Win Poker

When calculating odds, you need to use the number of discounted outs that will help you win the hand. As discussed before, it does you no good to improve your hand only to lose to a better hand. Let’s look at some examples to see better how you determine the number of discounted outs.
You have K♦ Q♣ and the board is J♦ T♣ 5♥ 2. You have eight strong outs to the nut straight with any ace or 9 and six weak outs to the king or queen. The six outs to the king or queen are weak since your opponent could ahead; have two pair or a set or is counterfeiting your outs.
In this example, a king would give you a pair but might also give an opponent a straight, two pair, or a pair with a better kicker. Note all the hands you would lose to if a king comes: KK, JJ, TT, 55, 22, AK, AQ. KJ, KT, K5, K2, Q9, JT, J5, J2, T5, and T2. If a queen comes, you would lose to QQ, JJ, TT, 55, 22, AK, AQ, K9, QJ, QT, Q5, Q2, JT, J5, J2, T5, T2, and 98.
How much you should discount your weak outs often depends on how many opponents you are against. In the example above, you have six weak outs. Against a lone opponent, if you feel that 50% of the time a king or queen will help you win, you should discount the six weak outs to three. In this case, you would play the hand as if you had an equivalent of 11 outs to win the hand, the three discounted outs and the eight strong outs to the nut straight. If you are against two opponents, you might estimate that a king or queen would win only once every six times; therefore, you would play as if you had nine outs, eight nut outs to the straight plus the one discounted out. Against three opponents, you should probably disregard the weak outs since it is unlikely a king or queen will win. In this case, you would play only if you draw to your eight nut outs is justified. Let’s look at some more examples.
You have A♣ T♥ and the flop is K♦ T♣ 5♠. You have two strong to the ten, unless an opponent holds KT or T5. Another ace would give you two pair, but your out is counterfeited if an opponent holds AA, AK, or QJ, so you should discount the out to the ace. All your outs should be discounted slightly for the possibility that an opponent holds a set. Depending on the number of opponents and the betting sequences, you should play this hand as if you had between two and four outs.
You have A♣ 9♥ and the flop is J♦ 9♦ 4♣ with several callers on the flop. You probably are against a flush draw, so the A♦ is counterfeited. You could also lose to another ace if someone has AA or AJ. Always account for the possibility of a set.
Hint: Whenever the flop is two-suited, you should discount a suited out against a lone opponent and probably disregard the out against several opponents for the risk that one of them holds a flush draw.
A common mistake made by many players is drawing to weak hands when flush draws are likely. As a general rule, most draws are not profitable with a two-suited flop arid several callers in the hand. The only exception to this is when the pot is exceptionally large. This is a key concept since you will be playing with a two- or three-suited flop about 60% of the time! This concept is discussed further in the flop chapters. For now, simply understand that you need to discount or disregard your outs based on the likelihood that they are counterfeited.
Another consideration when determining your outs on the flop is the possibility that you could improve on the turn only to see an opponent improve to an even better hand on the river.
Hint: When drawing on the flop, you should discount your outs a little, and maybe a lot, for the probability that your opponents could draw to an even better hand on the river.
There are very few hands that are a lock to win on the turn. Nut flushes can lose to a full house if the board pairs on the river. The nut straight can lose to a flush on the river. Your two pair could lose to an opponent hitting a set. When the flop is two-suited, these types of situations occur often since there are a lot of river cards that could hurt your hand.
Most players complain about their bad luck when they improve on the turn to lose on the river. Good players recognize that these types of situations occur a lot and include this possibility in their decision-making process. Borderline draws on the flop should often be folded for the possibility that you will lose on the river.
Now that we know how to determine the number of discounted outs and calculate the odds against improving to the best hand, we can look at how to apply odds at the poker table.

