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Let me spoil the ending of my review right up front. I believe that "The Mathematics of Poker" is the most important book on poker written in the last decade, arguably the most important poker book of the last 25 years. Despite this, I believe that this book will help relatively few poker players, and as such, its impact on the games played in most card rooms will be relatively minor.

"The Mathematics of Poker" is not a poker book with a mathematical focus; it is a college-level math text whose subject matter is game theory as it applies to the game of poker. It is not an easy read. This reviewer has a degree in mathematics, yet at several points I found the book tough to follow. I expect that most readers who have not taken college math courses will struggle to digest what lies between its covers.

Play on every street in no limit Texas Holdem poker is important. Some players put a great deal of thought into how they will play the hand pre-flop, on the flop, and on the turn, but then neglect the river. They may think the river is simple. The final card is out, and you have a good idea whether you have the best hand or not, and can bet, fold, call or raise accordingly. In fact, there are some unfortunate errors in poker strategy you can make on the river in no limit Texas holdem, and understanding some of these ideas will improve your overall game.

Bluffing Errors on the River
Bluffing on the river is a tactic that can be used to great effect in no limit Texas Hold em, but should not be overused. You need to be sure that your bluff is convincing, not just by the way you sell it, but by the play of the hand. For example: The board reads Jh 9h 5c. A player makes a bet of half the pot and you call. The turn is a 3d. You call a pot sized bet. The river is a 3s. The opponent makes another pot sized bet and you move all in. This is a poor situation to be on a bluff. In the first place, your opponent may have bet so many chips already that he feels pot committed and calls even if he believes you have him beat. In the second place, it looks for all the world like you were calling along with a heart flush draw and are pushing all-in in a desperation move to win the pot at the end. Finally, it is very difficult to sell the idea that you have a 3 in your hand. It is unlikely you would have called any reasonable bet on the flop if you were holding a 3, since you would have missed the flop entirely. Even calling a large bet on the turn with bottom pair is unlikely. The only hand an opponent can really put you on is Ah 3h, and that is enough of a longshot that your bluff will probably fail.

Folding Errors On the River
If you have been calling along in the hopes of catching a good river card and you don’t, do not be so quick to fold on the river. Remember that depending on the amount of a river bet that you have to call, you may be getting correct odds to show your hand down. If there is a $300 pot out there and someone has made a $50 river bet, they only have to be bluffing (assuming you can beat a bluff) one time out of every seven for you to be okay. Of course, if you cannot beat even the weakest of hands, you must fold, but if you have a situation for example where you have backed into bottom pair and you suspect your opponent has been leading with A K all the way and missed everything, you may consider a call. Making this kind of call on the river is a vital part of your Texas Holdem strategy.

Calling Errors On the River
There are certainly situations, however, where you must fold on the river. If you have been putting an opponent on a flush draw all the way, and the third of a suit comes on the river, you will probably have to fold, especially if you bet and are raised. Of course many opponents will bluff in this situation, but if you have made a confident read, to change it just because you don’t like the implications will be costly. Making a good laydown is one of the hardest things to do in poker. Learning to make correct folds can have dramatically positive effects on your bankroll.

If you play limit texas hold'em, you may find yourself at times playing in poker games that are not full-ring games of nine or ten people. If the casino is not able to fill your particular game, you may find yourself playing against five or fewer opponents. Many online sites even offer you the option of playing short handed games. Are short handed games right for you, and how should you adjust your strategy in short-handed games?

If you are an action player who likes playing a lot of pots, short handed Texas Hold’em may be a good option for you. The blinds are coming around twice as fast, and players are half as likely to have very strong hands. What all this means for you is that many hands you would fold in a full game you will end up playing, and many hands you would play conservatively in a full game you will end up raising. If you are a tight player who likes to sit back and wait for big hands, short-handed play is probably not your speed.

So what is the best short-handed limit Texas Holdem strategy? As with nearly any form of poker, aggression is key. When you play your hands, you have to play them strongly. If you like your hand, bet. If you get raised, you will often re-raise, even when you would not do this in a full ring game. You are much more likely to get heads-up in a short game, so that should be your goal. If you do not aggressively attack and defend your blinds in this game, other players will take them away from you, and in a game where the blinds come around much more frequently, this can be fatal.

