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No article next week as I take a short break for the holidays.
I'll be back after the new year with the next installment.
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Monday, December 21, 2009
No Limit Holdem 101: My Basic Theory of Poker
This is intended to be a series of articles about playing on-line no limit holdem cash games. There will be times where I venture into live poker and times where I venture into SNGs, MTTs, Satellites, and games other than no limit holdem, but for the most part this will target no limit holdem cash games.
For the 7th installment of this series, I’m going to cover the basis I use for my style of play – give the other guy the chance to make a mistake.
Poker is game where you try to make decisions based on incomplete information. If you had all the information possible visible, then there might still be more than one plausible play, but there would only be one OPTIMAL play. The preceding is called “game theory” by the way.
I’ve rewritten this particular article several times trying to decide exactly how deep I should get into game theory and exactly how much of my geekitude to reveal! In the end I decided to keep it fairly simple but hopefully delve enough into it that you can hopefully get the general concept.
Let me draw out a scenario for you. Imagine a poker game where all the cards were face up. Your hole cards, your opponent’s hole cards, the discarded cards, and the cards remaining in the deck were all visible. Well it really wouldn't be much of a game then would it? Everything is known and there really are no decisions to be made.
Now start hiding information. Take the discarded cards and the cards remaining in the deck and flip them over. You now know exactly what cards your opponents hold and what cards you hold, but you do not know what cards are left to come. In reality this is the situation you are striving to achieve in holdem. You try to put your opponents on hands so that you can reach this state of knowledge. From this state of knowledge all decisions can be optimized.
Now introduce the element of betting. Here is where we really get to start trying to optimize our play. Outs, odds, pot odds, implied odds, and predicting opponents behaviors all play into making an optimum decision.
In fact pot odds are an excellent example of the application of game theory. The optimal decision in the case of pot odds is governed my whether or not your odds of making the hand are outweighed by the amount of the bet you must make and the reward for making that bet. In the long term if you make the correct pot odds decision, then you are making the optimal play.
The key here is getting your opponent to make non-optimal decisions.
Some of the concepts I am going to discuss here as examples of getting your opponent to make non-optimal decisions will be concepts I will go into more detail in future articles, but I wanted to introduce them here as examples of optimal play and of getting your opponent to make non-optimal decisions.
Let’s go back to pot odds for a moment. We previously discussed using pot odds to make the decision on making a call. Another application of pots is use it to govern your betting to give opponent the wrong pot odds to make a call.
Without using a long drawn out example, let’s just say that you have a hand and you put your opponent on hand where he is 4 to 1 to make his hand on the turn. Making sure that he does not get 4 to 1 odds when you place your bet is giving your opponent an opportunity to make a mistake. If you bet such that your opponent is only getting 3 to 1 odds (1/2 pot), you are giving your opponent an opportunity to make a non-optimal play.
Another example of giving your opponent the opportunity to make a mistake is the huge over bet when you have made the nut hand. While making a huge over bet may induce your opponent to fold, your opponent may also put you on a bluff. After all, who would make a huge bet with a huge hand? While the play may not work the first time, against weaker opponents, you may be able to goad them into calling the over bet by making the over bet multiple times. Be careful here and make sure your have a truly big hand before using this play.
The two above examples should serve to illustrate the concept of game theory and giving your opponent the opportunity to make a mistake.
In the next installment we will talk about position in poker – what is it?
Read More......
For the 7th installment of this series, I’m going to cover the basis I use for my style of play – give the other guy the chance to make a mistake.
Poker is game where you try to make decisions based on incomplete information. If you had all the information possible visible, then there might still be more than one plausible play, but there would only be one OPTIMAL play. The preceding is called “game theory” by the way.
I’ve rewritten this particular article several times trying to decide exactly how deep I should get into game theory and exactly how much of my geekitude to reveal! In the end I decided to keep it fairly simple but hopefully delve enough into it that you can hopefully get the general concept.
Let me draw out a scenario for you. Imagine a poker game where all the cards were face up. Your hole cards, your opponent’s hole cards, the discarded cards, and the cards remaining in the deck were all visible. Well it really wouldn't be much of a game then would it? Everything is known and there really are no decisions to be made.
Now start hiding information. Take the discarded cards and the cards remaining in the deck and flip them over. You now know exactly what cards your opponents hold and what cards you hold, but you do not know what cards are left to come. In reality this is the situation you are striving to achieve in holdem. You try to put your opponents on hands so that you can reach this state of knowledge. From this state of knowledge all decisions can be optimized.