Overcards are cards higher than anything on the board. Let’s consider an example. You have
K♦ Q♥
and the flop comes
9♣ 6♥ 2♦
You have two overcards - can you call a bet? Can you bet? Many poker experts say that you can bet or call a bet in this sit¬uation. However, it takes a lot of experience and knowledge to know when you can play with just overcards. A bet with two overcards is usually a semi-bluff (you’re hoping to win the pot right there, but have chances of improving to the best hand). Most low-limit games are sufficiently loose and passive that a semi-bluff won’t work, so betting is probably not correct. We believe you are not losing much by folding in this situation if there’s a bet ahead of you. If it’s checked to you, take a free card and hope you turn top pair. In the situation above, if a queen or king falls on the turn, you probably have the best hand and can bet (or even raise).
Expert players are able to make some money with two overcards, but you are not giving up much by dropping them unless you have other possibilities (which we discuss below). Misplaying those overcards once or twice will cost you more than you could make by playing them correctly a dozen times. The problem with overcards is that you can win a little or lose a lot. Most of the time, you’ll have to throw them away on the turn because they don’t improve. Therefore, to make a profit with them, you must play aggressively when they do hit on the turn. If you pick the wrong time to do this, you may be raising with the worst hand. This is an area where you can improve your re¬sults by limiting your mistakes. Until you have a lot of hold’em under your belt and understand your opponents well, you can best limit your mistakes by staying out of these situations.
When you can play overcards
There are some situations in which you can call a bet with over¬cards:
Backdoor flush or straight possibilities. For instance, you have A♠-T♠ and the flop comes 9♥-6♠-2♣. Now you can call a bet since an ace or ten may give you the best hand, and another spade on the turn gives you the nut flush draw. If you’re hoping to make a backdoor straight, the turn should possibly give you an open end draw to the nuts. For instance, you have Q♣-J♣ and the flop comes 9♥-4♠-3♦. Again, you could make top pair on the turn, and a ten will give you a draw to two different nut straights. The higher your cards, the better, so if you do make the top pair on the turn, you will have fewer chances for an overcard to your top pair falling on the river.

A-K overcards on the flop
AK (often called “Big Slick”) is one of the most difficult hands to play if it “misses” the flop. You will either make top pair or two overcards with it, so you often find yourself wanting to con¬tinue with it, almost regardless of the flop. Do not fall victim to this trap. If you’re going to call with two overcards, AK is the hand with which to do it, but choose your places carefully. Look for situations where you’re virtually certain that hitting your pair will be good, you have backdoor draws, or suspect that an oppo¬nent is betting a draw. Furthermore, it is almost never correct to call a bet on the turn with an unpaired AK, unless you’ve picked up some other draw.
Once in a great while, you can raise with AK when it doesn’t pair on the flop, particularly if you suspect that the bettor doesn’t have a good hand. On rare occasions, this may cause the bettor to fold immediately, or at least get you a free turn card. If you are re-raised, or the bettor calls and then bets the turn, you are done with the hand. Realize that this is a deceptive play, and such plays have limited use in most low-limit games. Many players can not give up AK until the river fails to pair them; a classic tip-off is when somebody raises pre-flop and then passively calls a bet on the flop. If you detect such behavior, be prepared to bet hands that you might otherwise check on the turn; don’t give the two overcards a free chance to beat you.

A word of warning
In tighter games, you can use the flop to decide the chances that you’re up against two pair already. However, in a no fold’em hold’em game, many players are capable of showing you any two cards. For instance, in a tighter hold’em game you’d be more inclined to play overcards with a flop of T-5-2 since it would be unlikely somebody already had two pair. In lower limit games, you will see people win big pots with T5. This is another reason why it’s a marginal play to continue with just overcards in low-limit hold’em games.
You will routinely see your opponents continue playing (even calling a raise cold) with two overcards to the flop. You will also occasionally be sitting on the sidelines watching when your overcards would have made the best hand. Have faith, and throw them away the next time, too. For low-limit hold’em players, flopping two overcards is a marginal case of our next topic: what to do when the flop misses you completely.

Playing When the Flop Misses You
In completing our discussion of how to play on the flop, we need to remind you that this, unfortunately, will be the most frequent result of the flop: you get a very small piece of it, or less.
You’ll flop second or bottom pair with no overcards. Three to a Hush or straight and nothing else. One overcard. Your opponents will routinely call a bet in this situation, hoping to pick up a little more on the turn. This is where decisive action can save you a lot of money:
Fold and be done with it.
We have discussed essentially every case in which you can play beyond the flop. Every other time, your pre-flop investment is gone. Forget about it. Watch the rest of the hand. See how your opponents play, figure out what you would do in a similar situa¬tion. Get up and stretch, drink a glass of water. However, do not just throw in a loose call on the flop to see what happens next. This discipline alone will take you a long way toward becoming a winning hold’em player.