Big cards and pairs are great in when you play Texas Holdem fixed limit short-handed. Remember, even in a full ring game, most flops miss most people, so usually your big cards or pair will be best, and even when they are not, your opponents will often think they are. For example, you have 5 5 in a five handed game under the gun. You raise. You are in the worst position, but because you are short handed, you are only facing four people behind you, two of whom you will have position on for the rest of the game. Lets say you are called by the big blind and the button. The flop comes Q T 6, and you bet. The flop is very likely to have missed both players and you may win immediately, but a bet may still win you the pot against players holding hands like 7 7, A 6, or even T 8 if you continue to bet aggressively throughout the hand.

Small suited connectors are not that valuable in short handed limit hold'em, as even when you hit with them, which will be rarely, you will not make enough to justify the times that you miss. However, in position when other players have shown weakness, you can win by playing them aggressively just as with any other hand.

A popular online casino game is Pot limit hold'em, a variety of hold'em with a betting structure that allows you to bet up to the current size of the pot at any time, is a type of hold'em that presents a lot of play for a poker player. There are serious decisions to be made at every street, and the nature of the structure will inform these decisions a good deal of the time.

One decision that is seriously affected by the betting structure is what to do when you flop a set in pot limit hold'em. Flopping a set, or a card on the board that matches a pair in your hand, giving you three of a kind, is a slightly more common occurrence in pot limit than in no limit hold'em. The reason for this is that due to the pot limit structure, it is very difficult for players to shut their opponents out pre-flop, but it is still possible to win a big pot after the flop, so it is often profitable for opponents to call a pre-flop bet with even the smallest of pairs in the hope of flopping a set.

Two things can happen when you flop a set. You can flop a set on a threatening board or a non-threatening board. A threatening board is one where an opponent is likely to make a straight or flush. For example, if you have 8d8c and the flop comes 8h Kh Ts, this is a threatening board, as a heart could easily come to beat you.

In a no limit game, you must generally bet out to protect your set if the board is threatening. You have a powerful hand and do not want opponents drawing at a card that can beat you for free. On the other hand, if the board is not threatening to your hand, e.g. you have TcTs and the board is Ks Th 4d, you will often want to slow play, since it is
very difficult for opponents to catch up and you may trap someone to win a big pot.

In pot limit, the situation is almost the opposite. If you flop a set on a non threatening board, you should often bet out. It is key in pot limit to build a pot, so that you can make big bets later in the hand and get paid off. If you slow play and keep the pot small, many times you will not be able to get too much money when you spring your trap because the bet size will be limited. Unlike in no limit, a pot sized bet will not give away the great strength of your hand, because it is
commonplace to make a pot sized bet on the flop in pot limit when you are betting regardless of the strength of your hand.

In contrast, you may actually want to consider slow playing a flopped set on a threatening board. If someone else bets, you can make a large check raise and possibly give the draw incorrect odds to call. If a free card comes off, the pot will be small enough that someone who draws out on you will not be able to hurt you too badly.

As with all internet poker strategies, you should vary your play and not do the same thing every time. However, when you deviate from the considerations above, you must be prepared for the consequences and respond accordingly. This will give you the best chance to profit from your flopped sets.

Limit Texas Holdem is a game of big cards. If you are playing a tight, selective game, only entering most pots with premium holdings, you will often find yourself in a situation where you have flopped overcards, that is, two cards higher than any cards that appear on the board. It is important to know what to do with these overcards when you have them.

Some players will keep betting a hand like A K all the way to the river, even if they do not improve at any time. This is rarely an effective strategy. An unimproved A K is unlikely to win, and if someone continues to call you they in all likelihood have some kind of hand.

Your limit Texas Hold’em strategy on the flop should depend a lot on what has happened before the flop. If you were the pre-flop raiser, which you often will be with a hand like A K, you can go ahead and bet at a non-threatening board such as 8 7 3 of mixed suits if no one has come in in front of you. This gives you two ways to win the hand. You can win it outright as most players will put you on an overpair and fold and even if you get called, you can win if you hit an ace or king on the turn or river.

