Effective Odds

July 10th, 2006

When there is only one round of betting left and only one card to come, comparing your chances of improving to the pot odds you are getting is a relatively straightforward proposition. If your chances of making a hand you know will win are, say, 4-to-1 against and you must call a $20 bet for the chance to win a $120 pot, then clearly your hand is worth a call because you’re getting 6-to-1 pot odds. Those 6-to-1 odds the pot is offering you (excluding bets on the end) are greater than the 4-to-1 odds against your making your hand. However, when there is more than one card to come, you must be very careful in determining your real pot odds. Many players make a classic mistake: They know their chances of improving, let’s say, with three cards to come, and they compare those chances to the pot odds they are getting right now. But such a comparison is completely off the mark since the players are going to have to put more money into the pot in future betting rounds, and they must take that money into account. It’s true that the chances of making a hand improve greatly when there are two or three cards to come, but the odds you are getting from the pot worsen.

Reducing Your Pot Odds With More than One Card to Come
Let’s say you are playing holdem, and after the flop you have a four-flush that you are sure will win if you hit it. There are two cards to come, which improves your odds of making the flush to approximately 1,75-to-l. It is a $10-$20 game with $20 in the pot, and your single opponent has bet $10. You may say, “I’m getting 3-to-1 odds and my chances are 1,75-to-l. So I should call.”
However, the 1,75-to-1 odds of making the flush apply only if you intend to see not just the next card, but the last card as well, and to see the last card you will probably have to call not just $ 10 now but also $20 on the next round of betting. Therefore, when you decide you’re going to see a hand that needs improvement all the way through to the end, you can’t say you are getting, as in this case, 30-to-10 odds. You have to say, “Well, if I miss my hand, I lose $ 10 on this round of betting and $20 on the next round. In all, I lose $30. If I make my hand, I will win the $30 in there now plus $20 on the next round for a total of $50.” All of a sudden, instead of 30-to-10, you’re getting only 50-to-30 odds, which reduces to 1,67-to-l.
These are your effective odds — the real odds you are getting from the pot when you call a bet with more than one card to come. Since you are getting only 1,67-to-l by calling a $10 bet after the flop, and your chances of making the flush are 1,75-to-l, you would have to throw away the hand, because it has turned into a losing play — that is, a play with negative expectations. The only time it would be correct to play the hand in this situation is if you could count on your opponent to call a bet at the end, after your flush card hits. Then your potential $50 win increases to $70, giving you 70-to-30 odds and justifying a call.
It should be clear from this example that when you compute odds on a hand you intend to play to the end, you must think not in terms of the immediate pot odds but in terms of the total amount you might lose versus the total amount you might win. You have to ask, “What do I lose if I miss my hand, and what will I gain if I make it?” The answer to this question tells you your real or effective odds.
Let’s look at an interesting, more complex application of effective odds. Suppose there is $250 in the pot, you have a back-door flush draw in holdem, and an opponent bets $ 10. With a back-door flush you need two in a row of a suit. To make things simple, we’ll assume the chances of catching two consecutive of a particular suit are 1/5 * 1/5. That’s not quite right, but it’s close enough. It means you’ll hit a flush once in 25 tries on average, making you a 24-to-1 underdog. By calling your opponent’s $10 bet, you would appear to be getting 26-to-1. So you might say, “OK, I’m getting 26-to-1, and it’s only 24-to-1 against me. Therefore, I should call to try to make my flush.”
Your calculations are incorrect because they do not take into account your effective odds. One out of 25 times you will win the $260 in there, plus probably another $40 on the last two rounds of betting. Twenty times you will lose only $10 when your first card does not hit, and you need not call another bet. But the remaining four times you will lose a total of $30 each time when your first card hits, you call your opponent’s $20 bet, and your second card does not hit. Thus, after 25 such hands, you figure to lose $320 ($200 + $120) while winning $300 for a net loss of $20. Your effective odds reveal a call on the flop to be a play with negative expectation and hence incorrect.

 