Every once in a great while, you will be fortunate enough to flop a “complete” hand - straight or better.

When you flop a straight
This is the weakest of the complete hands, and is vulnerable to the most draws. Therefore, you want to play a flopped straight fast. Also, any time you flop a complete hand, your opponents will be slow to give you credit for it - you may get almost un¬limited raises from two pair or a set. Consider the following ex¬ample: you have
9♣ 8♣
in late position. There are three calls in front of you; the button and both blinds call. Now the flop comes
6♥ 5♦  7♥
There is a bet and two calls in front of you. Many players would just call in this situation - that’s a mistake - you should definitely raise. There are already nine bets in the pot, and there are many cards you don’t want to see on the turn. If any heart or five through nine falls on the turn, you no longer have the nuts. Furthermore, if somebody has flopped a set or two pair, he may choose to slow play it (which is also a mistake, though in this case it’s to his benefit). Your raise may cause him to re-raise im¬mediately and you re-raise again. Note that this puts enormous pressure on heart draws and hands like T♦-8♦, which is impor¬tant. Of course, playing this fast on the flop will knock out some players who have little or no chance to beat you. You’re better off paying that price and forcing draws to pay a premium. If you flop an ace high straight and there are no flush draws that worry you, you can slow down a little bit. If you have A♠-Q♠ and the flop is K♥-J♦-T♠, it’s OK to check and call or just flat call a bet. However, if a lot of action breaks out, you should take off the gloves and start raising yourself - if somebody has two pair or a set, you want to punish them now while you know you have the nuts. By playing slowly, you run the risk of a card such as the Q♣ falling (in which case you have to split the pot with any ace) or a very scary card like the J♥ (which makes full hous¬es possible and may give somebody a heart flush draw). The more players you have against you, the more inclined you should be to play your straight fast.
If you flop the non-nut straight (you have 8♦-7♦ and the flop comes J♠-9♦-T♣), it’s even more important to play fast. If an eight, queen, or king comes, you have essentially nothing, so you have to start swinging immediately. Even trying to check-raise is probably a mistake. Go ahead and bet, hoping you get raised so you can re-raise. If somebody has KQ (or Q8), you are going to lose some chips - you can’t give up this hand unless a cou¬ple of very scary cards hit.

When you flop a flush
This is another situation where many players make a serious mistake by not playing fast enough. If you flop anything but the nut flush, you must bet or raise to charge higher flush draws dearly. Suppose you have
Q♦ T♦
in middle position, you call along with four others, the big blind raises, and you all call. Now the flop comes
8♦ 5♦ 2♦
and the big blind bets out. Slowplaying is out of the question here. The pot is so big you’d be happy to win the whole thing right here (but that isn’t going to happen). Anybody with the A♦ or K♦ is going to call (which is correct for them). Raise imme¬diately. If somebody makes it three bets, you can flat call, but you still need to bet again on the turn if a blank comes - you don’t dare give a single bigger diamond a free card. Again, if somebody has flopped a bigger flush than you, you will lose some money. However, far more frequently you will have the best hand - but you must play it fast.
If a fourth diamond comes, you are now in a check and call sit¬uation, especially if anybody called your raise cold on the flop. There is still some chance you have the best hand, but you don’t want to call a raise with it. If a fourth of your suit comes and you have a lower flush (say eight or nine high), you may have to give it up. The fact that you most likely were well in front on the flop means nothing - throw your six card flush away if there is sig¬nificant action.
If you flop the nut flush, you can wait until the turn to raise or check-raise. However, as we discussed with the straight, if a rais¬ing war breaks out on the flop, you should start raising as well. If the board pairs, then don’t check-raise - you might be giv¬ing a full house a chance to make it three big bets. Bet out imme¬diately and hope you are called but not raised. If you are raised, you should call. Only if the board pairs twice should you be will¬ing to abandon the nut flush.