If you bet before the flop, the flop comes all undercards, it is checked to you, you bet and are check raised, you should fold the hand. A check raise indicates great strength, especially since the check raiser is aware that you showed strength before the flop, and you have nothing but unpaired high cards. You are almost certainly beat in this situation and even catching your pair will probably not help you.

If the board is very threatening, it's not a bad idea to check your overcards. If you bet, you are likely to win very little money when you have the best hand, and if you are betting into strong hands or draws, you will be ill equipped to continue with the hand. These types of mistakes will be very costly in the long run. Remember that the value of big cards is that when you flop a pair, it will usually be the best hand. When you don't, you don't lose anything by check folding and waiting for a better opportunity. It is difficult to intimidate opponents in limit hold'em due to the fixed bet sizes, so in most cases, getting out of line with overcards will be detrimental to your bankroll.

1 - Each chip in a short stack is more valuable in terms of cash-equity than each chip in a large stack. By calling in this situation I would have been risking chips of great value to pick up chips of lesser value.

2 - Folding removes any chance of busting. By folding, I would give my opponents a chance to bust on subsequent hands, which would move me up to a bigger payday.

After looking at these factors, it seemed that folding was the clear choice. But still, I had to think about how folding would effect my ability to win the bracelet - which was my primary concern. Would I be putting myself out of the running by giving up on so many chips? Not really.

When there are more than two players remaining, each additional chip you accumulate has a lesser impact on your ability to win the tournament. So when the chip-equity decision is a wash, you are better off folding than you are trying to accumulate more chips.

If you ever find yourself in a similar situation, you should also keep in mind that there's a big difference between moving all-in and calling all-in. When you move in, you can win the pot by forcing a fold. When you call, this obviously isn't possible.

If you're just learning to play the game of no limit hold'em, you are probably realizing that there is more to the game than just waiting for a big hand and betting as much as possible when you get it. No limit Texas Hold'em poker
strategy involves various tactics that maximize your win potential, including bluffing and slow playing.

The slow play is the opposite of a bluff. Whereas in a bluff you bet or raise to indicate strength when you are actually weak, in a slow play you check or call to indicate weakness when you are strong. The reasoning behind a slow play is that you do not want to scare your opponents into folding when you have a very strong hand. For example, let's say you are holding 88 and the flop comes Ah 8s 4d. An early position player who raised before the flop bets. An inexperienced player may get excited and move all in immediately, drooling at the prospect of winning all the raiser's chips. However if the raiser has a hand like AT, an all in move will likely cause him to fold, fearing an ace with a bigger kicker or worse. If you slow play by simply calling, he is likely to continue betting on every street, and you can spring the trap and raise him on the river once the pot has gotten too big to fold.

How to Slowplay
The important thing to remember when it comes to slow playing is that you generally only want to do it with a very strong hand. A hand like 9s 8c on a board of 8d 5h 3c is not one to slow play. You may have the best hand right now, but any card above 9 on the next two can put you way behind by giving the opponent a better pair. You would be perfectly happy to take the pot with a bet right here. You may check if you fear an opponent already has you beat, but if you sense you have the best hand, you should bet here.

Another occasion where it is generally unwise to slow play is when there is a big draw on the board. If you are holding 88 and the flop is Ah 8h 9d, you probably want to put in a bet if you have more than one opponent. Giving a free card here could be disastrous, as any heart could give an opponent a winning flush, and a 7 or T could make someone a straight. Even when you have a strong hand, you must make opponents pay for draws. The exception might be if you already have the draw beat.

If the flop to your 88 is 8h 7h 7s, this is a great opportunity to slow play, as you may let an opponent improve to a losing flush or straight that they will have to play you off with. On the other hand, it might be your opponent who fears a flush draw. For instance, if your opponent has made a preflop raise and you call with TT and the flop is AcTd7c you shouldn’t be worried about him having the draw, since he is most likely to have an ace so you can raise him even if there comes a third club on turn. In this instance you shouldn’t take the risk of letting him draw to a flush if he by chance would have a club in his hand so go ahead and raise.

