CardSharp

I want to make sure everyone is familiar with the concept of the “structure” of a poker game.  The structure of a game is simply a shorthand for a few related rules for a given game:

1. The number, location and size of the antes and/or forced bets (blinds and bring-ins) in a game
2. The rules for bet sizing in that game
3. The restrictions, if any, on minimum and maximum buyin amounts and rebuy amounts
4. In a tournament, the way these things change as the tournament progresses

These four rules, along with one concept I’ll discuss in a minute, are important to consider as a group because they all factor into one decision: whether or not to voluntarily put money in the pot with a given hand Read the rest of this entry »

Poker books, TV shows and forums love to talk about being “committed” to a hand. However, I’ve come to a realization over time while reading and watching all this stuff: no one can agree on what it means to be “committed”.  Everyone’s talking about it, but they’re talking about at least three different things and using the same word for them.  The result is rampant confusion, and an unhealthy dose of misinformation for any player trying to make sense of the concept. Read the rest of this entry »

Last time, I wrote that the play of the cards in holdem often times coveys very little information about the state of the hand.  This produces an interesting effect: since the available information at the end of the last betting round is usually very similar the information at the start of the next round, there is a general expectation on the part of the players that the last person to bet or raise last round will, if given the opportunity, bet first this round.  This concept is called the ‘betting lead’ and it’s important to understand both for the purposes of betting your hand correctly, and for interpreting other people’s bets. Read the rest of this entry »

This article is specifically for online players switching to playing live and new live players. When you start playing live, you unfortunately have to cope with one of the major downsides of live play: angleshooting, rules abuse, and dealer and player errors. These issues don’t arise in online play, by and large, but they matter quite a bit in live play.

Angleshooting, or rules abuse, is simply a player manipulating the rules or structure of the game to gain an advantage not derived from good play. It can take a lot of forms. Oftentimes the angleshooting villain is on a freeroll – his angle rarely works, but if it does, he profits and if it doesn’t he doesn’t lose anything. Read the rest of this entry »

part 1, part 2

The 10 most aggressive players in Vegas are broke – Bob Ciaffone in Improve Your Poker

This is probably going to piss some people off, but Bob’s exactly right. For the last 25 years, the poker literature has been pulling a bit of a con on unsuspecting players by claiming in almost unmitigated terms that aggression is good. Read the rest of this entry »

In this series I discuss how bets and raises are classified, and the thinking behind determining if a given bet or raise is correct.

Part 1

As you’ll recall from last article, there is a well defined system for classifying calls as correct or incorrect using odds math. That math essentially analyzes three relevant facts:

1. How much money you win if your call works (ie. you hit your draw, or have the best hand already) ($win)
2. How much you lose if your call doesn’t work ($lose)
3. How likely your call is to work (P(win))

At that point the expectation for the call is easy to calculate:

Expectation = $win * P(win) – $lose * (1-P(win))

The important thing to recognize here is that this formula is essentially

expectation = reward – risk

Read the rest of this entry »

In a couple of previous articles I’ve talked about classifying bets as either value bets or bluffs. This classification was originally derived looking at last street play in fixed limit games. I now want to revisit the topic and discuss earlier betting rounds and games with variable bet size.

Before I do that though, I owe it to my readers to explain why I’m so interested in classifying bets. Read the rest of this entry »

Previously, I discussed how bets can at least loosely be classified into one of two classes, value bets or bluffs. I now want to discuss the theory behind bluffing.

First, let’s reiterate what it means to bluff:

A bluff is a bet where you believe you do not have the best hand, and believe all of your opponents with better hands will fold if you bet.

Now, that seems like a pretty simple definition. But there’s actually a lot of complexity hidden in there. Read the rest of this entry »

Part 1, Part 2, Part 3

It’s time to talk personal playing philosophy. Over the last month or so, I’ve written a ton about strategy rhos and game theory. I’ve talked about several different rhos:

• The big strategy rho (part 1, part 2)
• bluffing & calling on the end (part 1, part 2)
• defending against a draw with a made hand (part 1, part 2)

If you read these articles carefully, you’ll notice that I’ve adopted three different and indeed incompatible approaches to poker strategy in the three series Read the rest of this entry »

Last article we looked at the set farming strategy, and saw that it was an effective way to take money from an opponent with a big pair if both players adopted certain strategies. We also looked at two possible “defenses” the guy with aces could employ – raising more or having a smaller stack. However, both of these are infeasible in many circumstances. You don’t have much control of your stack size, and raising the needed 10% of the effective stacks is often not feasible in deepstack games. Clearly there’s only one option left for the aces: they can’t always pay off the set for a full stack. In fact, against the strategy I described for the set farmer (check-fold postflop if no set), there’s no reason the aces should ever pay off the set. Any time the guy bets, or even calls, you know he’s got you beat (unless you also hit a set). This creates an odd strategy for the guy with aces – bet out every time, and if your opponent folds, fine. If he gives you any action, check-fold the rest of the streets. This strategy beats the set farmer out of almost 4BB/hand on average with the setup from the last article. Read the rest of this entry »

Like most people with websites, I occasionally look to see what phrases people are searching for to find my site. One of the recent ones was “what does it mean to be in position”. This sent the searcher to one of my pages, albeit not one that actually answered his question. While I can’t help that guy out (unless he comes back), I can answer the question for someone else.

It turns out that position is a bit of a complicated topic, because it really refers to several different concepts that are only slightly related. All of them have to do with the order in which the players act, but that’s where the similarities stop. Read the rest of this entry »

Last time, I explained what game theory is using examples from roshambo. That’s all well and good, but this isn’t a roshambo strategy site. So let’s look at the poker implications. As we stated, any time there is a strategy rho, you can minimize the worst result you can get by choosing randomly between the options in the head of the rho at some frequency. Thus far, for poker, we’ve only discussed one rho: the big rho of tight play, aggressive play, and calling down. This is certainly an interesting example of a strategy rho, but it’s lousy for a discussion of game theory. The reason is that it’s somewhat of an abstract concept – we haven’t defined what exactly each strategy entails, and therefore it’s impossible to figure out the exact expectation when two strategies meet. This makes solving the associated game theory problem of how frequently you should do each to get a game theoretic optimal result impossible. To that end I want to introduce a new rho: the bluffing and calling on the end rho. Read the rest of this entry »

Game theory is somewhat of a hot topic right now. The application of said theory to poker has always been a topic of discussion amongst certain mathematicians and players. Then The Mathematics of Poker was published, and it temporarily put game theory front and center in the poker discussion. However, I would happily wager that 90%+ of winning players at any level could not give a correct and comprehensive explanation of what game theory is.

So for all you folks who don’t really know what game theory is, or what it has to do with poker, never fear. CardSharp is here to help Read the rest of this entry »

Something rather silly happened on rec.gambling.poker today. One of the group’s less observant participants claimed that if you play 1/3 NL or bigger in a casino, the effects of the rake and other expenses are minimized. Fact is, that’s far from the truth. You have to play MUCH bigger than 1/3 NL before the rake and your other costs don’t have a major impact. To illustrate the point, I put together what I think is a fairly conservative list of expenses for a 1/3 NL player, and looked at what that did to your win rate. 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 »

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 »

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 »

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 »

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 »

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 »

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 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 »