When you flop a full house
With a pocket pair, you will flop a full house a little more than 1% of the time; with two cards of different rank, about 0.1% of the time (one out of a thousand hands). In general, your only concern at this point is how to extract the most money from the hand - your chances of being beaten are minuscule. With pocket pairs, you can flop a full house in two different ways: one of your rank plus a pair, or trips on the board. Of course, you prefer the former way - in the latter case there’s always the danger that somebody has the fourth one. First, let’s consider the “set + pair” scenario. Suppose you have
8♠ 8♣
in middle position with six callers. Now the flop comes
8♥ 5♥ 5♣
This is an excellent situation for you. Of course, you hope that the other two fives are in different hands and that there is a flush draw around as well. Your hand is altogether strong enough to slow play, but you may not want to do that. If one or two players have fives, you want them to start betting and raising immediately, so you might bet or raise once to get things going. However, you don’t want to scare anybody at this point. Let other people do the raising on the flop. If you’re lucky, the turn will complete the flush, and two other people will do all the raising for you while you are just along for the ride. Things will probably slow down on the river, and that’s when you can get in your raise(s). If no flush or straight draw is possible on the flop, you should slow down a lot, hoping the turn will give some people big draws (that are probably dead).
However, once the turn comes, you should start betting and raising. A person with a flush draw will only complete it one out of five times on the river. By raising on the turn, you get these people to call, trying to make their flushes and straights. You’re delighted if they make them on the river, but usually they don’t, so you need to collect from them on the turn.
The situation is somewhat different if your set is the lower of the two ranks on the board. Suppose you have those same black eights, but the flop is
8♥ T♣ T♠
This is a wonderful flop for you, but not quite as good as the first one. Unlike the first case, there is a small, but important chance you will get out drawn. Furthermore, you will usually have to pay off some pretty big raises when you are beaten. However, until almost guaranteed otherwise, you must play this as the best hand. This time, you can’t wait to show aggression. Start betting and raising immediately on the flop - with the negligible ex¬ceptions of TT or T8, you are winning for now. Don’t hesitate to cap the betting on the flop given the opportunity. The same is true on the turn - play the hand strongly. Be willing to put in a third bet on the turn, and only get nervous if somebody puts in a fourth bet. Sometimes you lose to a bigger full house with this hand, but worrying about that very much is seeing monsters under the bed. Play it for the best hand, and just be alert for the small possibility that one of those monsters is real. If the board pairs (such as two running sixes), you will probably have to fold. Fortunately, this doesn’t happen very often, but if you have been getting a lot of action on the turn, and then the turn card pairs, your full house is almost worthless. Furthermore, you’re going to get caught in a raising war if both tens are active. Give up and get out.
If the flop is all one rank when you have a pocket pair (.24% of the time), you have an awkward situation. If you have a big pair (tens or higher), you probably have to stay with it as long as no overcards fall. If an overcard to your pair hits, you are beaten by a single one of those as well as the fourth card of the flopped rank; now you can get out if there’s a lot of action. If you have a big pair you should bet the flop to avoid giving bigger cards a free card. Also, in this situation, almost anybody who has flopped the quads is going to slow-play. Use bets and raises on the flop to figure out who is willing to stick around. For instance, watch out for a player who calls a raise cold on the flop - pro¬ceed carefully. Plan to check and call on the turn and river - somebody with quads will probably wait for big bets to raise. If you hold two cards of different rank and flop a full house, the situation is similar to flopping top set with a smaller pair. Sup¬pose you hold
J♦ T♦
and call in middle position after two other callers. Now there is a caller behind you, a raise, and two cold calls. Everybody else calls. The flop comes
J♣ J♥  T♣
You’ve got the nuts, and the chance of your being out drawn at this point is almost nil. Unfortunately, it’s unlikely that you’re going to get much action from anybody. If somebody has the case jack, he’ll play with you - other than that you have to hope that there are some straight and flush draws out. You might as well start betting with this hand - hope that the last jack is, in fact, active, and that player starts raising. Many players will stay in with their draws here even though they’re drawing dead.