Now introduce the element of betting. Here is where we really get to start trying to optimize our play. Outs, odds, pot odds, implied odds, and predicting opponents behaviors all play into making an optimum decision.
In fact pot odds are an excellent example of the application of game theory. The optimal decision in the case of pot odds is governed my whether or not your odds of making the hand are outweighed by the amount of the bet you must make and the reward for making that bet. In the long term if you make the correct pot odds decision, then you are making the optimal play.
The key here is getting your opponent to make non-optimal decisions.
Some of the concepts I am going to discuss here as examples of getting your opponent to make non-optimal decisions will be concepts I will go into more detail in future articles, but I wanted to introduce them here as examples of optimal play and of getting your opponent to make non-optimal decisions.
Let’s go back to pot odds for a moment. We previously discussed using pot odds to make the decision on making a call. Another application of pots is use it to govern your betting to give opponent the wrong pot odds to make a call.
Without using a long drawn out example, let’s just say that you have a hand and you put your opponent on hand where he is 4 to 1 to make his hand on the turn. Making sure that he does not get 4 to 1 odds when you place your bet is giving your opponent an opportunity to make a mistake. If you bet such that your opponent is only getting 3 to 1 odds (1/2 pot), you are giving your opponent an opportunity to make a non-optimal play.
Another example of giving your opponent the opportunity to make a mistake is the huge over bet when you have made the nut hand. While making a huge over bet may induce your opponent to fold, your opponent may also put you on a bluff. After all, who would make a huge bet with a huge hand? While the play may not work the first time, against weaker opponents, you may be able to goad them into calling the over bet by making the over bet multiple times. Be careful here and make sure your have a truly big hand before using this play.
The two above examples should serve to illustrate the concept of game theory and giving your opponent the opportunity to make a mistake.
In the next installment we will talk about position in poker – what is it?
Read More......
Monday, December 14, 2009
No Limit Holdem 101: Holdem Math Part 5 (Putting It All Together)
This is intended to be a series of articles about playing on-line no limit holdem cash games. There will be times where I venture into live poker and times where I venture into SNGs, MTTs, Satellites, and games other than no limit holdem, but for the most part this will target no limit holdem cash games.
For the sixth installment of this series, I am going to tackle one of the most important aspects of poker: math.
When I first wrote this article to encompass everything I wanted to discuss about the math of holdem, it was so lengthy it was almost unreadable. So I’m going to break it into several parts.
The fifth math topic I’ll cover is putting it all together.
We are almost experts on holdem math now. We know how to count our outs, how to convert those outs into percentage or ratios, how to calculate pot odds, and how to think in terms of implied odds.
Okay, so not experts, but we are getting a good grasp of the fundamentals.
Now we need to put it all together and actually use math to help us make a decision.
Example one: A flush draw.
We are playing a cash table with $1/$2 blinds. Before the flop we were in the big blind with the Ace of spades and the six of spades (As6s). The action folds to the small blind who raises to $6. We decide to call and put another $4 in the pot bringing the total to $12. Both the blinds have stacks of about $200.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out with a pot sized bet of $12.
First we count our outs. There are 9 spades that we don’t know where they are and therefore could come to make our nut flush. So we have 9 outs (unless we want to discount our outs for any reason). We also have an Ace with 3 Aces unknown. That gives us 3 more outs. 12 outs times 2 is 24% of making our hand on the turn. That gives us 76 to 24 odds against making our hand. That’s right around 3.1 to 1.
Right now the pot is $24 with us having to make a call of $12. We are getting 2 to 1 to make the call.
Now we need to factor in implied outs. We are chasing a flush and an overcard. Both of these will be easy to see on the board and our opponent will likely shut down and abandon his Kings once the scare card hits the boards. We really can’t add anything to this with implied odds.
So we have 3.1 to 1 against us making the winning hand and we have 2 to 1 for pot odds. Since the odds against making our hand or less than our pot odds, we should not be making this call.
Example two: hidden straight draw with a low flush draw.
Same situation as above expect for the cards we hold. Now we have 5s6s. The action folds to the small blind who raises to $6. We decide to call and put another $5 in the pot bringing the total to $12. Again both players have around $200 stacks.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out with a pot sized bet of $12.