While these are good general rules, remember that to be successful in online poker, you must vary your play and not handle each situation the same way every time. You should adjust your strategy based on your opponents' play and you should mix things up in order to confuse observant opponents. This will dramatically improve your chances of success.

The bluff. It's what poker is all about. In no limit hold'em, where you can put someone at risk for all their chips at once, bluffing is a powerful weapon. In fact, bluffing is more powerful in no limit games than in any other forms of poker for this reason. But maybe you are the type of person who can't even pretend he didn't take the last cookie from the jar. If deception is not your strong suit, here are some basics regarding bluffing. Some people say that bluffing does not work in a Internet poker game - they have no idea what they are talking about.

Bluff Like You Mean It
Betting $10 into a $250 pot is not a bluff; it is a pot sweetener. When bluffing, you must bet enough that opponents will be afraid to call. Of course, this means if they do call you could lose quite a bit of money, but this is what makes bluffing so exciting. Be careful though; an excessive overbet may be red flagged by certain opponents as a bluff, since if you had a real hand, you would want to bet a small enough amount that you could get called.

Use the Semi-Bluff
A Semi-Bluff is a situation where you would prefer your opponent fold, but if he does not, you still have a reasonable chance to win the hand. For example if you have Ah 8h and the board is 6h Jh Ks Qd and you move all in, you are hoping your opponent will fold. If he does not however, you will still win the hand if a heart or a ten comes. This can be an effective play for a non experienced bluffer, since you are less likely to betray how much you don't want to get called.

Be Consistent
The number one rule in poker is to be consistent. If you have been flat calling a flop of Kh 3s Td and a turn of 6c, then move in when the 6s comes on the river, opponents with strong hands will be hard pressed to believe that you have them beat. You are representing trip sixes, suggesting that you called pre-flop, flop and turn bets with a hand that was way behind. This is not a likely scenario. Similarly, if running flush cards come on the turn and river and you bet to try to represent that flush, you may not be very convincing. On the other hand, if you have been flat calling with a flop of two hearts and move in when a third heart comes on the river, you may fool many opponents into believing you have drawn out on them.

One issue that may come up in your poker games is the issue of talking at the table. Some players love to talk at the table, others never say a word. Televised poker seems to bring out the talkativeness in a lot of players, for obvious reasons. Table “talk” is also possible online through the chat feature. How you handle the banter at the poker table is actually a vital part of your Texas Holdem strategy. Here are some things to think about regarding the issue of table talk.

The first thing you should be aware of is that the rule in many tournaments is that you are not permitted to say anything that may induce or discourage action during a hand. If your opponent wishes to enforce this rule, you may be warned not to say anything or incur a penalty. Most players accept talking as part of the game, and are happy to let you talk as it may give them some information, but some do not, and in a tournament situation, you will have to accept this. In a cash game, no matter if you are playing Texas Hold em, Omaha, or some other poker form, prohibitions on talking are less common, but it is still possible that a floorman will ask you to desist if there are complaints.

Assuming that happens, how should you use talking at the table to your advantage? Clearly, anything you say that can induce or discourage a call, depending on what you want, is to your advantage. Often, just getting another player to talk can give you important information. Players may talk more rapidly if they are weak, or stop speaking suddenly when they are strong. Talking is a behavior that you can observe and catalog at the poker table just like any other.

Talking can also make it easier to trap or bluff opponents. If you take a very friendly attitude with one of your opponents, chatting them up in a pleasant manner, they will probably think you are less likely to try and bluff them. Similarly, if you antagonize an opponent, he may call you just to prove that you aren't getting to him.

You should never be abusive or offensive while talking at the table, and you should never say things that will make players want to leave the game. A happy table is an action table, and if you get too many people upset, they will either tighten up or just take their chips and go home. You also do not want to instruct bad players. If someone makes a terrible play and wins, you should encourage them so they continue to make the same bad plays until luck catches up with them, rather than shame them into playing better and reducing your edge.