Mathematical Expectation in Poker

July 6th, 2006

I’ve reread my previous messages… Hmmm, I realized that the “hints” I used to state here are mostly like finger-alphabet… Those who could read them know this for sure. And those who haven’t met this in their everyday live can’t understand anything…
So I decided to explain some poker concepts once again. And I hope I’ll be more precise this time.
Anyway I’m ready to hear your comments and make necessary corrections.
The first thing I would like to deal with is mathematical expectation. The term comes from probability theory and indicates the mean value of the random variable in many identical experiments.
Poker plays can also be analyzed in terms of expectation. You may think that a particular play is profitable, but sometimes it may not be the best play because an alternative play is more profitable. Let’s say you have a full house in five-card draw. A player ahead of you bets. You know that if you raise, that player will call. So raising appears to be the best play. However, when you raise, the two players behind you will surely fold. On the other hand, if you call the first bettor, you feel fairly confident that the two players behind you will also call. By raising, you gain one unit, but by only calling you gain two. Therefore, calling has the higher positive expectation and is the better play.
Here is a similar but slightly more complicated situation. On the last card in a seven-card stud hand, you make a flush. The player ahead of you, whom you read to have two pair, bets, and there is a player behind you still in the hand, whom you know you have beat. If you raise, the player behind you will fold. Furthermore, the initial bettor will probably also fold if he in fact does have only two pair; but if he made a full house, he will reraise. In this instance, then, raising not only gives you no positive expectation, but it’s actually a play with negative expectation. For if the initial bettor has a full house and reraises, the play costs you two units if you call his reraise and one unit if you fold.
Taking this example a step runner: If you do not make the flush on the last card and the player ahead of you bets, you might raise against certain opponents! Following the logic of the situation when you did make the flush, the player behind you will fold, and if the initial bettor has only two pair, he too may fold. Whether the play has positive expectation (or less negative expectation than folding) depends upon the odds you are getting for your money — that is, the size of the pot — and your estimate of the chances that the initial bettor does not have a full house and will throw away two pair. Making the latter estimate requires, of course, the ability to read hands and to read players, which I discuss in later chapters. At this level, expectation becomes much more complicated than it was when you were just flipping a coin.
Mathematical expectation can also show that one poker play is less unprofitable than another. If, for instance, you think you will average losing 75 cents, including the ante, by playing a hand, you should play on because that is better than folding if the ante is a dollar.
Another important reason to understand expectation is that it gives you a sense of equanimity toward winning or losing a bet: When you make a good bet or a good fold, you will know that you have earned or saved a specific amount which a lesser player would not have earned or saved. It is much harder to make that fold if you are upset because your hand was outdrawn. However, the money you save by folding instead of calling adds to your winnings for the night or for the month. I actually derive pleasure from making a good fold even though I have lost the pot.
Just remember that if the hands were reversed, your opponent would call you, and as we remember from the Fundamental Theorem of Poker, this is one of your edges. You should be happy when it occurs. You should even derive satisfaction from a losing session when you know that other players would have lost much more with your cards.

A little quiz

June 28th, 2006

Today I was reading Winning Low-Limit Holdem by Lee Jones and I’ve seen a little quiz there.

You may check your skills here. The answers will be given after the quiz.

