 160 Minimum Age: 21 Poker Tables. Card Room Casino M8trix Details. Phone-in list: 1. 1887 Matrix Blvd. San Jose, CA 95110. Report missing or incorrect information. General Game Information Runs Always. All Vegas Poker is now part of PokerAtlas,.
Guest Post by Alex Rousso, May 22, 2014 Part 1 – How to use The MatrixIntroductionMatrix Poker Tournament
Poker has one of the longest learning curves of any game. Trying to learn the game can at first be bewildering. All the talk of odds and strategy seems like alchemy when you only know the basics.
But there’s a simple principle at the heart of the game which will govern 90% of what you need to know. From there, it’s just a question of playing the game, applying that principle and gaining experience.Matrix Poker Tournaments
I’m going to give you a simple tool – a representation of that principle – which will help make the right decisions in a hand of poker. Not just before the flop, but on every street and for pretty much any situation. Believe it or not, even high level pros are enacting an advanced form of what’s presented below; it’s that fundamental.
I’m going to assume you know the very basics of poker – hand values, how betting works, and so on. If you don’t know these things, most poker websites will have a beginners guide explaining them. The matrix below should then serve as your most fundamental learning tool in the game, something that you can keep coming back to. The basic principle of money-making poker
The principle is this:the way to make money in poker is to lose less from the bad situations and gain more from the good situations than your opponents do. That’s it. That’s money-making poker.
This principle is based on a very important observation: in the long run, everyone gets dealt the same mix of cards – you’ll end up having the same situations as everyone else, in the same frequency. You simply make money in the game by playing each situation more profitably than your opponents do. To be explicit: your task when you get Aces and your opponent gets Kings is to make more money than you lose in the reverse situation, i.e. when you get Kings and your opponent gets Aces . . .
. . . and so on through all the possible permutations in poker. As I say, if you play poker for long enough, eventually all possibilities will befall you in roughly equal measures in comparison to your opponents.
Another way to put it is that poker is a game of mistakes, and the key is to make fewer mistakes than your opponents. This is where the poker decision matrix comes in.
The matrix sets your hand against your opponent’s in terms of good hand versus bad hand. This may seem overly simplified, but you can add complexity (e.g. against multiple opponents) as you gain experience. When you start out in poker, the very first distinction you have to make is simply to play the good hands and fold the bad hands.
Before the flop, that’s a question of knowing which are the good hands. Once again, an introductory poker text will explain these.
After the flop, the permutations increase, and that’s where it starts to get more complex. A second distinction arises here. Bad hands (tend to) remain bad hands, but good hands split into two broad categories: those that remain good on their inherent strength (hands like AA, KK, etc.), and those which can improve on the flop. We’ll call these hands “development hands”.
Development hands are usually drawing hands such as suited cards, connected cards and low to medium pairs. They all have the potential to develop into major hands (i.e. flushes, straights and sets respectively). Once again, the simple approach at the beginning is to view these hands in a polarized manner. Either they do develop, in which case they are good hands, or they don’t, in which case they are bad. Play the good hands, fold the bad hands, add complexity as you become more experienced.
As I say, you can extrapolate to most eventualities in poker from the matrix. You may have heard, for example, that drawing hands are “semi-bluffing” hands. This simply means that until you hit them, you can assume it’s likely that your opponent has a better hand. If you bet your hand, it’s a bluff: to try to get your opponent to make a mistake by folding a better hand. However, if you hit your draw, you are subsequently betting for value: now you’re trying to get your opponent to call with a worse hand. Classifying the situations
The key to improving at poker is to get better at knowing whether the hand you hold is better or worse than your opponent’s. It follows that as you get better at the game, more and more of the situations you find yourself in can be pigeonholed as cell B or C in the matrix (see above), and fewer of them will be A and D. All the extra trickery such as reading tells, managing your emotions, understanding table dynamics, categorizing opponent playing styles, and so on, are simply augmentations of that basic approach.
In an ideal world, you’d like it to be clear whether you have the worse or better hand in all the situations you find yourself. That way, you know how you can get your opponent to make a mistake, which is how you make money from the game.
Cells A and D are essentially where you’re in the dark about your hand in comparison with your opponent’s. Those are the tough decisions. The key when you’re a beginner is to simplify your decisions by choosing hands which make it much more likely that you can identify the situation as either a “B” or a “C” rather than an “A” or a “D”. Getting to intermediate
That covers basic strategy for the beginner. To become an intermediate player, you have to learn how to make more profit, more frequently from the times you find yourself in cells B and C. For the record, advanced players not only excel at these two basic strategies (getting to cells B or C and playing them profitably when you get there), they also excel at determining what to do in cells A and D. In part two, I’ll explain the intermediate strategy in more detail.The Poker Decision Matrix – Part 2
The fundamental lesson from part 1 was this: beginners get better at poker by pushing more decisions away from cells A and D in the Matrix and towards cells B and C. The distinction we want to make is not between a good hand and a bad hand, but between knowing where we are in a hand versus not knowing where we are (regardless of whether we are ahead of or behind our opponent). Not knowing can be very costly.
