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ph_il
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Silver Level
Ive been getting these little articles in my email, so i decided to post them here. ill post every new one i get. oh and i take no credit for any of this..
Quick Counts - Part 1
By: Lou Krieger©
By: Lou Krieger©
Some folks are numbers people. Others aren’t. Most among us fall somewhere in bëtween. We run the gamut bëtween those who are quite mathematically literate and those who never met a number they really liked ¾ or even understood. While you might be prone to say, “different strokes for different folks” right about now, the fact remains that there are mathematical and
statistical underpinnings to pöker that cannot be ignored. You can try, of course, but you do so at your own peril. After all, these relationships are always at work, and they don’t care whether you pay attention to them or bury your head in the sand like an ostrich.
I’m somewhere in the middle. I’m not a numbers guy ¾ not by a long shot. That’s the province of Mike Caro, David Sklansky, and an entire coterie of pöker players who post to the Internet newsgroup, rec.gämbling.pöker ¾ many of whom are as quick and facile with numbers as a magician with a hatful of rabbits.
For those of you who are numerically challenged, or statistically phobic, this column is for you: A simple, easy-to-use, paint-by-numbers piece. It’s not the whole answer either, not by a long shot. And it won’t provide the same kind of clarity and depth of understanding that a knowledge and familiarity with mathematics and statistics will. But it is a crutch, and for those of you who need it, it’s a lot bëtter than nothing at all.
Quick Count Number 1: How Many Opponents?
Consider these common situations:
If you have three opponents, you are right on the borderline bëtween aggression and caution ¾ and I’d lean a bit more on the side of caution in most cases. With four or more opponents, it becomes progressively more unlikely that your prayers will be answered. Anytime you have four opponents or more, you can usually count on the flop helping someone. If you’re not that certain someone, it’s best to assume that one of your opponents now has a hand that’s bëtter than yours.
When that happens you need a draw to a good hand ¾ or some other reason, aside from your intuition, the fact that you’ve got your mojo working, or the coming of a long-awaited harmonic convergence ¾ to pay for another card.
The moral to this story is simple. As long as you can count to three, that’s all the mathematics you need know to provide a foundation for play when confronted with these kinds of decisions.
Quick Count Number 2: How Many Times Does the Flop Have to Hit You?
I called in late position with 7c-6c and five others also took the flop, which contained a seven. What should I do? While a bit more information is needed to answer this question, you can make a couple of assumptions that generally prove out. If overcards flop and there is any appreciable action before you act, you can usually count on at least one of your opponents having a hand that’s superior to yours. If the flop contained all low cards ¾ perhaps it was 7-3-2 of mixed suits ¾ you might have the best hand right now. When that’s the case, go ahead and bët, especially if you believe it would force some of your opponents to fold, thereby reducing the likelihood that one of them would get lucky on a subsequent bëtting round.
What if you call from late position with the same hand, only to have the button or one of the blinds raise? With more than three players active, you’re forced to call the raise. But now you know the odds favor one of your opponents having a hand that’s bigger than yours. So you take the flop knowing that it will have to hit you twice to give you much hope. If you’re incredibly lucky it will hit you three times, and serve up a straight on a silver platter. But the odds of that are really miniscule. You’ve got about a two percent chance of flopping two pair, and that coupled with the chance of flopping a straight or flush draw, or the minor possibility of flopping trips will allow you to see the flop.
But if none of those longshots comes to fruition, and the flop did not hit you twice ¾ three times hit is even bëtter ¾ you are skating on thin ice if you continue to play your puny pair of sevens in the face of any appreciable action.
In the next issue, the second and final installment of Quick Counts will explore the number of outs for various hands, provide you with some handy odds to use whenever you’re confronted with common hold’em situations, and we’ll also delve into counting the pot and comparing the payoff that it offers ¾ the pot odds, as it’s called ¾ with the odds against making your hand. Once you can do this, and it’s not difficult at all, you’ll be able to play within the mathematical parameters of the game. In other words, you won’t find yourself taking the worst of it simply because you might be confused by the seemingly difficult mathematical computations that go into these decisions.
statistical underpinnings to pöker that cannot be ignored. You can try, of course, but you do so at your own peril. After all, these relationships are always at work, and they don’t care whether you pay attention to them or bury your head in the sand like an ostrich.
