CardSharp

I’ve become convinced that the most common mistake beginning poker players, and in particular NL holdem players, make is playing what I call ‘backwards poker’.

Backwards poker is when a player refuses to put money in the pot when he knows he has the best of it, but is all too willing to put money in the pot when it’s very possible he may have the worst of it.

Now, it should be obvious that backwards poker is a really bad idea. The whole point of playing poker is to wager a lot of money when you have the best of it, and not to make wagers where you have the worst of it. So why would anyone choose to do just the opposite? Good question. Read the rest of this entry »

If you ask top poker pros what distinguishes them from merely good players, they very often say the same thing: “changing gears”. So what exactly are they talking about? Read the rest of this entry »

In this series I discuss topics that are well known within the gambling community, but that may be new to players who come to the game of poker from a non-gambling background.

A parlay is a bet where multiple things have to go your way for you to win the bet. The terms is most frequently used in sports betting. In a standard sports parlay, you can combine multiple team or total bets where you would normally lay 11:10 into one bet. Since it’s more difficult to have all the components come in than it is to win a standard bet, the house offers more attractive odds – usually they pay 13:5 for a 2 team parlay and 6:1 for a three team parlay. Note of course that these odds still have a built-in house edge as with any sports betting – you would get paid 15:5 and 7:1 respectively on a gentleman’s wager.

Parlays occur in poker all the time, but they’re not always obvious. Consider the following fairly common situation in limit holdem: Read the rest of this entry »

Sorry I’ve been dormant so long. Life interfered. I should be able to write regularly again, and I’ve got a lot of material I’m planning to post. Read the rest of this entry »

A while back I wrote about the horserace paradox. I want to continue that discussion specifically in the context of poker.

A common decision in poker arises when you have the option of betting aggressively to drive out opponents or being passive as a means of keeping them in the hand. It should be obvious that this is in some ways related to the scenario in the horserace paradox article, where additional opponents with a limited chance to win cause a frontrunner to perform worse. I got to thinking about this issue because of a number of columns in Roy Cooke’s Real Poker II in which he advocated letting additional opponents in preflop in limit holdem when holding pocket aces because by calling they were making a mistake and therefore he must be benefiting by conservation of money. My intuition at the time was that Cooke was wrong and that those players were often not making a mistake by calling. But I wasn’t certain. Subsequently I’ve thought about it more, and I’m convinced Cooke was wrong but the situation is much more complicated than I originally thought. Read the rest of this entry »

The flop is the defining moment in holdem. Play before the flop focuses on setting yourself up to flop something good. Play after the flop is about figuring out what your opponent flopped and drawing at or defending against draws made on the flop. Before the flop you’re dealing with hypotheticals unless you hold a big pair. After the flop you’re dealing with a much better defined situation.

Because the flop serves as a dividing line for the hand, it’s the perfect place to take stock of your situation. Misunderstanding the implications of the flop is the primary cause of costly stack-sized mistakes. So here are some things you should figure out before proceeding: Read the rest of this entry »

Reading the board quickly and accurately is an important skill for both players and dealers. It is the process of looking at the community cards and determining the following information:

1. What hands are possible on the current board
2. What draws are possible (assuming there are cards to come)
3. Where a given set of hole cards sits into the range of possible hands, or how two hands compare Read the rest of this entry »

One mistake I see a lot of holdem players making is that they incorrectly estimate the strength of their hand on the flop. This can lead to some ugly mistakes in play. While most players eventually learn by experience what hand/board combinations are strong and which are vulnerable or near-certainly beat, this process can be expensive and is mostly unnecessary. Here’s a quick and dirty method for figuring out where you stand on the flop that you may find helpful.

Read the rest of this entry »

A while back we did a big example of odds math and discounting outs.  These examples were somewhat complicated because I wanted to give a comprehensive picture of what can be involved in an odds problem.  Indeed, these problems were so complicated that the math really pushed the edge of what a player could be expected to do at the table.  In other words, those articles fell slightly short of my own standards of what constitutes good poker math.  I want to rectify that here and also present the process I use to do so as a template for simplifying other poker math problems. Read the rest of this entry »

In the last NL holdem I wrote about basic starting hand selection for deepstack play. The key concept was to play hands that are likely to make the nuts, in position, for a raise. Now I’m going to discuss some associated topics and some exceptions to the rule. Read the rest of this entry »

A key concept in holdem, especially in NL, it “hot and cold” comparison of starting hands – namely the the odds of each pair of hole cards winning in a two hand matchup that always goes to the river. While it’s not important to memorize these odds exactly (and I’m not even going to bother calculating them exactly here – that’s what poker stove is for), it is important to know them in an approximate sense because a lot of correct preflop strategy in holdem is a direct result of this concept. Read the rest of this entry »

