bet at 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.

This is generally a very good flop for you. Suppose you have raised with
A♣ J♣
in late position, four other players have called, and there has been no other raise. The flop comes
J♦ 9♥ 2♥
You probably have the best hand right now. However, there are a lot of things than can go wrong. If the turn card is
K♥
you will have to fold if there’s any substantial action. Therefore, you want to raise immediately on the flop, and make it expensive for flush draws and overcards to stick around. Even if the board is less threatening (for instance, J♦-6♥-3♣), you still want to raise on the flop. This may get out hands like KQ, which you would like to do. If it’s checked to you, bet. If you’re in early position and you get the first flop, you have a problem. You would like to check-raise, but you must be very sure that somebody will bet. You definitely don’t want to give a free card to somebody with KQ or two hearts. If somebody in late position raised before the flop, he may well bet on the flop, giving you the opportunity to check-raise. If you are the first per¬son to act after the raiser, this would be a perfect time to check-raise, as you have a good chance of making it a heads-up contest.
If you were the preflop raiser, be more inclined to bet (rather than check-raise) on the flop if the flop hits you. Being the pre-flop raiser, you’re almost expected to bet, and this gives you the chance to re-raise if somebody raises behind you.
Note that if you have K♣-J♦ and the flop comes K♦-8♥-3♣, the check-raise is an excellent play because you aren’t afraid of an overcard (except an ace) on the turn. If it’s checked around, that’s unfortunate, but not likely to be catastrophic. It may also confuse your opponents when you bet on the turn. For instance, if the turn is the T♦, somebody with a ten may call you both on the turn and the river, not believing you have the king.
Let’s return to the situation where you have A♣-J♣ and the flop is J♦-9♥-2♥. If you raise and are re-raised (or bet and are raised), you must decide how to continue. If you think that raising again will limit the pot to you and the raiser, it may be worth re-raising, even if you suspect he has you beaten right now. By eliminating the other players, you are giving yourself a better shot to win the pot (even though it will cost you an extra bet here). For instance, many players would stay in here with a hand like Q♥-9♦. For one bet, that would not be a terrible play. How¬ever, if you re-raise and force that person to call two bets cold, he will probably fold. By knocking him out, you save the pot for yourself if a queen, nine, or two more hearts fall.
If you don’t think you can eliminate other players or you are sure that the raiser has a strong hand, you can back off - call the raise and then check and call to the river. It will be difficult to fold in this situation unless the third flush card hits or a king or queen hits. If your opponent continues to bet into you then, you might think about dropping. However, if you call a bet on the turn, you must be absolutely sure of your opponent if you decide to fold on the river. By that time, the pot will be quite large, and you will be making a catastrophic mistake if you fold incorrect¬ly. We are not urging you to call every bet on the river. Nevertheless, an incorrect fold in this situation can be very expensive, depending on how badly you mis-estimate the odds that you are beaten versus the pot odds.

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.

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.

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.

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?

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