I’m somewhere in the middle. I’m not a numbers guy ¾ not by a long shot. That’s the province of Mike Caro, David Sklansky, and an entire coterie of pöker players who post to the Internet newsgroup, rec.gämbling.pöker ¾ many of whom are as quick and facile with numbers as a magician with a hatful of rabbits.
For those of you who are numerically challenged, or statistically phobic, this column is for you: A simple, easy-to-use, paint-by-numbers piece. It’s not the whole answer either, not by a long shot. And it won’t provide the same kind of clarity and depth of understanding that a knowledge and familiarity with mathematics and statistics will. But it is a crutch, and for those of you who need it, it’s a lot bëtter than nothing at all.
Quick Count Number 1: How Many Opponents?
Consider these common situations:
- I have ace-king and the flop missed me entirely. Should I come out bëtting?
- I have a pair of eights. If one overcard flops, what’s the likelihood that my hand is any good?
- All else being equal, does my bluff stand a chance of winning the pot?
If you have three opponents, you are right on the borderline bëtween aggression and caution ¾ and I’d lean a bit more on the side of caution in most cases. With four or more opponents, it becomes progressively more unlikely that your prayers will be answered. Anytime you have four opponents or more, you can usually count on the flop helping someone. If you’re not that certain someone, it’s best to assume that one of your opponents now has a hand that’s bëtter than yours.
When that happens you need a draw to a good hand ¾ or some other reason, aside from your intuition, the fact that you’ve got your mojo working, or the coming of a long-awaited harmonic convergence ¾ to pay for another card.
The moral to this story is simple. As long as you can count to three, that’s all the mathematics you need know to provide a foundation for play when confronted with these kinds of decisions.
Quick Count Number 2: How Many Times Does the Flop Have to Hit You?
I called in late position with 7c-6c and five others also took the flop, which contained a seven. What should I do? While a bit more information is needed to answer this question, you can make a couple of assumptions that generally prove out. If overcards flop and there is any appreciable action before you act, you can usually count on at least one of your opponents having a hand that’s superior to yours. If the flop contained all low cards ¾ perhaps it was 7-3-2 of mixed suits ¾ you might have the best hand right now. When that’s the case, go ahead and bët, especially if you believe it would force some of your opponents to fold, thereby reducing the likelihood that one of them would get lucky on a subsequent bëtting round.
What if you call from late position with the same hand, only to have the button or one of the blinds raise? With more than three players active, you’re forced to call the raise. But now you know the odds favor one of your opponents having a hand that’s bigger than yours. So you take the flop knowing that it will have to hit you twice to give you much hope. If you’re incredibly lucky it will hit you three times, and serve up a straight on a silver platter. But the odds of that are really miniscule. You’ve got about a two percent chance of flopping two pair, and that coupled with the chance of flopping a straight or flush draw, or the minor possibility of flopping trips will allow you to see the flop.
But if none of those longshots comes to fruition, and the flop did not hit you twice ¾ three times hit is even bëtter ¾ you are skating on thin ice if you continue to play your puny pair of sevens in the face of any appreciable action.
In the next issue, the second and final installment of Quick Counts will explore the number of outs for various hands, provide you with some handy odds to use whenever you’re confronted with common hold’em situations, and we’ll also delve into counting the pot and comparing the payoff that it offers ¾ the pot odds, as it’s called ¾ with the odds against making your hand. Once you can do this, and it’s not difficult at all, you’ll be able to play within the mathematical parameters of the game. In other words, you won’t find yourself taking the worst of it simply because you might be confused by the seemingly difficult mathematical computations that go into these decisions.