1. Give three reasons why the flop is the most crucial point in a hold’em hand.
2. What is the most common mistake made by low-limit hold’em players on the flop?
3. What is the most important use of the check-raise in low-limit hold’em games?
4. How should you normally play A♠-Q♠ if the flop comes Q♦-J♥-2♣ and you were the only one who raised before the flop?
5. How should you normally play A♠-5♠ in late position if the flop comes A♥-8♦-4♣, there has been no raise before the flop, and you have six opponents?
6. How should you normally play Q♥-Q♣ in early position against five opponents if the flop comes A♣-T♦-4♦ and there was one raise pre-flop?
7. If you have T♦-9♦ and the flop comes T♣-9♠-4♣, what should you do, and why?
8. Suppose you have K♥-K♦, you have raised before the flop, and six players take the flop, which comes K♣-7♦-2♥. What should you normally do?
9. You have A♣-T♣ on the button. Six people take the flop, which comes J♣-9♦-4♣. There’s a bet and three calls in front of you. What should you normally do?
10. You have 9♥-8♥ in late position. There is no raise pre­flop, and five people take the flop, which comes T♦-6♣-3♣. It is checked until the player to your right bets. What should you normally do? Now assume the same situation, but there was one raise pre-flop. What should you normal­ly do?
11. Suppose you have T♣-T♦ in middle position, there is a raise before the flop and five callers. The flop comes T♥-8♥-8♠. How should you normally play? What would be a reasonable alternative play?
12. Suppose you have 5♠-3♦ on the big blind and get to see the flop for “free.” The flop comes 4♣-7♣-6♥. You have four opponents. How should you normally play?
13. You have J♦-T ♦ on the button and are the fourth caller (no raise). The flop comes 7♣-6♥-2♥. There is a bet and one call in front of you. How should you normally play? Now suppose the flop comes 9♣-4♥-2♦. How does this change the situation?
14. You have 6♠-5♠ in middle position with four opponents, and no raise pre-flop. The flop comes T♣-6♥-3♣. There’s a bet and a caller in front of you. What is typically the best play in this situation?
15. You have A♦-A♠ in late position and raise before the flop, ending up with two opponents. The flop comes K♣-T♣-4♦. The first player to act bets, the second folds. You raise and the first player makes it three bets. What would be rea­sonable plays in this situation?
16. You have Q♣-J♠ on the big blind, and there are five callers including you. The flop comes 8♥-J♦-2♥. You check, as does everybody else until the last player to act, who bets. You check-raise, and the original bettor is the only one to call. Now the T♣ comes on the turn. What should you nor­mally do?
17. You have A♥-9♥ on the button and are one of six callers. The flop comes A♣-3♦-8♣. You bet and get two callers. The turn is the 6♠ - they check, you bet, and they call. The river card is the J♣ and again they both check. What’s probably your best play here?
18. You have A♥-K♦, you raise under the gun, and get three callers. The flop comes 7♥-K♣-3♠. You check, planning to check-raise, but it’s checked around. The turn is the J♥, you bet and get one caller. The river is the 8♠. Should you bet or check, and why?
Answers:
1.a) The flop determines the likely winner of the hand.
b) It is when you must make a crucial play/no-play deci­sion.
c) (In structured-limit play only) you can gain informa­tion using cheaper bets that will allow you to make the correct decisions on later, more expensive, cards.
2. Calling bets and raises with hands that have little or no chance of winning the pot.
3. To force players to call two bets instead of one, often mak­ing it incorrect for them to call at all.
4. Aggressively. Raise or check-raise. Assume you have the best hand until somebody represents something better.
5. You have to play very cautiously. Against this many play­ers, there’s an excellent chance that somebody else has an ace with a better kicker. If there is a raise, you should get out. If there is a bet and a couple of calls, you should prob­ably get out. If it’s checked to you, go ahead and bet, hop­ing to win the pot right there.
6. Unfortunately, you can be almost sure that you’re beaten. In spite of the large pot size, you should normally check, and fold if there’s a bet. As you get to later position, if it’s checked to you, it might be worth an exploratory bet. If you get called there, then you probably shouldn’t invest any more money in the pot.
7. You should play very fast. Do whatever is necessary to get lots of bets in on the flop. While you almost assuredly have the best hand, there could be some very big draws out against you, and you want them to pay heavily to draw.
8. You should bet or raise immediately on the flop. The flop is just about perfect for you - it’s virtually impossible you won’t have the best hand on the turn. However, there is so much money in the pot, there’s no reason to slow-play. Furthermore, after you raised pre-flop, your opponents will expect you to bet, so you haven’t given out any informa­tion.
9. Normally you should raise. You are about a 2:1 dog to make your flush, so you are actually raising for value here. Also, your raise may get you a free card on the turn, should you need one. Note also that an eight or queen on the turn gives you an open-end straight draw as well; you may be able to bet your draw for value on the turn.
10. In the First case, you can’t call with your gutshot straight draw - there are not enough bets in the pot, and you must worry about a raise behind you or a check-raise in front. If there was a raise before the flop, you can usually call because the pot has gotten so large.
11. You have flopped a monster hand, and the chance of your being beaten is tiny. However, the pot is huge (10 small bets on the flop), so there’s probably no point in slow-play­ing. On the other hand, slow-playing this hand is a reason­able approach - you’re not worried about getting beaten, and you’re willing to let some lesser hands catch up.
12. In spite of a relatively small pot, you must do everything you can to eliminate opponents immediately. You could be up against a club flush draw or a big straight draw (such as 9♥-8♥). It’s even possible you’re dead against 85, but that’s unlikely. You must bet and/or raise on the flop.
13. Even though you have two overcards, you should normally fold. You have no backdoor flush chances, and the 7-6 com­bination on the flop makes two pair more likely. In the sec­ond situation, you have backdoor straight and flush chances and there’s perhaps less chance that you’re already up against two pair. You can call a bet here.
14. You’ve missed the flop - your second pair with no kick­er is useless. Fold immediately.
15. You could call and then call your opponent’s bets on the turn and river (assuming he bets). It’s possible he has al­ready made two pair or a set, but with this flop you can’t fold yet. On the other hand, if you suspect your opponent is raising with a king or a draw, you could raise once more and try to regain control of the hand, forcing him to check on the turn. An alternative is to call and then raise on the turn.
16. You should probably bet out. You may run into two pair or even a straight, but you have to take that chance on the turn. You don’t dare give a heart flush draw a free card, or a jack with a smaller kicker a free card with which to beat you. On the river, you should usually check, since now there are no “free” cards to give, and you’re not sure if you want to be called or not.
17. You should typically check. As in the above situation, the board is fairly scary, and you just have one pair with a me­diocre kicker. If you bet and get called, you can’t be very happy. If an opponent bets into you on the end, you should call. If the river card were the J♦ instead of the flush-com­pleting club, you should bet.
18. Go ahead and bet here. There are many worse hands that will call you. The flop that got checked around may con­fuse some people; you will probably get called by a worse king and maybe even a jack.
How many right answers do you have?

Poker players (part 2)