So let’s reform the poker decision matrix to study which situations we are more likely to know where we are. This time, we’ll consider each situation in terms of how sensitive it is to information you have about your opponent’s hand:Matrix 3: Sensitivity to information about your opponent’s hand
As you can see, I’ve discounted situations where we have a bad hand. Yes, for many people the appeal of poker is playing a big pot where their opponent finally folds and they get to show 7-3 offsuit proudly, but you rarely see how much money they blow trying to chase that glory. If you want to make money from the game as a beginner, best to keep it simple at first, and deny yourself this conceit.
How to make money on roulette table top. I’ve also now split the hands we play into development and premium. Let’s consider the six relevant cells in turn, and the kind of things you need to look for to increase your chances of making a profit:Premium Hand (You) v Premium Hand (Opponent) – Medium/High Sensitivity
This cell is quite high on information sensitivity. But don’t beat yourself up if you lose the lot with your KK against AA. The primary thing here is that by playing tighter, you’ll increase your wins in this cell because your opponents will be more likely to think that weaker hands are premium. For example, more often in a tournament they will go all in with AQ than you do. So you’ll find yourself in more AK v AQ match-ups than the reverse AQ v AK.
As time goes on, you will become more sensitive to the information that’s out there. Some players will only ever four-bet preflop with Aces. To them, you can fold your Kings. Some players will think that all sorts of rubbish is worth gambling with. Against them, you can happily call it all off with Jacks.Premium Hand (You) v Development Hand (Opponent) – High Sensitivity
To the beginner, and indeed the seasoned pro, this can be one of the trickiest situations to deal with. Is your opponent stubbornly calling with a great made hand, or a draw? When the draw hits and they start betting, are they bluffing or do they have it? This is why this cell is the most highly information sensitive. You can lose your stack here and feel justified in doing so, but will always wonder after the fact whether it was “obvious” that they had it.
Some tips: give more credit to tight players – if they bet, and keep betting, they probably do have it. Loose players come in different shapes and sizes. Some love drawing hands, some love any old trash and just try to represent that they’ve hit. Keep an eye on playing styles throughout the game. Sticking with your hand can be a risk, make sure it’s an informed one.Premium Hand (You) v Bad Hand (Opponent) – Low sensitivity
This is one of the few areas in poker where ceding control of the hand to your opponent might be more profitable. Dan Harrington called it “rope a dope” because you’re trying to give the impression that you will let your hand go if only you are pushed enough. Sure, occasionally their 8-5 offsuit will hit two pair on the river and you’ll lose a big one, but overall, you’ll make more than you lose, and that’s the name of the game.(Good) Development Hand (You) v Premium Hand (Opponent) – Low sensitivity
As mentioned in part 1, this is a relatively easy one. Of course, you won’t know that you’re up against a premium hand, but in some cases you can have a good idea. Tight players play premium hands straightforwardly, almost broadcasting how anxious they are not to get their Aces busted AGAIN. It’ll be hard to bluff any kind of opponent with this class of hand, but you can certainly get value from most of them if you hit.(Good) Development Hand (You) v Development Hand (Opponent) – Medium/Low Sensitivity
This is a funny situation, reminiscent of the Seventies cartoon “Spy vs Spy” where two opponents try ever more to outgun each other. The key here is that your selection of these hands will be tighter than your opponents’. You are more likely to bet nut flush draws (i.e. A-6 suited rather than Q-6 suited) and high straight draws (J-T makes more nut straights than 7-6). If both you and your opponent hit a flush, you’ll have a big pay day.
The reason for the medium element of information sensitivity is because you’ll have a tough decision if you miss. Is your Ace high good anyway so you don’t need to bluff the river? If your opponent has hit, will they let go based on the betting line you’ve taken? Be sensitive to how you’ve bet during the hand and make sure a river bet makes sense to your opponent (as a value bet, I mean!). Players who look like they’ve been drawing for the whole hand and then suddenly bet on the river when the draw hasn’t come in are easy to pick off.(Good) Development Hand (You) v Bad Hand (Opponent) – Medium Sensitivity
The fact that your opponent could have anything won’t help with your marginal hands. Of course, if you hit your draw, that’s the easy part. But if you miss it’s tough to know whether a bluff will get through in this situation. I think this is the most appropriate spot for a so-called “three barrel bluff” – i.e. if you’ve semi-bluffed the flop and the turn with your draw and you think your opponent has nothing brilliant, it’s probably profitable to fire the third barrel on the river. After all, they know you’re tight and probably wouldn’t go this far with nothing. However, at this point in the hand, you should be satisfied that your opponent does not hold a monster and is practising his own “rope-a-dope”.