First we count our outs. There are 9 spades that we don’t know where they are and therefore could come on the turn or river to make our flush. So we have 9 outs. But do we really want to count these as this would make a very low flush. This depends on your read on your opponent. For the sake of argument, let’s say we just know that he’s playing an unsuited King. No need to discount any of our outs. We need to then add another 6 outs to make our straight draw (we’ve already counted the 3s and 8s as spades.) That gives us 15 total outs. So we have a 30% (15 x 2) chance of making our hand on the turn. So our odds are 70 to 30 against us making our hand. That’s 2 1/3 to 1 against making our hand.
Right now the pot is $24 with us having to make a call of $12. We are getting 2 to 1 to make the call.
So based strictly on the pot odds we should NOT be making this call (but it is fairly close).
But now we need to consider the implied odds and see if this makes for a good call or not. If any spade hits the board, our opponent is likely to shut down the betting. If however a non-spade 3 or 8 comes, our opponent is very likely to fire at this pot and we are now getting the right odds to make this call. We are getting no implied odds if we make the flush but high implied odds if we make the straight and that is more than enough add to the pot odds to make this an easy call.
Now you can see why in the last installment I referred to implied odds as more an art than a science. Implied odds require a high degree of predicting your opponent’s actions and that can be tricky indeed.
But wait a minute; isn’t it the rule of two and FOUR? What happened to the freaking FOUR? Good question.
The FOUR applies to your odds of making your hand on both the turn and the river and should be used in all-in situations after the flop. If the flop bet puts either you are your opponent all-in then that is where you use the FOUR as your factor to calculate your percentage of making your hand on the turn and river combined.
Example three: all-in on the flop.
We are playing a cash table with $1/$2 blinds. Before the flop we were in the big blind with the Ace of spades and the six of spades (As6s). The action folds to the small blind who raises to $6. We decide to call and put another $4 in the pot bringing the total to $12. The small blind has $36 left. You have him covered.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out by going all-in for $36.
First we count our outs. There are 9 spades that we don’t know where they are and therefore could come to make our nut flush. So we have 9 outs (unless we want to discount our outs for any reason). We also have an Ace with 3 Aces unknown. That gives us 3 more outs. 12 outs times 4 is 48% of making our hand on the turn. That gives us 52 to 48 odds against making our hand. That’s right around 1.1 to 1.
Right now the pot is $48 with us having to make a call of $36. We are getting 1.33 to 1 to make the call.
Our pot odds are greater than our odds of making the hands (1.33 is more than 1.1) so we should make the call.
I know some people use the rule of four for the flop regardless, but that is a mathematical error. The fact of the matter is the rule of four is your chance of making the hand on both the turn and the river. In order to use four you will have to calculate both the known bet on the flop and the unknown bet on the turn.
Now this doesn’t mean that you never use the rule of four on the flop unless there is an all-in involved. What it means is that you need to calculate the betting on the turn while you are on the flop in order to use the rule of four to justify your call on the flop. If you suspect your opponent will move all-in on the flop, then you can use those numbers to calculate your pot odds and compare those to your hand odds.
Yes. These calculations can get very tricky on the logic. Even though this about math it is based on your read on your opponent. If you don’t have a read on your opponent, then you are going to be hampered in some of the more complex aspects of holdem math.
Well, that’s it for the math of holdem (except I will be referring back to the math as we discuss further concepts in the future.)
In the next installment I’ll take a step back and talk about my basic theory behind holdem – Giving the other guy the chance to make a mistake.
Read More......
For the sixth installment of this series, I am going to tackle one of the most important aspects of poker: math.
When I first wrote this article to encompass everything I wanted to discuss about the math of holdem, it was so lengthy it was almost unreadable. So I’m going to break it into several parts.
The fifth math topic I’ll cover is putting it all together.
We are almost experts on holdem math now. We know how to count our outs, how to convert those outs into percentage or ratios, how to calculate pot odds, and how to think in terms of implied odds.
Okay, so not experts, but we are getting a good grasp of the fundamentals.
Now we need to put it all together and actually use math to help us make a decision.
Example one: A flush draw.
We are playing a cash table with $1/$2 blinds. Before the flop we were in the big blind with the Ace of spades and the six of spades (As6s). The action folds to the small blind who raises to $6. We decide to call and put another $4 in the pot bringing the total to $12. Both the blinds have stacks of about $200.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out with a pot sized bet of $12.
First we count our outs. There are 9 spades that we don’t know where they are and therefore could come to make our nut flush. So we have 9 outs (unless we want to discount our outs for any reason). We also have an Ace with 3 Aces unknown. That gives us 3 more outs. 12 outs times 2 is 24% of making our hand on the turn. That gives us 76 to 24 odds against making our hand. That’s right around 3.1 to 1.