As I stated previously, starting hand selection is not as critical to success in deepstack no limit holdem as it is in other forms of poker. Various players have adopted radically different strategies and yet still achieved good results. However, that doesn’t mean you should neglect the subject altogether. What it does mean is that rather than present an ironclad system I’m going to give some suggestions that most players, especially those new to the game, should have reasonable success with. Read the rest of this entry »

As a result of Saturday’s column, I’ve had an interesting email conversation with Mike Caro about the subject of big folds in tournaments. I suppose it’s always a little bit dicey criticizing someone’s work, because you never know how they’re going to respond, but I’m glad to report that Mike and I had an interesting discussion and reached common ground on the subject. Read the rest of this entry »

I want to like Mike Caro. I really do. Every discipline needs it’s mad genius, and the man certainly has the hair for the job. But I can’t deny his Poker Player column is making a encore appearance on “Nonsense Debunked”. That’s not a good thing. This week’s nonsense is about tournament bubble play. Here’s the setup in Caro’s own words from the Oct. 1 2007 ‘Poker Player’: Read the rest of this entry »

Many of yesterday’s Things You Should Know about NL Holdem focused on the effects of deep stacks and implied odds on the game. I think one of the easiest ways to get your head around the effects of deep stacks is to consider what would happen if the stacks were infinitely deep. As you might expect, stacks that are merely very deep have the same properties, but sometimes not to quite the same degree. If the idea of “infinitely deep” stacks bothers you, just think about a stack that’s 1 million big blinds deep – ie. a 2 million dollar stack at 1/2 NL. Here are some effects of those huge stacks: Read the rest of this entry »

A rather unusual situation has developed in US poker at the moment. Cash game no limit holdem has become by far the most popular form of casino poker in the country, but there is almost no good information on how to play it published in book form or on the web. In an effort to plug that gap, I’m going to publish a series of articles on the game that should contain sufficient information to take a player to at least the intermediate level.

To get started, I want to present some central concepts for NL holdem. The idea is to get you in the right frame of mind for thinking about NL play. These are in no particular order. Read the rest of this entry »

I was playing crappy Colorado casino poker yesterday when a noteworthy situation arose. The game was $5 limit holdem. That’s right, 0ne $5 blind and all bets are in increments of $5. It’s hard to imagine a worse structure. But this isn’t about the structure. It’s about one of the worst plays I’ve ever seen at limit holdem. And It’s a bad play that happens surprisingly frequently and that many players probably don’t even think of as bad play at all. Read the rest of this entry »

There is a classic logical fallacy, the Emperor’s nose fallacy, that all poker players need to be aware of because it appears so often in poker reasoning (especially in poker books and forums) and has become increasingly common of late. Read the rest of this entry »

In poker, play on the last betting round (aka  street) takes on a decidedly different nature from play on any other round. Because there are no cards to come, the relative rankings of the players’ hands are fixed, and as such all betting revolves around uncertainty about opponent hole cards, not uncertainty about the cards to come. This simplified environment causes many issues that are murky and complicated on earlier betting rounds to become more clear, and as such play on the end is the perfect framework for introducing a number of important poker topics.

In the last installment of this series, we discussed the two fundamental types of bets & raises – value bets and bluffs. Now I want to talk about calling on the end. For the time being, assume that play is heads-up and you are facing a bet, and thus you have the option of closing the betting by calling. Also remember from last time that excessive aggression on the river with mediocre hands has a high probability of splitting your opponent’s range and being incorrect. So only rarely in this situation will you be raising – and almost never with a mediocre hand. That leaves the player with a mediocre holding two reasonable options – call or fold. Read the rest of this entry »

In last week’s article on odds, I went through a complicated example of deciding if you should call with a draw. The point of this example was to show, in a big-picture sort of way, how odds are used to make poker decisions. Now I want to explore one small aspect of that more closely.

Specifically I want to talk about discounting outs. Read the rest of this entry »

Ever since I wrote the last bankroll management article, I’ve been getting search hits for “craps bankroll management”. I feel sorry for these folks, because I doubt anything I said dissuaded them from their belief that somehow they could beat craps if only they played their money right. It’s important to understand why there are useful bankroll management principles that apply to poker, but there’s nothing to be done about craps. The difference is that poker, if played correctly, offers you a series of positive expectation wagers. Craps, in contrast, offers you only negative expectation wagers. So if you keep playing craps, in the long run, you will always lose. In contrast if you play poker skillfully you will always win in the long run. The problem, in poker, is to get to that long run without going broke in the process. That’s what the previous bankroll management article was all about – making sure you have enough money in you bankroll to weather the swings and get to that perpetually profitable long run.

