The Mathematics of Poker

A very good book that you should read to better understand poker odds is ‘The Mathematics of Poker’, by Bill Chen and Jerrod Ankenman. You can get a free copy with your frequent players points at Pokerstars. If you have not yet registered, note that there is no pokerstars rakeback, but instead they have a great VIP Club.

I found it to be an informative and challenging read. Short review: This is one of the most important books about poker ever published. For a longer review you can read Terrence Chan’s great early review of the book.

Few books on gambling take a truly analytical approach. In fact, the only other book in my library which comes close is ‘The Theory of Gambling and Statistical Logic’, Revised Edition, by Richard Epstein. Unfortunately, that book has very little real poker content. Chen and Ankenman do the world a service with their thorough analysis of poker. Their methodology is clear, the problems and solutions are interesting, and their insights into the game are remarkable. They’ve also done an excellent job of keeping most of the mathematics accessible to anyone who has a solid grasp of algebra.

Here is an example of the kinds of insights you can get from reading and understanding this book. They have a topological representation of the solution to the one street heads-up finite pot game with a maximum of two bets.

The strongest hands are at the top of their chart, and the weakest hands are at the bottom. The action maps as: f=fold, k=check, c=call, b=bet, r=raise. Each column represents the optimal strategy for the game. The strategy for the first player is in the X column, and the strategy for the second player is in the Y columns. If X bets, then the Y(b) column is used, if X checks, then the Y(k) column is used. It’s important to note that the actual location of the boundaries are not illustrated here, only their relative ordering.

Some basic insights from the solution: You need a stronger hand to check-raise with than you bet-call with. You should fold some of your value bets. Your bluff raises should be done with hands which are stronger (not weaker) than your bluffs.

This is just one example of how deep the book goes, so this is not for you if you are not mathematically inclined.

 
Steaming in online poker

hello, this is a post about reverse bragging, only because it’s got me so steamed.

I invested in the FTP $8k guarantee tourney last night. The cards are hitting for me and I’m making the right plays. About 1/3 the field has dropped off. I’m 2nd in chips. Excellent beginning and this does not happen too often to me.

A hand comes up where I know I am a huge favorite. I actually forgot the specifics of this hand because of the two that happened after it. I get all my chips in on the turn. Sure enough, my opponent hits one of his 2 outs on the river.

The very next hand I put my opponent in on the turn. The board is Q557, I have a 5. He has a 7. Guess what lands on the river?

The very next hand, I am down to 215 chips with AK offsuit and, knowing it is the best I will likely see before I am blinded out, I push. Only caller has KJ offsuit so he is dominated. Flop contains a Jack, I do not improve.

2nd in chips to rail bird in 3 consecutive hands where my opponents had 2, 2, and 3 outs respectively. Why is that my best tourney finish to date? Well, I’ve finished a few multi table tournaments in the money and one of them well into the money. But this one more than any other really has given me confidence in my game. I had my chips in with the very best of it. If I can do that on a consistent basis, I will win a big one eventually. So, it’s the best finish because it’s given me the confidence to hit these particular tourneys all that much harder.

Sorry, partially a bad beat story, partially venting… but at least there’s some redeeming quality in the lesson there. Make the correct moves and do not worry about the outcome, this is rule number one in poker.

 
Mastering bluff induction

There are so many ways to make a good bluff and this depends on many factors. but no matter what, this is hard to master. On the other hand knowing how to induce your opponents to make a bluff is even harder. One sure thing is that it depends a lot on your opponents’ style. To buy hand histories in order to uncover your opponents’ styles before you meet them is certainly a way to get an edge.

The crux is to understand the best cases for succeeding with bluff induction. And as was said, it is crucial to know which are the poker players who will get caught in such a trap.

One first situation where you want to get bluffed is when you have a fantastic hand. In this case, several options are possible for you. You can check every street if you feel that your opponent is prone to react to apparent weakness. You just need to call each of his bets. He could believe that you have a drawing hand if the board is drawy.

Or you can make a low raise, thus allowing him to shove over you. If your stacks are both deep, performing the min-raise will in some situations push him to send all of his remaining chips on the felt.

The opponents’ style is the most important aspect to pay attention to. It is obvious that to induce an opponent to bluff, it is preferable for you than he be aggressive and capable to go pretty far with his continuation bets, almost a maniac. To perform this move, you have to select your targets and understand them well to know what triggers them. Theoretically, the more your opponent is aggressive and likes to bluff, the easier it will be to take a maximum of his chips with this play. Conversely, a very passive or suspicious player will often stop betting after getting called once.

Inducing your opponent to bluff is hard in general and you must fully control the situation. Note that you should avoid floating too much, as it will be costly in the long-run. Reserve the float play to these special situations where you want to induce a bluff.

Inducing a bluff while winning a big pot is one of the most memorable moment in the game of poker, and you will really feel like you are on top of the world. So practice this method for future enjoyment at the poker table.

 
Poker tournament strategy

Of all the advice they may receive on strategies to improve their game of poker, players new and not new will often hear this one: “Have patience!”. Indeed patience is often what will make the difference between winning and losing money at a poker table.

The lack of patience in poker will often lead to bankruptcy. Why?