June 22nd, 2006

PREDICTABLE PLAYERS

The average player
The average player does not do anything too extreme, he likes to play, but he is not overly aggressive with his hand nor does he play too passively. He will bet when he has a good hand, he will raise when he has a great hand, he will call when he has a passable hand, and he will fold when he has a poor hand. The average player will give himself excuses to stay in the hand rather than fold. The average player may be different at different limits. The average player in a $20/$40 game is a better player than the average player in a $5/$10 game. The average player in a $20/$40 game knows to play a little bit tighter (although he will still play too many hands) and knows a few tricks such as raising with a flush draw on the flop, although he may not know exactly why it may be a good play. The average player in a 5/10 game does not do anything overtly stupidly like call two raises with 96o, but he plays even more hands than the average player in a 20/40 game. The average player will put in a bluff now and then but not all that often. When he raises, you can usually count on him having a premium hand.
The calling station
The calling station likes to play along, and follow with everyone else. He does not want to disturb the game and perturb any of his fellow comrades by unnecessarily raising. When the calling station bets, you know he thinks he has a good hand. When the calling station raises, you better run for your life, because he has a monster. The calling station will play many hands, has no problem limping in while in early position, calling a professional player’s early position raise, or calling a bet when he has a pair of 8’s when there are three overcards on the board. Beware, the calling station could be unintentionally trying to rope-a-dope you. If you play too aggressively into him without a made hand, he will simply call you down with a middle pair or a bottom pair. You do not want to bluff the calling station because he thinks it is a social game like the one in his hometown where everyone plays just about every hand to the River and show the winning hand. He is our friend and as our friend, he will not get scared by your actions, he thinks you are his friend as well. A calling station is always a bad player.
The rock
Strangely enough, the rock and the calling station have some similarities. Like the calling station, the rock will only bet with good hands and only raise with very strong hands. As with the calling station, you must be very careful when the rock bets or raises. It is important to give both the calling station and the rock respect when they show aggression. That is where the similarities end. The calling station plays a lot of hands, while the rock plays very few hands. The rock may sit there for hours folding his starting hands and will have no problems folding his blinds. He is the prime candidate to steal the blinds from, but when he does play a hand, watch out. The rock usually thinks he is a better player than the average player. He values patience above all else, and since he is the most patient at the table, he usually thinks he is the best. In some games, he may be right. Some rocks will open up their game when they lose a few bad beats because they cannot believe the worse players are beating them, but most of them will have more discipline, which is why they were rocks to begin with. A rock is typically a good player, although he will not extract as much edge out of the game as better players will, a rock would not be defined as a sharp player. Rocks can be long term winners in low limit games and some middle limit games, but they will need to expand their game and creativity in order to win in the higher limit games.
The solid player
The solid player is a player who has some idea of correct play. He knows he needs to be patient to win at this game, but he is not overly tight. He will play more hands than a rock and he will usually be aggressive when he does play. If he raises from early position, he is predictable because he will have a quality hand. If he open-raises from late position, his hand will be harder to predict because he understands he can loosen up in that position and he is not afraid to try to steal the blinds. You normally want to avoid the solid player when he is raising. He may not bluff or semi-bluff enough because he does not usually take too many chances. Some players will play like a solid player only to morph into a different type of player after a while at the table. The solid player is a good player.
UNPREDICTABLE PLAYERS
The loose aggressive player
The loose aggressive player likes to play a lot of hands. Unlike the calling station, he likes to play them with raises instead of calls. He will raise and bet when his cards are warranted, but he may sometimes bet and raise when it is not clear that he has the best hand at the moment. The loose aggressive player likes to bet on the come. He will use the free card raise as often as he can, even if he just has overcards. Once he raises for the free card, he oftentimes feels compelled to keep betting due to the perceived weakness of his opponents if they are just calling him. It may feel necessary to rope-a-dope the aggressive player by flat out calling him instead of scaring him off with a raise or a re-raise. At times you may feel that he has just enough to go toe-to-toe with you even though you have the nut hand. The loose aggressive player is always trying to steal the blinds, even from middle position. He will bluff more often than the average player and he loves the semi-bluff concept and overdoes it. Because he plays so many hands and is aggressive with them, it may be harder to predict his holdings. They may sometimes run you over when they actually have the goods. Loose aggressive players are usually not good players, however they can get in some streaks where it may seem like they are the best player around.
The maniac
The maniac is Mr. Hyde to the loose aggressive player’s Dr. Jekyll. The maniac is completely out of control and raises sometimes even without looking at his hole cards. Everyone is licking their chops to get a piece of this guy. Maniacs will raise and bluff way too often and they will usually lose their money quickly. Maniacs may not play like maniacs all the time. Sometimes players who are just having a bad day turn into maniacs when they are on full tilt. This can happen after they have been dealt a couple of bad beats which could lead them to play very aggressively in order to get back to even. The maniac is a horrible player.
The professional players
The professional players are the best players and the ones that you least like to see at your table. They could be playing poker as their main source of income or they could be playing it as a supplemental income. They are playing poker mostly to win unlike other players who may be playing for the gamble, the entertainment or just the competition. Professional players understand the importance of playing aggressively when they have a solid hand and they also understand the importance of choosing their hands selectively. They will try to extract the most amount of edge from their opponents when they have the best of it, but try to get away cheaply when they have the worst of it. Professional players have thought about and studied the game, be it through reading, talking to other players or just thinking about the game. Professional players will still have a wide range of characteristics in their style. Some will be more aggressive than others, some will bluff a bit more than others. Of course, there are always those who consider themselves as professional players who really are not.
Players can change styles depending on if they are winning or losing
There are players who will try to play solidly when they first sit down, and continue to play solidly if they start off winning. But some players can change their styles drastically if they start to lose, particularly if they take a bad beat. All of a sudden, these players will go from playing solid to being a bit more aggressive, semi-bluff and bluff more. If they continue to lose and get some of their bluffs called, or better yet, get another bad beat, they could wind up opening up their game and could turn into a maniac-type of player.
This is one of the situations where having played with the player in the past and knowing this particular characteristic is very useful. If it is the first time you ever played with him and he plays like this, you may assume this is how he plays and use that information the second time you play at the same table with him. But the second time around, he may be running good and playing solidly, in which case, your perception of him will be completely off.