There’s another aspect of poker management that’s worth discussing, and it’s probably a lot closer to what those craps players are thinking of when they think bankroll management: figuring out when to stop playing. Read the rest of this entry »

We’ve already talked about odds in a general sense here and here. Now I want to take that foundation and talk specifically about odds in poker.

Odds, as applied to poker, are really fairly simple but somehow the poker literature has gotten itself turned around and explained them in a very awkward way. Read the rest of this entry »

Keeping accurate records of your play is important for all poker players. It’s essential for tax purposes to know how much you won or lost in each session, but there’s lots of additional benefits to be gained by having comprehensive records. Specifically, good records will help you improve your win rate over time by highlighting situations where your results are consistently different from your expectations. This process will enable you to develop your game selection intuition. Read the rest of this entry »

In the Fish Psychology series, I explore the reasons that losing players continue to play, and look at ways to keep them coming back for more.

Our first explanation for long run losing play is that the player does not in fact believe they are losing. Notice that I’m talking specifically about the long run. It’s very easy in the short run to believe your expectation is positive when in fact it’s not, and we’ll talk about that in another article, but I’m more interested in cases where people continue to believe they’re winning when any rational examination of the evidence would indicate they’re not. Read the rest of this entry »

I want to pose a simple question: why do losing players continue to play?

This question should be of supreme interest to anyone considering a career in poker or considering playing at high stakes. It should be obvious that poker games cannot exist without losing players – if the players with a negative expectation made a policy of quitting a game, that game would quickly cease to exist since in any given lineup there’s always someone who has a negative expectation[1] and who would thus be quitting. Read the rest of this entry »

Before we get started on the fundamental theorem of poker, I want to introduce a concept that I hope is very obvious nay axiomatic – conservation of money. Simply put, playing poker neither creates nor destroys money. Or put another way, if your results are that you won X everyone else at the table’s collective result is that they lost X and vice versa.   Stated in mathematical terms, everyone’s results sum to zero. Note that the house, if collecting rake, is one of the participants in this equation. Hopefully we can agree this is pretty obvious stuff.  I mention it because it’s the starting point for the fundamental theorem of poker. Read the rest of this entry »

Previously, I’ve tried to convince you that doing your poker math in odds notation is far easier, once you get used to it, than using percentages. Now, I want to show you how to do some of the arithmetic usually associated with percentages faster and easier using odds. But first we need to lay some groundwork. Read the rest of this entry »

I’d like to say a little bit about my philosophy on mathematics in poker. Generally speaking, there seem to be two vocal camps on this topic. One camp is full of math-phobic players and writers (often forum posters) who will try to convince you that poker is a game of psychology, not numbers. The other group is the ever-growing number of mathematician players and writers who seem to talk about equilibrium solutions and similar high math incessantly. Read the rest of this entry »

In poker play on the last betting round, or street, takes on a decidedly different nature from play on any other round. Because there are no cards to come, the relative rankings of the players’ hands are fixed, and as such all betting revolves around uncertainty about opponent hole cards, not uncertainty about the cards to come. This simplified environment causes many issues that are murky and complicated on earlier betting rounds to become more clear, and as such play on the end is the perfect framework for introducing a number of important poker topics. Furthermore, since there are no more cards to come, most versions of poker (excluding split pot games) with the same betting structure play very similarly on the last street. Read the rest of this entry »

In amongst the grand strategic concerns of poker, there are some small things you can do that will improve your game and keep you out of trouble. Little “good habits” that usually don’t make a difference, but every once in a while save your butt. These things take almost no effort once you form the habit, so adopting them is essentially a freeroll. No cost and potentially substantial gain. Read the rest of this entry »

Bankroll management is a controversial topic, because the term means different things to different people. For a long time, the term has been used to describe fad systems that claim (incorrectly) to beat various house banked negative expectation games like craps. These methods, such as variations on the Martingale system, are of no real use for any purpose. The reason is simple – no amount of varying your bet size will change a negative expectation into a positive one. If the odds are against you, they will still be against you no matter how much or how little you bet. Read the rest of this entry »

You’ll often hear poker players discussing “the nuts”, but what is it? The simple definition is that the nuts is the highest ranking hand that anyone can hold at a given time. The concept applies to all forms of poker, but is most meaningful in community card games like holdem and especially Omaha. It turns out the nuts are a more complicated subject than you might think at first glance. Read the rest of this entry »

In this series I discuss topics that are well known within the gambling community, but that may be new to players who come to the game of poker from a non-gambling background.