In poker, you are always trying to play with an edge. If you feel that talking at the table gives you an advantage, either by helping you control your opponents or by giving you information, you should do it. If not, you shouldn't feel the need to talk at all. If you want, you can even bring a sign to the table saying “I do not talk about poker or answer questions during the game”; that generally settles the table talk issue neatly.

Two consecutive card of the same suit, also known as suited connectors, are some of the most interesting hands to play in no limit Hold'em. When you start playing Texas Hold'em, especially if you learned by watching shows like the WSOP on television, you may easily fall in love with these cards. Most players quickly find that they are getting into some very costly and tricky situations when playing suited connectors too often. Once you are a more experienced player, you can play suited connectors much more profitably. Here are a couple of things that you must consider to play suited connectors effectively.

Beware of Trouble Situations
When you play suited connectors in no limit Holdem your position is of great importance, especially if there generally are preflop raises. Then you shouldn’t play suited connectors unless you are on the button and there are at least four people in the pot already. But if there is a raise and a re-raise you should fold, no matter which position you are in. You certainly don’t want to get caught in a raise war.

If you play 7c 8c, the flop comes Kh 9c 7s and you feel obligated to call a reasonable sized bet, you probably should not be playing these hands to begin with. If you continue to play because you have a good read on your opponents and sense weakness, that is fine, but if you have difficulty releasing your hand if you catch any part of the flop, you should not be playing these kinds of hands. Your goal with suited connectors is generally to see a flop cheaply and hit the flop hard with a well disguised hand. Even if you make a flush you must be able to release the hand in certain situations, despite the fact that this may have been your goal coming into the hand.

Decide If You Will Bluff Before the Flop
If you limp in with a suited connector hand and periodically raise when you miss the flop entirely, you may be setting yourself up for trouble. Usually your best approach when you miss with suited connectors is to check and fold and hope you can hit next time. The idea most of the time is to invest a little to win a big pot, and making a big pot with nothing does not usually achieve this goal. If you are planning to bluff if you miss, you should usually raise pre-flop and assess the texture of the flop before bluffing. Sometimes you will decide a threatening board is a good one for you to bluff at, other times you will decide the board probably hit somebody hard and back down. This decision should be based in part on your assessment of your opponents and should also be considered before you enter the pot to begin with.

If the above concepts are foreign to you, you are probably not ready to make suited connectors a regular part of your repertoire until you integrate these ideas. They can still be played under the right circumstances, but playing suited connectors too often if you do not have the requisite skill can be very expensive.

A valuable tool in your poker repertoire is the check-raise (also called “sandbagging”). A check- raise, where you let someone else bet for you so you can trap them for an additional bet, was once considered “dirty poker” and frowned upon by many, although it was almost always allowed. These days, most people accept check-raising as a crucial part of poker. The check-raise is often used in online casino poker. Especially in shorthanded Texas Hold’em games it is an integral part. But many Hold’em players overuse the check-raise and really has no idea when its proper to use it. Here are some basic ideas that will help you decide when to check raise.

You Have a Strong Hand, But One That is Vulnerable
Often you will find yourself with a hand that is probably best right now, but may not be after more cards come out if you have many opponents, something that’s not unusual in for instance low limit online Texas Hold’em. You don't want to scare anyone away, but you're not sure how much heat you can take after the flop, turn or river. Examples of hands like this are big pairs before the flop, such as AA, KK, or QQ, or a hand like two pair after the flop in Hold’em. Rather than check call or make a small bet and allow someone to take a card off cheaply that can beat you, or bet too much and fail to get value out of a strong hand, this is often a good time to check-raise. Of course, you run the risk of having it checked around, so you should consider your position. The earlier you are in the hand, the more likely you are to get an opportunity to check-raise.

You Are Trying to Earn an Extra Bet
Especially useful in limit poker, a check-raise can be a good way to earn a bet that you might not otherwise have gotten. Let's say someone is betting aggressively the whole way with what you are sure is top pair. You've been checking and calling with a lower pair. On the river, you back into two pair. Rather than bet and alert your opponent that you hit something, you might go for a check-raise and try to get two bets instead of zero or one. The same tactics are applicable when you have something very good right from the start like a set in Texas Hold’em, a check-raise in the latter rounds can earn you an extra bet or two. Note that if you are drawing for a flush and you hit it, you are probably better off betting out, as your opponent may be afraid to bet again if the board has become unfavorable, this is particularly true in Texas Hold’em and Omaha where its easy to determine opponents hands by looking at the community cards.