All-Blogs

Poker players

June 22nd, 2006

Knowing how the other players play is one of the keys to achieving success at Limit Hold’em. When sharp players know their opponents well, sharp players will know how their opponents act and think.
Understanding how your opponents play is more useful when pots quickly become heads-up as opposed to being multi-way pots. This means it is more useful in shorthanded games and less useful in low limit games. In shorthanded games, pots will become heads-up on the Flop more often than in full games because fewer players are needed to fold to get to that point. In low limit games, players will play looser in general, so more players will be seeing the Flop and beyond. When the opponents play looser, the tighter players can correctly expand their playable hands with good drawing type of hands. So the looseness in low limit games compounds upon itself. With many players, it becomes tougher to use any one player’s tendencies to your advantage, since there are other players in the hand to consider as well. With that said, any player who knows how his opponents play will always be better off than a player who does not.
I will break down player stereotypes into two major categories, predictable players and unpredictable players. Both categories have their share of bad players and good players. Players can be predictable whether they play loose or tight, but generally predictable players are passive. Players can be unpredictable whether they play loose or tight, although generally the unpredictable players are more on the aggressive side. Sometimes certain players may become extremely predictable in certain situations when they are not normally.
PREDICTABLE PLAYERS
Predictable players are easier to play against than unpredictable players. When predictable players act, the strength of their hand will typically be clear based on their actions. It may be that when they bet or raise, they have a strong hand. It may be that when they have a strong hand, they never raise on the Flop but always wait to raise on the Turn when the bet size doubles. Conversely, it may be that when they raise on the Flop they never have a made hand but are raising for a free card. A good, sharp player has a better idea of the strength of predictable players’ hands based on their actions, although a poor player may not pick up on it. Different players will be predictable in different ways.
UNPREDICTABLE PLAYERS
Unpredictable players are not necessarily good or bad players. When they act, it is tougher to pinpoint their hand compared with pinpointing a predictable player’s hand. Unpredictable players will use strategies such as bluffing and semi-bluffing often, sometimes too often. Even though good players can be somewhat unpredictable, there is only so far they can take this. If they are too unpredictable, it will mean they are playing too many hands, and giving up too much edge for the quest to be unpredictable. Instead, good players will choose his spots to be unpredictable, spots where playing unpredictably may give them the greatest edge. Players who try to play unpredictably all the time invariably play too many hands and thus are giving up too much edge for their trickiness.

How you should play a hand before the flop (continued)

June 20th, 2006

Your position
Your position is simply where you are in relation to the button. Being on the button is the best position because you will act last in all but the first betting round. Being one to the left of the button is then the worst position.
Position is perhaps the most undervalued component of good hold’em play. It’s easy to see that bigger cards are better, suited is better than non-suited, and if there is raising going on, you need a stronger hand to play. However, many (if not most) low-limit hold’em players make their playing decisions without considering their position. If you play without careful attention to your position, your bankroll will suffer.
By acting after other players, you know what they will do (check, bet, etc.) before they know what you will do on a given betting round; this gives you an advantage. For instance, suppose you have a very strong hand. If your opponent acts before you and bets, then you raise. If he checks, you bet. Regardless of his action, you get the maximum amount of money in the pot. On the other hand, if you’re first to act, then you must decide between betting immediately, hoping he will call, or trying to check-raise. If you check with the intent of raising and he checks too, you have lost the bet you would have made had you bet and he called.
Here’s another example of the importance of position. Suppose you have 55 as your starting hand. If you are the first to act before the flop, you normally shouldn’t call. We will cover this in detail shortly, but you need a lot of opponents to play small pairs. Suppose you call with your 55 in early position. If the next player to your left raises and scares out the other players, you now wish you hadn’t called the original bet. However, suppose you are on the button. If somebody raises early and limits the pot to two players, you fold, knowing you’re doing the right thing. But if six players call in front of you and there’s no raise, you can call with your fives. Simply being closer to the button means you have more information about how many opponents you will have and how much you’ll have to invest, enabling you to play this hand.
There is one aspect of position that is perhaps not as important in low-limit hold’em as it is in the higher limits. In tough hold’em games, when the flop doesn’t hit anybody, the player last to act can often bet and win the pot immediately. Because of the number of “calling stations” that are often in a lower limit game, it’s unlikely you’ll be able to do that. However, good position is still vitally important, and you must consider it at all times.
For the purposes of this text, we will consider a nine-player table. We’ll declare the first four positions to the left of the button “early position,” the next three “middle position,” and the last two (including the button) “late position.” Of course, you’ll need to adjust this for the exact number of players at your table. When doing so, tend to err on the side of caution; if you can’t decide if it’s early or middle position, call it “early.”

Your relative position
There is another aspect of position to consider - let’s call it “relative position.” It is where you sit in relation to specific other players at the table. Obviously, your position with respect to the button will change as it moves around the table. Your relative position to another player will be less volatile. For instance, if you sit immediately on a player’s left, then you’ll act after him on every hand with the exception of ones on which he has the button. If you sit directly opposite him at the table, you will act before and after him equally often.
If there is a player who is very aggressive and raises a lot, you’d generally like to be to his left. That way, you’ll see those raises coming before you act and can drop your marginal hands. If you sit to his right, too often you call one bet only to have him raise behind you and now you wish you’d saved the first bet.
If, however, that player bets and raises almost always (let’s say 90-95% of the time), then you want to have him on your left. Because he’ll be initiating action so frequently by betting or raising, you’ll effectively act last after he has started the action. For instance, this gives you the opportunity to check-raise the entire table when you make a strong hand. Remember, for this to be correct, that particular opponent must be almost guaranteed to bet or raise when given the chance. Otherwise, keep him to your right.
In general, you’d like to have loose passive players to your left. They behave predictably so you’re more willing to have them act after you. You will have an easier time predicting what they’ll do, and will make the right play more often.
You may even want to move into an empty seat that gives you better position with respect to certain players.