Note that initially we are discussing a split two pair - when you have two different ranks in your hand, and you flop one of each of them. We will discuss the “pair on the board” situation later in this chapter.
Two pair is a powerful hand that you can play quite strongly. However, it is rarely strong enough to slow play. If you are play¬ing quality hands, your two cards will be close to each other in rank (AXs being the obvious exception). That means that if you flop two pair you have to worry about a straight draw, if not a made straight. Adding the possibility of a flush draw, you have a hand that demands to be played fast; you need to reduce the odds for drawing hands.

When you flop top two pair
Suppose you have
J♦ T♦
and the flop comes
J♣ T♥ 5♥
You can be almost certain that you have the best hand right now.1 However, you are susceptible to lots of draws. You are es¬sentially even money with somebody who has
K♥ Q♥
Remember also that in low-limit games, the pot has already got¬ten big. You should do whatever you think will get the most money in the pot on the flop. If you think that a player behind you will raise, bet out immediately and hope you get to re-raise. If you think somebody will bet but not raise, check-raise. Of course, this is a situation where you don’t want to give a free card, so if there’s any doubt in your mind, bet.
If somebody puts in a third or fourth raise on the flop, you need to consider the possibility that he has a set. Now it might be cor¬rect to check and call on the turn and river. If you put in the last raise on the flop, you can bet this hand all the way to the end if the board is not threatening. For instance, suppose the final board is J♣-T♥-5♥-8♦-7♥. You should definitely bet when the 8♦ hits on the turn, but the 7♥ on the river is a terrifying card, as any nine makes a straight, and a flush is possible. You should check, and call if there is no raise. If there’s a raise, you’d have to fold here.
Even if the flop is J♣-T♥-7♥ (which makes a straight possible), you should play this hand aggressively. If somebody has a straight, he will probably let you know it quickly (he will be afraid of the flush draw as well). Again, in this situation, you can back off and just call bets. The board will have to become very scary before you should drop this hand.

When you flop “top and bottom” or bottom two pair
These hands are still strong, but they are vulnerable to the board pairing and draws. Suppose you have
7♣ 6♣
And the flop comes
Q♦ 7♥ 6♠
If another queen hits, you have just about nothing (but can at least fold with a clear conscience). Therefore, it’s all the more important that you get your bets in on the flop. Also, don’t be so eager to re-raise a second or third time as you would with top two pair. In the situation above, you’d like to believe that nobody was playing Q7o, but in low-limit hold’em, your opponents will routinely show you that (and Q6o, too).
As we discussed before, you should normally be playing cards that are fairly close in rank. Thus, you won’t be flopping top and bottom pair too often, with the occasional exception of AXs. When you flop two pair with that hand, play it fast. Many low-limit players will play any hand that contains an ace, and you could quite conceivably be up against the other two aces. If that’s the case, you can make a lot of money, and you don’t want to give them free cards with which to make a bigger two pair or pair the middle card on the flop. This also insures that you’ll be charging the straight and flush draws as much as possible.

Two pair with a pair on the board
This situation is far less desirable than a split two pair. For in¬stance, you have raised with
Q♣ Q♦
and the flop comes
T♥ 8♠ 8♥
Unfortunately, in low-limit games, many players are willing to play almost any two cards, so it’s hard to figure the probability of somebody having an eight. There is one obvious consideration - the more opponents you have, the more likely it is that one of them has flopped trips. If the entire table takes the flop, and there’s lots of action, you must get out. While you may have the best hand, you can’t play it with any degree of cer¬tainty, and somebody with an eight may just wait and then check-raise you on the river.
In the above situation, it’s worthwhile for you to bet on the flop, hoping to win the pot right there. However, if you get called, you have to slow down. You could be up against somebody with a ten, which is fine, but you also may have run into an eight. You should now check on the turn, but be prepared to call a bet on the river. Somebody may represent an eight and you can catch the bluff, but don’t give somebody who really does have an eight the opportunity to raise you on the expensive bets.2 Note that betting on the turn and river is a lose-lose situation for you. If you have the best hand, nobody can call you (for fear of the third eight). If you don’t have the best hand, you’ll get called or raised. If you bet the flop, and check the turn, you should be prepared to call a bet on the river if you don’t have a lot of opponents and no over¬cards to your pair have fallen. If they check to you again on the river after you’ve checked the turn, you should bet. One final thought about this situation: many players would never raise with an eight on the flop - they would wait until the turn to raise. If that’s the sort of player you’re up against and he raises on the flop, then you can treat your queens as the best hand and keep betting.
Obviously, if the board is paired over your pocket pair, you can fold at the first opportunity. In this case, you might not win even if you catch your miracle card.
The situation is similar if you pair one of your cards, and the oth¬er two cards are a pair. For instance, you have A♦-J♣ and the flop comes J♠-6♥-6♦. You can play it as you would the first ex¬ample. However, note that if you catch your miracle card (anoth¬er jack), you will now terrify somebody with a six, and he will just check and call, if that. Furthermore, you have to split the pot with the case jack if somebody has it. Therefore, this hand is even weaker than the first example and should be treated as such.