Quick Counts - Part 2
By: Lou Krieger©
By: Lou Krieger©
This is the second in a two-part series aimed at the numerically challenged, statistically phobic, and other Pöker players otherwise unaware of the degree to which Pöker dwells within mathematical and statistical parameters. While there’s much more to this subject than two articles can cover, it’s a start ¾ an introduction of sorts ¾ to a topic many players are prone to avoid, even when they know bëtter.
Previously we discussed why the number of opponents in any given hand is important. You learned that there is a gaggle of plays that stand a good chance of succeeding against one or two opponents, but generally fail against four opponents or more. There are also hands and tactics that work bëtter against a full complement of opponents than they do against one or two.
We also discussed the importance of knowing how many times the flop has to hit you when considering how to play your hand. With A-K, one hit will frequently suffice. With a hand like 7-6, you probably need the flop to hit you twice, particularly if someone has raised.
Quick Count Number 3: How Many Outs Do You Have?
This concept is analogous to counting the number of times the flop has to hit you. But when you’re counting outs, you’ve already seen the flop and are trying to determine how many good cards are left in that deck. Knowing how many chances you have is vital information when trying to decide whether to continue with a drawing hand.
One of the nice things about hold’em, as compared to 7-card stud, is that the number of discernable outs is always the same for any given situation. If you’re playing stud, you may hold four hearts on your first four cards, but the number of hearts remaining in the deck has to be determined by counting your opponents’ exposed cards as well as those you’re holding.
But in hold’em, if you begin with two hearts and two more pop up on the flop, you have nine outs ¾ two in your hand and the two that flopped subtracted from a total of 13 hearts in the deck. It’s that simple. Unless an opponent has inadvertently exposed a heart, any time you flop a four-flush you have nine outs ¾ no more, no less.
If you flop an open ended straight, you have eight outs. With two pair you might have the best hand right now, along with four additional outs to a full house. If you flop a set, there are seven cards that will help you on the turn. One gives you four of a kind. Three cards will pair one of the board cards and three will pair the other, giving you a full house in either case, and ameliorating any concerns about an opponent catching a card to make a straight or flush.
Even if the turn card is no help, it still provides three additional outs on the river. Now there are nine cards that will pair the board, giving you a full house, along with that elusive case-card that will give you quads.
Quick Count Number 4: What Are the Odds You Need to Know?
It’s not difficult to learn how to figure the odds for common hold’em situations, but there’s not enough room in this column to teach that to you. Instead, a chart is provided that you can commit to memory.
The odds against an event occurring are shown in the right-hand column. The chances of success, expressed as a percentage, are shown in the middle column, and the number of outs is shown on the left. Is there a relationship bëtween them? Of course. Whenever you flop a flush draw, there’s a 35 percent chance of succeeding. That means you have a 65 percent chance of failure, which converts to 1.9-to-1 odds against making a flush.
You can learn to do the math without any special computational ability. It’s comforting to be able to do it ¾ trust me ¾ and nice to know that you don’t have to rely on anyone but yourself to calc the odds. Doing, as opposed to memorizing, also facilitates learning.
Quick Count Number 5: Pot Odds versus Implied Odds
There’s no cheap, easy trick here. To figure pot odds, you need to keep track of the amount of money in the pot. The easiest way is to count the number of players active on each round, account for the blinds if they’ve folded, and be sure to adjust for higher bëtting limits on the turn and river.
This is half of Pöker’s basic equation: Does the money offered by the pot exceed the odds against making your hand? If you have a flush draw, and the odds against making your hand are 1.9-to-1, you need to know that the pot will more than offset those odds before deciding whether to play or fold. If the pot promises a return of two-to-one on your investment, it certainly pays to call when the odds against your ultimate success are only 1.9-to-1.
But how do you know whether the pot will grow large or stay small? That’s where implied odds come in. Implied odds are your best estimate of the money likely to be in the pot once all the bëtting is complete. This estimate, when compared to the odds against making your hand, is frequently the linchpin in your play-or-pass decision.