TBC

How you should play a hand before the flop

June 20th, 2006

Your decision to call, raise, or fold before the flop must be based on several factors. Among the most important are:
1. Your cards
2. Your position
3. Your relative position
4. How much money you must invest initially
5. The number of players in the hand.
6. How your opponents play
If you ignore any of these factors when making your first playing decision, you are not likely to be a winning hold’em player.

Your cards
Starting hands (the two cards that are unique to your hand) in hold’em fall into some natural categories. You will learn that hands in different categories do well in different situations, so you need to understand and remember these categories.
Pocket Pairs: two cards that are a pair, for example, “pocket 9’s.” Since the difference in value between pocket aces and pocket deuces is so huge, we will separate the pocket pairs into three sub-categories: aces down through jacks are “big” pairs, tens through sevens are “medium,” and sixes through twos are “little” pocket pairs. These subcategories are, of course, somewhat arbitrary, but this is a reasonable division.
Big Cards: two “big” cards, ace through jack. A♣-Q and K♥-J are examples of offsuit big cards. A♥-K♥ and K♠-Q♠ are examples of suited big cards.
Connectors: two cards one apart in rank. They have the ability to make straights and, if suited, flushes and straight flushes. Examples are T -9 and 6♣-5 ♠. Note that QJs has the distinction of being both “Big Cards” and a “Suited Connector.” We sometimes include in this group the lesser quality hands with gaps between the ranks. For instance, 9♠-7♠ is a suited “one-gap.” T♣-7♣ is a suited “two-gap.”
Suited Aces and Kings: fairly self-explanatory. Examples are A♠-8♠, K♥-9♥. Of course, a suited ace is much stronger than a suited king because if you make a flush with it, you have the nut flush, whereas the king high flush can be beaten by the ace high flush. Having an ace high flush is much better than having a king high flush. Having a king high flush is only a little better than having a queen high flush.
Believe it or not, even if you chose to play only hands that are in these categories, you would be playing too many hands. Some of them are not strong enough to play in certain positions and some of them (32s comes to mind) are generally not strong enough to play anywhere. However, many of your opponents will play every hand that fits into the above categories, and a lot more as well.

TBC

Some more hands

June 16th, 2006

1/ You hold 6 5 in the big blind. An early player calls, the button raises, the small blind calls, and you call. Four players see the flop of 9 6 3. You bet out. The early player calls and the button raises. The small blind calls and you call. All four players see the turn of 5. The small blind bets. You raise, the early player reraise, and the small blind calls. There is $320 in the pot. What do you do? (The answer is below  in black font. Mark all the space below in order to know the right answer.)   Answer: Call. You are most likely against a flush. There is also a chance you could be against a straight or a set. You have four strong outs to a full house unless an opponent has 99, or possibly 66 or 55. Four outs are 11 to 1 requiring only a $220 pot for calling to be correct. Note that your raise on the turn was questionable, as a flush was a high possibility given that three opponents paid two bets on the flop to see the turn. In the actual hand, the player called and lost to the early player who showed A Q.   2/ You hold Q J in early position. An early player calls, the next early player raises, and you call. A middle player, the cutoff, the button, and the big blind all call. Seven players see the flop of 9 8 6. The cutoff bets and the button raises. The first early player calls and the preflop raiser folds. You call and four players see the turn card of K. The cutoff bets, the button calls, and the early player calls. There is $430 in the pot. What do you do? (The answer is below  in black font. Mark all the space below in order to know the right answer.)  Answer: Call. Calling bets on the turn for a gut-shot straight is rarely correct unless the pot is quite large. In this hand, the pot is large and your call will close the betting so that you don’t risk a raise behind you. Your four outs are to the nuts since the board is not two-suited or paired. Four outs are 11 to 1 against improving requiring a pot of $330 to justify a call. In the actual hand, the player called and the T fell on the river. He bet and one opponent showed T 9.   

3/ You hold A 3 in middle position. A middle player limps in and you call. The cutoff, button, and small blind all caps. A wild unpredictable player raises from the big blind and everyone calls. Six players see the flop K Q J. The big blind bets, you call, the cutoff raises, and you both call. The turn is the K. The cutoff bets and the big blind raises. There is $360 in the pot. What do you do? (The answer is below  in black font. Mark all the space below in order to know the right answer.)  Answer: Fold. You are 4 to 1 against hiding the flush and are getting sufficient pot odds of 6 to 1 on the flush if it would win. However, there are several problems with calling in this situation.   Assuming that your opponents don’t already have a full house, couples of your outs are probably counterfeited and should be disregarded since it is likely that at least one of your opponents holds a king. In this case, you will lose to the Q or to another spade if it matches your opponent’s kicker card. This reduces your outs to seven, which is 6 to 1 against improving and is even money with a pot of $360; however, this is your best case. With a pair on the board, you need to discount your outs for the decent chance that you are drawing dead to a full house. Possible hands of your opponents include KK, QQ, JJ, KQ, and KJ. Some players may add outs for the possible straight; however, you would lose to a full house or KT. Even if the straight won, you would probably only split the pot.   In the actual hand, the player called. The flush came on the river. The big blind folded and the cutoff showed K9. The player collected a large pot in this particular case, but his call has a long run negative expectation given the pot size and betting sequences that occurred in the hand.   