Previously I’ve written on the topic of odds. I want to expand on some of the concepts presented there and introduce the important concepts “risk & win”, “expectation” and “price”. Read the rest of this entry »

Sunk costs are a concept from economics that applies directly to poker. A “sunk” cost is a cost that has already been paid, and that you can’t get back. For example, if you ran a restaurant, your city licensing for the year is a sunk cost. Even if you stopped running the restaurant, you couldn’t get that money back. Read the rest of this entry »

This strategy “rule” is a key concept in NL holdem preflop play. It was originally published by Bob Ciaffone in Pot Limit & No Limit Poker. The rule is as follows:

Any time you’re considering calling a preflop bet on the basis of a combination of implied odds and position, the size of the bet relative to the effective stack size is the primary factor in whether or not you call. If it is less than 5% of the effective stacks, you have an easy call. If it’s more than 10%, you have an easy fold. Anything in between is a judgment call. Read the rest of this entry »

Full Tilt Poker has a commercial where their sponsored players declare “We play above the rail. We play the man, not just the cards.” It’s an admirable sentiment – there’s no question that poker played at the highest levels is a game of people rather than a game of cards. However, I think there’s something wrong with the idea when applied to online play, and I think an example hand will illustrate the point. Read the rest of this entry »

Here’s something to ponder: imagine that you are suddenly transformed into an incredibly skilled poker player. Specifically, you have a positive expectation at any fair game you could sit at. Let’s further assume you play in a poker town like Las Vegas, LA, or Atlantic City where you had numerous different games & stakes available to you. Now, what game would you play?

Read the rest of this entry »

Here’s a concept from economics that should be near and dear to the heart of ever poker player – opportunity cost. Read the rest of this entry »

In a previous post I discussed the use of rho structures to describe game strategies. Now it’s time to apply that theory to the practical subject of poker strategy. Unlike the previous post, I’m now going to describe strategies in a more general sense rather than the formal definition I provided earlier. This doesn’t change the basic fact that strategies form rho structures. Read the rest of this entry »

In this series I discuss topics that are well known within the gambling community, but that may be new to players who come to the game of poker from a non-gambling background.

Imagine a race between two horses. Horse A is a remarkably reliable horse, and will always complete the race in essentially the same time. Horse B, on the other hand, is remarkably inconsistent. Sometimes it runs a very fast race, far faster than A, and sometimes it runs a very slow race, far slower than A. Which behavior horse B exhibits is random, and P(fast race) is 0.3 or the odds are 7:3 against horse B running a fast race. Read the rest of this entry »

In this series I discuss topics that are well known within the gambling community, but that may be new to players who come to the game of poker from a non-gambling background.

A freeroll is a gambling situation in which you cannot lose money, but have a possibility of winning money. As you might imagine, such situations are usually quite attractive, and they come up in gambling and poker surprisingly frequently. Read the rest of this entry »

In this series I discuss topics that are well known within the gambling community, but that may be new to players who come to the game of poker from a non-gambling background.

Gamblers have a funny way of talking about how likely it is that something will occur. Instead of citing the percentage chance that some event will occur, they cite the “odds” that it will occur. Odds notation works as follows: the odds that something will happen is the ratio between how many times it will happen and how many times it won’t. The bigger side of the ratio is always stated first, so you have to specify whether the odds are “in favor of” or “against” the event occurring. For example, if you have a race with 6 horses, and each is equally likely to win the race, then you could say the odds are 5:1 against horse #3 winning the race. On the other hand, if you had a race with 6 horses, and 4 of them were black, and all had an equal chance of winning, you could say the odds were 4:2 in favor of a black horse winning.

Read the rest of this entry »

So, Wil Wheaton’s hanging up his poker spurs. Not just getting canned from pokerstars (which was inevitable), but giving up poker. And he explains pretty clearly why: Read the rest of this entry »

If you haven’t read up on what a rho is, first familiarize yourself here.

Now, I said that I would eventually explain what that experiment has to do with poker, but that’s still one post away. Before I get to that I need to discuss rhos in the context of game play in general, namely the types of strategies that a player can adopt when playing a game. Read the rest of this entry »

Got nothing better to do? Here’s something to keep you entertained. I promise this will get to the subject of poker strategy in a future post, but for now I’m hoping your love of mathematics will keep you riveted. This works OK as a thought experiment, but if you’ve got time on your hands I suggest you actually try it. Here we go! Read the rest of this entry »