There’s no formula to follow in making these estimates, but these four guidelines will help:
Previously we discussed why the number of opponents in any given hand is important. You learned that there is a gaggle of plays that stand a good chance of succeeding against one or two opponents, but generally fail against four opponents or more. There are also hands and tactics that work bëtter against a full complement of opponents than they do against one or two.
We also discussed the importance of knowing how many times the flop has to hit you when considering how to play your hand. With A-K, one hit will frequently suffice. With a hand like 7-6, you probably need the flop to hit you twice, particularly if someone has raised.
Quick Count Number 3: How Many Outs Do You Have?
This concept is analogous to counting the number of times the flop has to hit you. But when you’re counting outs, you’ve already seen the flop and are trying to determine how many good cards are left in that deck. Knowing how many chances you have is vital information when trying to decide whether to continue with a drawing hand.
One of the nice things about hold’em, as compared to 7-card stud, is that the number of discernable outs is always the same for any given situation. If you’re playing stud, you may hold four hearts on your first four cards, but the number of hearts remaining in the deck has to be determined by counting your opponents’ exposed cards as well as those you’re holding.
But in hold’em, if you begin with two hearts and two more pop up on the flop, you have nine outs ¾ two in your hand and the two that flopped subtracted from a total of 13 hearts in the deck. It’s that simple. Unless an opponent has inadvertently exposed a heart, any time you flop a four-flush you have nine outs ¾ no more, no less.
If you flop an open ended straight, you have eight outs. With two pair you might have the best hand right now, along with four additional outs to a full house. If you flop a set, there are seven cards that will help you on the turn. One gives you four of a kind. Three cards will pair one of the board cards and three will pair the other, giving you a full house in either case, and ameliorating any concerns about an opponent catching a card to make a straight or flush.
Even if the turn card is no help, it still provides three additional outs on the river. Now there are nine cards that will pair the board, giving you a full house, along with that elusive case-card that will give you quads.
Quick Count Number 4: What Are the Odds You Need to Know?
It’s not difficult to learn how to figure the odds for common hold’em situations, but there’s not enough room in this column to teach that to you. Instead, a chart is provided that you can commit to memory.
The odds against an event occurring are shown in the right-hand column. The chances of success, expressed as a percentage, are shown in the middle column, and the number of outs is shown on the left. Is there a relationship bëtween them? Of course. Whenever you flop a flush draw, there’s a 35 percent chance of succeeding. That means you have a 65 percent chance of failure, which converts to 1.9-to-1 odds against making a flush.
You can learn to do the math without any special computational ability. It’s comforting to be able to do it ¾ trust me ¾ and nice to know that you don’t have to rely on anyone but yourself to calc the odds. Doing, as opposed to memorizing, also facilitates learning.
Quick Count Number 5: Pot Odds versus Implied Odds
There’s no cheap, easy trick here. To figure pot odds, you need to keep track of the amount of money in the pot. The easiest way is to count the number of players active on each round, account for the blinds if they’ve folded, and be sure to adjust for higher bëtting limits on the turn and river.
This is half of Pöker’s basic equation: Does the money offered by the pot exceed the odds against making your hand? If you have a flush draw, and the odds against making your hand are 1.9-to-1, you need to know that the pot will more than offset those odds before deciding whether to play or fold. If the pot promises a return of two-to-one on your investment, it certainly pays to call when the odds against your ultimate success are only 1.9-to-1.
But how do you know whether the pot will grow large or stay small? That’s where implied odds come in. Implied odds are your best estimate of the money likely to be in the pot once all the bëtting is complete. This estimate, when compared to the odds against making your hand, is frequently the linchpin in your play-or-pass decision.
There’s no formula to follow in making these estimates, but these four guidelines will help:
- Know your opponent.
- Count the pot.
- Estimate the amount of money likely to be wagered in subsequent bëtting rounds.
- Know your own chances of success.