Alex Rousso is a food importer, journalist, poker player and coach with a PhD in Memetics - the study of cultural evolution. He has written extensively about winning psychology and risk in everyday life, on topics including financial risk management, game theory, statistical analysis, emotional discipline, and risk psychology. He has a BA from Nottingham University and MSc and PhD from the University of East Anglia. Alex is an Omaha/Omaha-8 specialist and a columnist for Bluff Europe and Titan Poker.Further Reading:
Get Amazing Benefits by Signing Up
Poker and the Bible
Texas Hold’em Poker Guide
Why Poker Is Better than Sex
What do you think about the Poker Matrix? Comment below and let us know! View the discussion thread. We will abbreviate the types of Texas Hold’em formations as follows: 1p – one pair; 2p – two pairs, 3k – three of a kind; st – straight; fl – flush; fh – full house; and 4k – four of a kind. By hand we mean the card configuration of the entire board (community board and your own hole cards), along with the number of your opponents in play at the moment of analysis. This holds for any poker variation.For any type of formation F , we denote by the probability of F being achieved by river by your own hand and by the probability that at least one opponent will achieve something higher than F, if you will achieve F.
For any hand and type of formation F, we call the pair the strength vector of that hand with respect to F.Example: Community cards: (8♦ 5♠ 2♣) (flop stage) Your own hole cards: (2♥ J♦) 4 opponentsFor full house (fh), we have and (For computing we must consider all possible reconstitutions of the community board in the river stage, in the assumption you achieve a full house by river, then calculate the q probability for each case, and then using some probability formulas for obtaining the overall probability. This process of calculation is described in detail in the chapter Evaluating the strength of a hand of the book Texas Hold’em Poker Odds for Your Strategy, with Probability-Based Hand Analyses). The strength vector of this hand with respect to full house is (2%, 41%) and reads as follows: You have about 2% chance for achieving a full house by river; in case you do achieve it, your opponents have about 41% chance of beating it.Definitely, it is a weak hand with respect to full house: only 2% chance of achieving it and then 41% chance of loosing (59% of winning) with it. Thus, you might consider other inferior formations to analyze.
If is the strength vector of a hand with respect to F, we call the number the strength indicator of that hand with respect to F.
In our previous example, the strength indicator of the hand with respect to full house is .
is also a probability, namely the probability that you will achieve a formation of type F by river and none of your opponents will achieve something higher, if you achieve it.
If we were to consider all types of formations (from one pair to four of a kind) and do the same calculations for each of them, we would end up with seven strength vectors, one for each type of formation. These seven vectors would give us the whole image of the strength of that hand. In fact, they form a 2 x 7 matrix of probabilities.
For each hand, we call the matrix the strength matrix of that hand.
On the first row of the strength matrix are the probabilities of the own hand achieving the various types of formations by river. On the second row are the corresponding probabilities that your opponents (at least one) will achieve something higher than you by river, if you will achieve that expected type of formation. Each column corresponds to a type of formation (1p, 2p, 3k, s, fl, fh, 4k). Each hand has an unique associated strength matrix, whose elements are calculable manually or by software program.
Conventions. The following conventions were established in order to compute a strength matrix more easily:
- Straight flush has not been included on the last column as the highest type of formation. In fact, it is included in the flush type. When you hit a straight flush, there is nothing to analyze - you should put all in.
- We replace by 0 the elements of any column of a type of formation that is included at the moment of analysis or will be included – should it occur – by river in a superior type of formation. By this convention, the ignored type of formation F gets a null probability of being achieved and consequently a null probability for the opponents to beat it if it occurs . Thus, it practically comes out of the hand analysis. For instance, the strength matrix associated to a hand in turn stage where you have a full house, has the form .
In this case, one pair, two pairs, and three of a kind cannot be achieved as the full house includes and cancels them, and straight is impossible since you have at maximum two cards of it. Thus full house and four of a kind remain to be dealt with.
Interpretation. As the strength of a poker hand can only be expressed through mathematical probabilities of final events, the strength matrix is the most adequate object to picture such strength. When we evaluate the strength of a hand by interpreting its strength matrix, we actually assume a scale on which to place that strength, and implicitly a relation order over all possible hands. This is what “how strong is it” means in mathematical terms. Assuming we have the strength matrix of a hand we want to analyze, how will we actually interpret it? The rough rule is: The higher the p-probabilities and the lower the q-probabilities, the stronger the hand. However, if we consider the p row, it is better for the p-probabilities to be higher in the second part than in the first, as the second part corresponds to the most valuable achievements. In fact, a high value of a p-probability for only one type of formation of the second part (s, fl, fh, or 4k) may be sufficient for considering the hand strong enough for aggressive raising, as example. Having high values of the p-probabilities in the first part (for 1p, 2p, or 3k) is not a positive factor in the hand’s strength, since consequently we will have lower values in the second part, which means that the most valuable formations are unlikely to be achieved. This happens because the sum of the p-probabilities has an upper bound. The strength matrix cannot be interpreted only by the p-row. The q-probabilities are also important, as they can raise or temper the trust one may have in the corresponding p-probabilities with respect to the outcome of the decision made basing on them. For example, if a strength vector for a type of formation shows (0.55, 0.73), one may not rely on that good p-probability of over 50%, as long as the opponents may beat him/h
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