4/ You raise in early position with A K. A middle player calls and both blinds call. Four players see the flop of 9 5 3. The big blind bets, you raise, the big blind reraise, and you call. The turn is the 2. The big blind bets. There is $320 in the pot. What do you do? (The answer is below  in black font. Mark all the space below in order to know the right answer.)  Answer: Call. The worst case scenario is that your opponent has a set or two pair. A straight is doubtful based on the betting sequences in the hand. Even in the worst case scenario, you still have four good outs to a gut-shot straight. A gut-shot draw is 11 to 1 requiring a pot of $440; however, you also have additional outs if your opponent is betting a pair. These outs are counterfeited however if your opponent holds A9, A5, A3, K9, K5, K3, a set, or two pair. I would discount the six outs to the ace or king down to three outs; therefore, J would play the hand as if I had seven outs, which is 6 to 1. Odds of 6 to 1 require a $240 pot; therefore, calling is justified. In the actual hand, the 4 came on the river giving the player a straight while his opponent showed 5 3.    5/ You hold A K on the button. A middle player calls and you raise. The big blind reraise and you both call. Three players see the flop of Q J 8. The big blind bets and you call. The turn is the 9. The big blind bets. There is $270 in the pot. What do you do? (The answer is below in black font. Mark all the space below in order to know the right answer.)   Answer: Fold. You have 10 outs to improve your hand; however, an ace is counterfeited or already no good if your opponent holds AQ, AJ, AT, AA, QQ, JJ, or TT. All of these hands are possibilities from a reraise in the big blind. In fact, the only reasonable hand that you could expect to beat if an ace comes is KK. If the river is a king, your situation is worse as you could not heat any reasonable hands, and will only split if your opponent holds AK also. You have four strong outs to the gut-shot straight, although there still is the possibility you might split. Four outs are 11 to 1 and require a pot of $440 to be profitable. In the actual hand, the player folded.    

 

Some cases to think over

June 15th, 2006

1/ You hold 9d 6d in the small blind. A middle player and the button calls. You call and four players see the flop of As Qh 6c. The middle player bets and the button calls. There is $120 in the pot. What do you do? (The answer is below in black font. Mark all the space below in order to know the right answer.)

Answer: Fold. You have five outs to improve your hand, which is 8 to 1. The pot odds are only offering 6 to 1 so you should fold. Even with better pot odds, you would need to discount your outs for the possibility that you are drawing practically dead to AA, QQ, 99, 66, AQ, A9, A6, K6, Q9, Q6, J6, and T6. Rarely draw to two small pair unless the pot is exceptionally large, and preferably when an ace is not on the board since there is a better chance that your outs are counterfeited with someone holding Ax {any hand with an ace in it).

2/ You hold As 9d in the small blind. A middle player and the cutoff call. You call and four players see the flop of Qc Td 9h. You check, the big blind bets, and the middle player and cutoff both call. There is $140 in the pot. What do you do? (The answer is below in black font. Mark all the space below in order to know the right answer.)

Answer: Fold. You have five outs to improve your hand; therefore, you are 8 to 1 against improving requiring a pot of $160. In addition, with so many callers, there is a good chance that one of your opponents flopped a straight, a set, or two pair with this type of flop. If an opponent has two pair, your outs are reduced to three if they hold a 9 also. If an opponent holds a pair, your ace is counterfeited against AQ or AT. Even in the best case scenario where you improve to the best hand on the turn, with so many opponents there will be many ways you could lose on the river. You need very good pot odds to draw with such a dangerous flop against so many opponents. In the actual hand, the player folded. One opponent showed Q9 and the other KJ.

3/ You hold Ad Tc on the button. An early player and middle player call. You raise and the small blind calls. Four players see the flop of Qs Th 9d. The middle player bets. There is $10 in the pot. What do you do? (The answer is below in black font. Mark all the space below in order to know the right answer.)

Answer: Raise. Note how your hand and the flop are almost identical to the previous problem; however, there are two main differences. First, the pot was raised preflop, giving you better pot odds. Second, two opponents have checked, indicating weakness. This differs from the previous hand where you already had three callers, making it difficult for you to have a winning hand. Your opponent could be betting a straight draw with a weak pair, in which case you may currently have the best band.

In low-limits, most opponents slowplay straights, sets, or even two pair, so usually you do not have to worry about those hands. Even if your opponent has top pair, you have five outs, which is 8 to 1. The pot odds are 10 to 1 so calling is justified; however, I prefer raising in this situation. Raising will drive out the other opponents from weak gut-shot draws and may allow you to possibly take a free card on the turn. Raising will also give you information on the flop about your opponent’s hand once you see how he responds. In the actual hand, the player just called and hit a full house when an ace fell on both the turn and river. The bettor folded and the early player showed A8.

4/ You hold Qs Jh in the big blind. A middle player, the cutoff, and the small blind call. Four players see the flop of Ad Ts Td. The middle player bets and the cutoff calls. There is $6 in the pot. What do you do? (The answer is below in black font. Mark all the space below in order to know the right answer.)

Answer: Fold. You have four outs to the gut-shot straight, and this is reduced to three outs if one of your opponents has a flush draw. You also are drawing dead if one of your opponents holds AA, TT, AT, or KT. Three outs are 15 to 1 and the pot is only $6. In the actual hand, the player called both the flop and turn and got his straight when the K♦ fell on the river. Unfortunately, one of his opponents had 6♦ 5♦ and hit a flush. Straight draws go down in value when the flop is two-suited or paired, especially when they are only gut-shot draws.