You're Bluffing
A check-raise bluff can be extremely effective. Because a check-raise indicates such strength, it is very hard for an opponent to call without a powerful hand. This works best if you've have raised earlier on and then passed on initiative to the other player by checking and calling all the way until the turn, when you put in the check-raise. It is not or the faint of heart, as you will be putting chips in the whole way with a weak hand, and if you check on the turn and your opponent checks behind you, you probably have to bet out on the river, but then you there is a great risk of being called, especially in fixed limit games. It is very hard to put someone on a bluff in this situation. Be sure when you make your check-raise your opponent is not already pot committed. If there are enough chips in the pot relative to how much he would have left if he folded in this situation, he may have to call even if he believes you have him beat.

You might have read Super/System and Sklansky. You've put in a lot of hours at the virtual poker table. You can always point out your friends' mistakes when you watch them play. Yet somehow at the end of the month, you're in the red at poker. How can you understand all the strategy and not be a consistent winner? Perhaps it is in one of the following areas where your problems lie?

You Lack Discipline
It's one thing to play correctly when you first sit down to play. It's quite another to play the exact same way five hours later, especially when you have sustained some devastating bad beats. If you are a player who starts to loosen up when he sees a loose player doing well, or throws away pocket queens before the flop because you lost your whole stack with them the last time someone flopped two pair, you may need to work on your discipline, or at the very least, learn to get up from the table when you're not playing your best.

You're Too Emotional
There's nothing wrong with targeting a weak player at the poker table if you're doing it for the right reasons. However if you are targeting a player because he drew out on you after making a loose call, or because he talks too much, or because you just don't like him, you are probably putting yourself at a disadvantage. Ask yourself if you are the type of player who enters pots that he shouldn't just to get back at an obnoxious opponent, or just in the hopes of beating a weak player out of a big pot, even if the situation doesn't merit you being in the hand. If this sounds like you, you may need to get better control of your emotions. Especially when playing online poker it’s easy to go “on tilt” and act irrationally but if you play live you have to control your emotions because there are people around you. Learn how to do the same when you play online poker as well.

You're Playing Over Your Head
Poker is a game of short term luck, and if your bankroll can't withstand the swings, it doesn't matter how well you play. Be sure your bankroll allows you to stay in the game for a long time, to give your skill a chance to overcome the luck element. If you find yourself running out of money in a game you think you can beat, you may need to build your bankroll at a lower limit before you get back in that game. A good bankroll in fixed limit should be approximately 200 times bigger than the limit you are playing at, for instance if you play $5-$10 limit you should at least have $2000 in your bankroll.

It's Not As Easy As It Looks
If everyone who said they were a winning player really were a winning player, poker would grind to a halt, since the few players who were losers would quickly run out of money and quit. Statistics suggest that only around 10% of the poker playing population is consistent winners. This means that although it may seem like everyone around you is winning, they really aren't in the long haul. Winning poker takes experience, patience and discipline. Don't push too hard to succeed. If you play solid, consistent poker at limits you can handle, you can be a winning poker player.

The pros often say they're not going to play big pots without big hands, but Allen applies this principle better than most. Over the two days leading to the final table (about 18 hours of play), Allen played a total of four big pots. In two of them, he had sets. In one, he had the nut flush and, in the last, he had pocket Aces and was all-in pre-flop against pocket Kings.

When he had something like top pair, Allen played far more cautiously. He'd simply call bets or check one street so that he could control the size of the pot. When the big money went in, Allen had a hand that would hold up.

When his chips got low, Allen didn't panic. He didn't push his chips in the pot with dreadful cards. While he had enough chips to survive a few rounds with the blinds, he waited for a hand that could win at showdown.

Of course, it took some luck to survive when his stack got low, but by being calm and patient, Allen gave himself the best possible chance to see another day.