Right now the pot is $24 with us having to make a call of $12. We are getting 2 to 1 to make the call.
Now we need to factor in implied outs. We are chasing a flush and an overcard. Both of these will be easy to see on the board and our opponent will likely shut down and abandon his Kings once the scare card hits the boards. We really can’t add anything to this with implied odds.
So we have 3.1 to 1 against us making the winning hand and we have 2 to 1 for pot odds. Since the odds against making our hand or less than our pot odds, we should not be making this call.
Example two: hidden straight draw with a low flush draw.
Same situation as above expect for the cards we hold. Now we have 5s6s. The action folds to the small blind who raises to $6. We decide to call and put another $5 in the pot bringing the total to $12. Again both players have around $200 stacks.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out with a pot sized bet of $12.
First we count our outs. There are 9 spades that we don’t know where they are and therefore could come on the turn or river to make our flush. So we have 9 outs. But do we really want to count these as this would make a very low flush. This depends on your read on your opponent. For the sake of argument, let’s say we just know that he’s playing an unsuited King. No need to discount any of our outs. We need to then add another 6 outs to make our straight draw (we’ve already counted the 3s and 8s as spades.) That gives us 15 total outs. So we have a 30% (15 x 2) chance of making our hand on the turn. So our odds are 70 to 30 against us making our hand. That’s 2 1/3 to 1 against making our hand.
Right now the pot is $24 with us having to make a call of $12. We are getting 2 to 1 to make the call.
So based strictly on the pot odds we should NOT be making this call (but it is fairly close).
But now we need to consider the implied odds and see if this makes for a good call or not. If any spade hits the board, our opponent is likely to shut down the betting. If however a non-spade 3 or 8 comes, our opponent is very likely to fire at this pot and we are now getting the right odds to make this call. We are getting no implied odds if we make the flush but high implied odds if we make the straight and that is more than enough add to the pot odds to make this an easy call.
Now you can see why in the last installment I referred to implied odds as more an art than a science. Implied odds require a high degree of predicting your opponent’s actions and that can be tricky indeed.
But wait a minute; isn’t it the rule of two and FOUR? What happened to the freaking FOUR? Good question.
The FOUR applies to your odds of making your hand on both the turn and the river and should be used in all-in situations after the flop. If the flop bet puts either you are your opponent all-in then that is where you use the FOUR as your factor to calculate your percentage of making your hand on the turn and river combined.
Example three: all-in on the flop.
We are playing a cash table with $1/$2 blinds. Before the flop we were in the big blind with the Ace of spades and the six of spades (As6s). The action folds to the small blind who raises to $6. We decide to call and put another $4 in the pot bringing the total to $12. The small blind has $36 left. You have him covered.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out by going all-in for $36.
First we count our outs. There are 9 spades that we don’t know where they are and therefore could come to make our nut flush. So we have 9 outs (unless we want to discount our outs for any reason). We also have an Ace with 3 Aces unknown. That gives us 3 more outs. 12 outs times 4 is 48% of making our hand on the turn. That gives us 52 to 48 odds against making our hand. That’s right around 1.1 to 1.
Right now the pot is $48 with us having to make a call of $36. We are getting 1.33 to 1 to make the call.
Our pot odds are greater than our odds of making the hands (1.33 is more than 1.1) so we should make the call.
I know some people use the rule of four for the flop regardless, but that is a mathematical error. The fact of the matter is the rule of four is your chance of making the hand on both the turn and the river. In order to use four you will have to calculate both the known bet on the flop and the unknown bet on the turn.
Now this doesn’t mean that you never use the rule of four on the flop unless there is an all-in involved. What it means is that you need to calculate the betting on the turn while you are on the flop in order to use the rule of four to justify your call on the flop. If you suspect your opponent will move all-in on the flop, then you can use those numbers to calculate your pot odds and compare those to your hand odds.
Yes. These calculations can get very tricky on the logic. Even though this about math it is based on your read on your opponent. If you don’t have a read on your opponent, then you are going to be hampered in some of the more complex aspects of holdem math.
Well, that’s it for the math of holdem (except I will be referring back to the math as we discuss further concepts in the future.)
In the next installment I’ll take a step back and talk about my basic theory behind holdem – Giving the other guy the chance to make a mistake.
Read More......
Monday, December 7, 2009
No Limit Holdem 101: Holdem Math Part 4 (Implied Odds)
This is intended to be a series of articles about playing on-line no limit holdem cash games. There will be times where I venture into live poker and times where I venture into SNGs, MTTs, Satellites, and games other than no limit holdem, but for the most part this will target no limit holdem cash games.