5/ You hold Jc 9c in the big blind. An early player calls, the next early player raises, and the button, small blind, and you call. Five players see the flop of Jd Th 9h. You decide to check and the early position player bets into the preflop raiser who decides to raise. The small blind and you call. The early player reraises and the preflop raiser caps the betting. The small blind calls. There is $11.50 in the pot. What do you do? (The answer is below in black font. Mark all the space below in order to know the right answer.)

Answer: Call. With so much, action you are probably against a straight, so you will need to improve. You have four outs to a full house, which is 11 to 1 against improving, but you are getting 12 to 1 pot odds assuming the early position player calls. If you do hit one of your outs, you should win a lot more bets. In the actual hand, the player folded. An opponent with Q♣ 8♥ won the hand. Although this player saved some bets since a jack or 9 did not come, the actual result of the hand does not mean his play was correct. In the long run, he would make more money by calling with the implied pot odds he was receiving.

Odds, Pot Odds, and Implied Odds

June 14th, 2006

To play poker well, you must understand the terms odds, pot odds, and implied odds. Let’s be sure that you grasp each term thoroughly before we go on.

Probability and odds
“Probability” is the likelihood of an event happening. It is a number between zero and one, and is often expressed as a percentage. For instance, a .70 probability of rain today is the same as a 70% chance of rain.
“Odds” are another way of expressing probability and are more applicable to games of chance such as poker. Odds are shown as a pair of numbers separated by a colon; the pair represents a ratio between the probability of an event happening and its not happening. Being somewhat whimsical, we could say (from our example above) that rain is a 7:3 “favorite” today. That is, the odds of rain are 7:3 in its favor; for every seven times it rains on a day like today, there will be three dry days. The opposite of favorite is “underdog” (or “dog” for short). If you say, “That team is a 5:2 underdog,” you mean that for every two times they win in this situation, they will lose Five.
What do odds mean to betting? Let’s consider the weather forecast above. You and a friend decide to bet on whether it will rain. Given that you know rain is a 7:3 favorite, what is a “fair” bet? If you choose to bet on rain, and your friend bets on no rain, you should put up $7 for each $3 he wagers. Over 10 days, it will probably rain seven times. You will collect $3 from your friend on each rainy day for a total of $21. On the remaining three days, it will not rain. Your friend will collect $7 from you on each dry day for a total of $21. Thus, on any given day, one of you will pay the other, but in the long run, you will both expect to break even. Now, suppose you can find somebody willing to put up $4 for each $7 you bet, but you know that rain is indeed a 7:3 favorite. You still lose $21 on the three dry days, but you collect $4 each of the seven rainy days for a total of $28. In 10 average days, you make a $7 profit! This book will teach you to find and exploit opportunities where you have a similar edge over your opponents.
Let’s look at a hold’em example. Suppose you have flopped a heart flush draw. That is, you have two hearts in your hand, and two more come on the flop. What are the odds of making your flush on the next card (the turn)? There are a total of 13 hearts in the deck; you have seen four of them, leaving nine more. You have seen a total of five cards (your two plus three in the flop). That leaves 47 unseen cards, of which nine are the hearts you want to see. There are 38 cards that do not make your flush and nine that do; the odds are 38:9 “against.” You are a 38:9 (slightly worse than 4:1) underdog to make your flush on the turn.

Pot odds
Pot odds are the odds being offered to you by the pot compared to the amount of money you must invest in it. For instance, suppose after the river card is turned up, there is $30 in the pot. Your opponent bets $6. The pot now has $36 in it, and you have to call $6 to see his hand. You are getting pot odds of 6:1. You will also hear the expression “the pot is laying you 6:1.” Now your choice is (relatively) easy: if you are no worse than a 6:1 underdog to win the pot, you call the $6; otherwise you fold.
Pot odds also apply to draws. Suppose you have a draw that is a 3:1 underdog to be made. For you to call a bet there should be at least three times as much money in the pot as the amount you must call. Of course, that includes any bets that precede your call. For instance, if the pot contains $15 and your opponent bets $6, the pot now contains $21 and is laying you 3.5:1. Since you are only a 3:1 underdog, you can call.

Implied odds
Going a step beyond pot odds are implied odds. More accurately, they might be called implied pot odds. When you compute pot odds, you can only consider the money that’s already in the pot.
The concept of implied odds lets you ask the question, “If I make the hand I’m drawing to, how much more money will I win than what’s already in the pot?”
For example, suppose you have a flush draw with one card left to come. You know you are about a 4:1 underdog to make your flush. There is $16 in the pot, and your opponent bets $6. The pot (now $22) is laying you about 3.7:1, but you’re a 4:1 dog to make your flush. According to strict pot odds, you can’t call. However, suppose you’re “sure” that your opponent will call a $6 bet on the river if you make your flush. Now you can act as if the pot contains $28 (what it currently contains plus the $6 more you will win if you make your flush). You can make the $6 call with your flush draw.
Of course, when considering pot odds or implied odds for a draw, you must be “sure” that you will win the pot if you make your draw. If you’re not sure, then the pot must lay you a higher price to make your draw correct. Also, when considering implied odds, you must be just as sure that your opponent will call your bet after you have made your hand.