There are mainly two types of errors that a poker player can make: either bet too much with weak hands or play too many hands. But apart from wisdom and patience, you must also prepare and implement a coherent game strategy which adapts to each table and situation.

A good poker player knows that his strategy will be different every time. There is a strategy game for ring games, a strategy for single table tournaments and another strategy for multi-table tournaments. Here are some helpful tips for the last category.

For multi-table tournaments, we must distinguish between the early, middle and late stages. In the early stage, when there are tables full of mediocre players, ready to shove and double up randomly, it is recommended to play conservatively, waiting until most of these players have been eliminated. In this phase of the competition, professionals are accustomed to playing only the top hands pre flop (AA, KK and AKs).

The middle stage of a poker tournament is when most of the bad players who play at random have already been eliminated. The game is intense, the players remain focused on developing robust strategies to win pots.

The final table or latest stage of the tournament brings together the best players who stayed upright until then. In exceptional cases there could be among the finalists poor players who had great luck. In that case the game becomes aggressive, the blinds increase fast and the short-stacked players are obliged to make moves or to get eliminated. In principle you should still play tight pre flop at the beginning of the final table.

For single table tournament, there are also the same steps to go. The strategy game for the first step remains the same as multi-tables. We only play big hands. The risk of bluffing is not justified, because the blinds are ridiculously small. At the final stage which is the heads-up where only two players remain in contention, the odds are more on the side of aggression. There are two ways to attack the enemy: the repeated all-in or the progressive growth of the pot.

 
Poker player motives

This blog will talk about players’ styles among other things related to gambling. The primary topics of interest that we have are poker strategy and poker psychology.

There is a strong relationship between players’ styles and players’ motives. If you know how someone plays, you also know a good deal about why he plays (and vice versa). In addition, players with extreme styles are so dominated by their primary motives that they are rigid and predictable. They act in a certain way even when it is self-defeating.

For example, maniacs are so addicted to action that they cannot keep themselves from jacking it up, even when a little voice in them says, “Slow down.” Calling stations have such a strong need to get along with others and such a strong aversion to acting aggressively that they just call, call, call, even when they know they should raise or fold. Rocks are so conservative and timid that they let aggressive players run over them.

However, many extreme players have selective memories or kid themselves about why they play the way they do. They essentially make excuses for yielding to their impulses. For example, maniacs tend to remember the times they had a huge win or pulled off an outrageous bluff, while ignoring their losses. Or they say silly things such as, “You have to be in to win.”

Maniacs are usually extremely optimistic; they keep thinking they are going to get lucky. Rocks have the exact opposite attitude. They are pessimists who always fear the worst. If you asked a rock why he did not raise with a king high flush, he would not say, “Because I’m a wimp.” He would probably say, “I thought he might have the ace.”

We will focus on the extreme players because it is easier to see the pattern – in yourself or other people – but all loose-aggressive players have a strong need for action, and so on. In general, the more extreme a player’s style is, the more his primary motives overwhelm his other drives – including the desire to win.

Conversely, the more balanced a person’s motives are, the more flexible, rational and effective he will be – at the poker table and everywhere else. The relationship between styles, motives, and fears is especially important when you are trying to develop yourself as a player. If you do not understand why you play the way you do, you cannot overcome the inner forces that cause you to beat yourself.

Always ask yourself whether your ratings on motives are consistent with the way you play. Any inconsistencies suggest that something is wrong. For example, if you rate making money as your primary motive, but you lose regularly because you can’t resist tough games, you should recognize and try to resolve this contradiction.

Try to find out what is really happening inside your head and at the table and you will become a better poker player.

 
Poker luck

In any game, it is very evident that hard work rewards the dedicated players. Luck does affect your emerging as a player, but hard work rewards much more. In some games but not all, the harder you work, the luckier you get.

Good luck results from deliberate and strategic hard work and planning. People do not get lucky on their own. They turn lucky when they put in hard work, and that is how they need to be if they want luck to favor them. The scenario is pretty much the same in poker also. This is very similar to the situations in other games as well. But in poker, luck is not all that you need. It is believed that the luckier you get, the worse you tend to play in fact.

Every player appreciates poker luck, and would want to save it for a rainy day as well. But, luck is actually the opponent of a poker play. A weaker player wins a pot and we believe that he has the luck to get it. A bad player does not open up, always comes from behind most often, make perfect catches, and so on. A bad player can seek to become lucky at any time. So, they are considered to be much lucky when compared to others. They have several ways of obtaining lucky.

Good players are sometimes showered with luck, as can be seen at the WSOP. But actually they choose the mathematically correct action. Sometimes certain players are accused of having poker luck. Sometimes a player feels like what his instincts tell him. The luck of the good player is actually due to his preparation. The good player often obtains luck because of the mistakes of his opponents.

Good players may also be accused of being with a player who overbets his hand and gives them five or four extra bets. You are also lucky that the other rivals would have given you extra bets. But the point is that a good player will induce and extract extra bets from rival more frequently than a bad player.

When playing poker you would also want to obtain luck from your opponents and it will be like receiving it on a silver plate. Poker luck is very essential especially when you are holding a very high hand and you would want your opponents to increase the pot size for you. This is the normal poker luck that is obtainable by the good poker players, but luck would never come upon you if you are expecting to beat your opponents while you are holding a very low hand.

 
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