The most common way this can happen is when you have Axs, hoping to get a flush draw, and just an ace flops. For instance, you have
A♥ 6♥
one in front of the button. Five people call in front of you, you call, and then the button calls. Now the flop comes
A♠ T♦ 5♣
You have flopped top pair, but you can’t like it very much. You have six opponents, and if any of them has an ace, you are prob¬ably out-kicked. In a situation like this, if there is much action, you will have to get out. Sometimes when you get out, you will later discover that you had the best hand on the flop, but that will be the exception. If there is a bet and raise in front of you, you should probably drop right there and save yourself further an¬guish. If there is a bet and a lot of callers, the decision is less clear, but you should probably still fold.
If there is a bet and you are first to act after the bettor (players between you folded or the bettor is on your immediate right), you might want to raise. This is a positional raise designed to get you a free card. On your best days, everybody but the original bettor will fold, and he will check to you on the turn. You then check as well. You hope that he will continue to check on the riv¬er, but you should probably call a bet if he bets on the end. If the bettor re-raises on the flop, you can probably drop your hand right then.
Note that we did not recommend calling in this situation. This is an excellent example of tight-aggressive play. Either get out, or use your position to get a free card if possible. There is one ex¬ception to this. If the bettor is a maniac or a habitual bluffer, you might do well to simply call all the way. If he is bluffing, you will win more money by letting him continue to believe his bluff might work. If he has a better hand, then you lose less by not rais¬ing.
If you are in late position and it’s checked to you, go ahead and bet, but hope that all your opponents fold. If not, maybe you’ll gain a free turn card. If you’re called on the flop, prepare to check all the way from there. If you check the turn and some¬body bets on the river, you should probably call if the board doesn’t look too scary.
If you are in early position with such a hand, you may simply have to check and fold if there is significant action behind you. You have no position to use, and you cannot be the least bit sure you have the best hand. If everybody checks on the flop and the turn is not threatening, go ahead and bet, hoping to win the pot right there. If you are called, check on the river and hope the hand is checked through. However, you probably want to call a bet on the river in this situation. Many of your opponents will au¬tomatically bet top pair on the flop and assume you will, too. Since you didn’t bet on the flop, they will assume that second pair is good (or may be bluffing completely). If you are raised on the turn, you can probably fold (note that it will cost you two big bets to get to the showdown now). This whole discussion points out perfectly our concept of the dominated hand. You will be sorely tempted to call bets (and raises) all the way to the river with your top-pair-no-kicker hand, and yet time after time you will get shown a pair of aces with a better kicker. In the long run, especially against many oppo¬nents, you will come out ahead by dropping that hand as soon as it misses its flush draw. Note that if you get one of your flush cards on the flop, you are in a different situation. Suppose you have
A♦ 4♦
and call on the button after six others have called. If the flop is
A♠ 9♦ 5♣
you should call a bet on the flop. If the turn is a diamond, you have picked up the nut flush draw, and can easily call a bet. If you do not pick up your flush draw (or otherwise improve) on the turn, you are back to the earlier situation and probably have to drop.
An alternative in the above situation is to raise on the flop, and then plan to check the turn. Once you’ve done that, you will probably need to call a bet on the river, as your check on the turn may well induce somebody to bet.