For the fifth installment of this series, I am going to tackle one of the most important aspects of poker: math.
When I first wrote this article to encompass everything I wanted to discuss about the math of holdem, it was so lengthy it was almost unreadable. So I’m going to break it into several parts.
The fourth math topic I’ll cover is implied odds.
In “Phil Gordon’s Little Blue Book”, Phil defines implied pot odds as “A calculation of pot odds based not on the money that’s currently in the pot but on the total money that you anticipate will be in the pot at the end of hand.”
In other words you are trying to predict the betting that will happen in future rounds should you hit your draw and should you miss your draw.
Implied odds are complicated and imperfect. You don’t really know how your opponent will react in future rounds of betting, but you must do your best to incorporate your predictions into your calculations.
One key guideline to remember here is that the harder your hand is for opponent to read, the higher your implied odds will be. If your opponent doesn’t think he’s beat, then he’s more likely to put more chips into the pot.
So, what hands have high implied odds and what hands have low implied odds? Sets generally have high implied odds. You hold the pair and the third card is on the board. A set is one of the hardest hands to put an opponent on. Conversely trips are not a high implied odds hand. You hold one card and the other two are on the board. Your opponent will be wary of your bets since he can easily see the pair on the board.
Straights using connected cards from your hand that form the middle of a straight are higher in implied odds that straights using connected cards from your hand that form the top end of the straight. An opponent looking at a board of 589 will not as readily put you on a straight as an opponent looking at a board of 789.
Flushes are generally the lowest implied odds of any hand. It is easy for your opponent to see the three suited cards on the board and react accordingly.
A quick note on a concept I’ve seen called reverse implied odds. The concept here is that if you hit your draw but you still don’t have the best hand, that you will put a lot of chips in the pot when you are beat. For instance if you Have a suited King and make your flush but your opponent was playing the suited Ace. You have bad reverse implied odds because you made the second nut flush and you may loose a lot if you don’t put your opponent on the nut flush.
This is really is a convoluted way of saying what will happen if I was wrong in counting my outs. Be very careful when counting your outs. It usually isn’t wise to chase 2nd best draws.
Well, that’s it for implied odds.
In the next installment, we will talk about putting it all together and making a decision based on math.
Read More......
For the fifth installment of this series, I am going to tackle one of the most important aspects of poker: math.
When I first wrote this article to encompass everything I wanted to discuss about the math of holdem, it was so lengthy it was almost unreadable. So I’m going to break it into several parts.
The fourth math topic I’ll cover is implied odds.
In “Phil Gordon’s Little Blue Book”, Phil defines implied pot odds as “A calculation of pot odds based not on the money that’s currently in the pot but on the total money that you anticipate will be in the pot at the end of hand.”
In other words you are trying to predict the betting that will happen in future rounds should you hit your draw and should you miss your draw.
Implied odds are complicated and imperfect. You don’t really know how your opponent will react in future rounds of betting, but you must do your best to incorporate your predictions into your calculations.
One key guideline to remember here is that the harder your hand is for opponent to read, the higher your implied odds will be. If your opponent doesn’t think he’s beat, then he’s more likely to put more chips into the pot.
So, what hands have high implied odds and what hands have low implied odds? Sets generally have high implied odds. You hold the pair and the third card is on the board. A set is one of the hardest hands to put an opponent on. Conversely trips are not a high implied odds hand. You hold one card and the other two are on the board. Your opponent will be wary of your bets since he can easily see the pair on the board.
Straights using connected cards from your hand that form the middle of a straight are higher in implied odds that straights using connected cards from your hand that form the top end of the straight. An opponent looking at a board of 589 will not as readily put you on a straight as an opponent looking at a board of 789.
Flushes are generally the lowest implied odds of any hand. It is easy for your opponent to see the three suited cards on the board and react accordingly.
A quick note on a concept I’ve seen called reverse implied odds. The concept here is that if you hit your draw but you still don’t have the best hand, that you will put a lot of chips in the pot when you are beat. For instance if you Have a suited King and make your flush but your opponent was playing the suited Ace. You have bad reverse implied odds because you made the second nut flush and you may loose a lot if you don’t put your opponent on the nut flush.
This is really is a convoluted way of saying what will happen if I was wrong in counting my outs. Be very careful when counting your outs. It usually isn’t wise to chase 2nd best draws.
Well, that’s it for implied odds.
In the next installment, we will talk about putting it all together and making a decision based on math.
Read More......
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