There is a problem in low limit poker. It’s a very annoying problem for players who play right poker. I mean if you consider pot odds and implied pot odds and make your bets according to them it may be very offensively for them to see other players winning huge pots with 75o. If the story continues they may even go on tilt with the situation.
Do you know this story well?
Have you ever seen that damn suckers at your table?
BUT they may also be right. They may be right calling you all the streets ACCORDING TO POT ODDS! And that’s the problem of low limit poker.
In low limit poker the pot will normally be quite large on the flop because there are many callers pre-flop. Furthermore, these players want to call your bets on the flop - they did not come down to the card club to fold! Assuming you have the best hand, you now have two possible scenarios:
1. If you have an excellent hand - one that is unlikely to be beaten, regardless of the turn and river cards - you are happy to have all these people calling your bets and raises.
2. If you have a good hand - one that is probably best right now, but susceptible to being beaten - you would like to eliminate as many opponents as possible. This, of course, is the much more common scenario.
The combination of a large pot and people’s desire to call puts you in a bad situation when you have a good, but beatable, hand. Your opponents’ instinct (which is to call a lot) coincides with correct play. That is, it may be correct for them to call your bet because the pot is large, but they are calling in part simply be¬cause they want to call.
Suppose, however, we make your opponents pay two bets rather than one to continue playing. Now, even with a relatively large pot, they may be making a serious mathematical mistake by call¬ing. As we have said before, this is how you make your money at low-limit hold’em.
A classic example
You are on the big blind with
A♥ Q♦
There are three callers, and then a raise in late position. You (correctly) call the raise. Now the flop comes
Q♣ 7♥ 5♠
At this point, you suspect you have the best hand. However, if you bet out immediately, you will be putting the 11th bet into the pot, making it correct for hands such as 98 and 65 to call. Oppo¬nents with those hands might well call anyway, but you want them to make a mistake by calling when they’re not getting suf¬ficient pot odds. Now suppose you check, and it’s checked to the pre-flop raiser. When he bets, you raise; the players in the middle have to call two bets cold. Instead of getting 11:1 pot odds, the player directly behind you is getting only 13:2. If he has 98 or 65, he may decide to fold rather than call two bets. If he chooses to call, you make money because the pot odds do not justify his call.
But suppose you check, and the person immediately to your left bets. Now some people call, and then you raise. If the original bettor re-raises, the other players are forced to call two (more) bets cold - another mistake. If the bettor doesn’t re-raise, the other players are getting correct odds to call the raise. Neverthe¬less, the net effect is that you get a lot of money into the pot when you are a big favorite and your opponents have weak draws.
You will find that your opponents in low-limit hold’em will not be as observant as those in higher limit games. However, most people remember being check-raised. If you use the check-raise often on the flop, some of your opponents will become hesitant to bet into you for fear of being check-raised. This can be a sig¬nificant advantage for you, as in the following example. You call in middle position with
8♦ 7♦
and the flop comes
A♥ 9♦ 3♣
Everybody, including you, checks to the player on the button. If he bets, you can’t call because you didn’t get any of the flop. However, he remembers your check-raising him twice during this session, so he checks his A5, and the turn comes
6♦
Now you are happy to call a bet on the turn as you have picked up an open-end straight-flush draw! Admittedly, this is an exceptional case (you caught the best card you could have hoped for), but any time you get a free card with a hand that couldn’t call a bet, you have gained a significant advantage. In this case, the specter of your check-raising got you the free card.
The problem with the check-raise.
When you decide to check-raise, you must be fairly sure that somebody behind you will bet. If you check with the intent of raising but nobody bets, a terrible thing has happened: you have given a free card. This is another reason why you have to watch and study your opponents. In the first example above, you would really like to check-raise. However, if the alternatives are betting out immediately or having it checked around the table, then you should of course bet.
Sometimes the reputation that you get for check-raising works to your disadvantage - people are unwilling to bet for fear that you will check-raise! This is good when you have a bad hand with which you’d like to get a free card. It’s bad when you have a good hand and want to check-raise. Since you could use a free card more often than you have a check-raising hand, it’s OK that your opponents are intimidated. However, if your check-raise is to work, you must be confident that at least one of your oppo¬nents is prepared to bet.
Note: in a very small number of public cardrooms and casinos, check-raising is not permitted. It is also prohibited in some home games. If so, your only potent weapon to use up front is gone. You must play extremely tightly in front, and bet all your good hands immediately. Hold’em without the check-raise is a crippled game.

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.

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

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

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.