CardSharp

In NL holdem when the pot is raised preflop the last preflop aggressor often bets out on the flop regardless of whether or not he connected well with the flop. This bet is called a continuation bet and it is the central feature of betting action on the flop in NL holdem. This article discusses flop play from the perspective of the preflop agressor. I’ll follow up with another article in the future that looks at flop play from the perspective of the preflop caller.

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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.

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Well, it’s WSOP time again, and I flew out to Vegas for a weekend of mid-stakes action. In no particular order, here are some random observations:

• There’s actually PLO being spread during the series. For those that like PLO, this is a good thing. There were 5/5 games at the Rio, and a mixed PLO/NL holdem game at the Bellagio.
• Pot limit games with novice players are a total mess
• The limit holdem games get much better during the series
• Ballys is a good place for a poker player traveling on the cheap to stay. I got a basic room at a bargain basement rate, slipped the checkin clerk a $20, and ended up in a giant suite. The furnishings weren’t the best (except the bed, which was very nice), but I got way more than I paid for. Being just across the bridge from the Bellagio is a huge time saver. Staying at the Bellagio would have been even more convenient, but a poker rate basic room there would cost me about twice what my suite cost me at Ballys.
• Above the $1000 buyin point, I think the limit games are currently softer than the NL games.
• The Venitian has a great poker room. Too bad they have a hard time getting much non-tournament action.
• The WSOP action is not saving the Mirage limit games - they’re effectively dead. Bummer.
• Dealer quality at the Rio sucks during the series.
• The BBQ place in the Caesars food court is pretty tasty.
• The gap between mid and high limit holdem is very confused at the moment - no one’s sure what to spread. 50/100 with green chips seems like the best option, but Bellagio had 60/120 (didn’t see the chips) at one point. None of these games seem to go reliably, whereas 100/200 was totally reliably.
• The 1/2NL at Ballys (which I played while waiting to leave for my flight) is ridiculously easy. Anyone looking for a place to get started in NL would be wise to stop by Ballys.

Anyways, this may or may not be of interest to people. But those were the things that struck me.

I played quite a few games during my most recent Vegas trip, but by far the most interesting was the 30/60 holdem last Sunday morning at the Bellagio. They had a lot of action on account of the WSOP - two tables at 10:00 in the morning, both full, neither of them must move. What made it interesting was that my opponents were worse than I’ve ever seen at a game that big. Out of 9 opponents, only 1 was playing decent poker. The rest made a number of mistakes that really stood out. This is the kind of game that I wish I could bottle up and bring home with me. Alas, they’re still in Vegas and I’m not. Oh well.

It’s worth discussing what these noticeable errors were. Players considering tacking mid-limit holdem would be wise to consider this list and purge these errors from their game. Because while these opponents were making errors at a rate higher than normal, the errors they were making were all the classics.

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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.

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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

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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.

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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.

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I was listening to the local country station today, and they happened to play a Toby Keith song where he’s discussing his semi-pro football career. The lyrics go

Semi-pro always means semi-paid

Which got me to thinking about the economics of athletics in comparison to poker.

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Last Time we talked about top-pair and overpair type hands, and the desirability of keeping the pot relativly small post flop with these hands. I want to continue that discussion, and provide some additional details and specifics that weren’t in the first article:

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Not too long ago, I wrote about the payoff rule:

The Payoff Rule For Big Bet Poker

Situation: The pot was small, you are on a made hand, and you believe your opponent was on a draw. On the last street you bet your made hand for some amount (BET) that charged the draw to see the next card. The draw had probability P(draw) of hitting. There was ESS money behind in the smaller of your two stacks at the start of the previous street.

Now, the draw hits and you have to decide how to proceed. If BET > P(draw) * ESS, you should aways be willing to get money in and pay off the draw, up to and including wagering your entire stack. If BET < P(draw)*ESS, you should try to limit the percentage of your remaining stack that goes in on future streets based on the fraction of how much smaller BET is than P(draw) * ESS. In other words, apply pot control. If you can’t accomplish that, you need to fold some percentage of the time on future streets such that you pay off no more than that amount on average.

The payoff rule is not an absolute thing - the more money that was in the pot to start, the more willing you should be to pay off. If your opponent may have a made hand you beat instead of a draw, you should pay of more. If your opponent may have a made hand that beats you, you should pay off less.

Now, we originally derived this rule in the context of set farming. I’d like to re-visit that example, and see how the pot control works in practice.

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For those not familiar with the terms, “small ball” tournament play is a style of play in NL tournaments (usually holdem) where you avoid large confrontations unless you believe you have a huge edge - a small positive expectation in tournament chips isn’t enough to justify going all in against someone.

For some reason, small ball is a concept that a lot of people have a hard time grasping, or believing is correct.

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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

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It’s always good to get mail, and here’s an excellent question:

Hi Wayne,

…

[in the context of NL holdem] I am winning with pocket pairs without exception and I win with Axs at a nice clip but suited connectors are losers. Unless the suited connector is in the T/J range or above they are consistent losers and I think that they should not be played. In fact a recent article in Card Player suggested just that. What is your opinion?

My first thought is that you should not be overly concerned about taking wagers you expect to make money on and passing on those that you expect to lose money on. That’s perhaps the most fundamental concept of winning gambling. So if you’re winning, there’s no real reason not to keep doing what you’re doing. That said, it’s also true that a lot of other players win a lot of money by playing suited connectors lower than JTs. So it’s clear you’re doing something different from them when you play those hands. I have no way of knowing what that is, but I can take some guesses:

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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.

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It’s time for one of the most important things I’ve got to say about no limit Texas holdem. We’ve talked previously about the topic of set farming when discussing the 5/10 rule. Specifically,

Set farming is calling a bet preflop with a small to medium pocket pair (which is unlikely to be best by the river if it doesn’t improve) hoping to hit a set (3 of a kind made with one on board plus your pair). It’s a longshot play where you rarely hit, but when you do you have a hand that’s almost certainly best, and you can comfortably get your stack in.

Set farming is a very central part of correct NL play. In fact, against certain opponents, it is the single most profitable tactic in your arsenal. To understand why, consider this hypothetical hand:

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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.

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There are a lot of silly rumors floating around about what this year’s WSOP main event is going to look like. All we really know at this point is that it’s going to be a poker-free circus with a high probability of the winner being a total assclown, just like the last two years. That’s what ESPN wants, of course, so that’s what Harrah’s wants. Of course, it could be fixed if someone really wanted to. Maybe if the enough name players demanded it, something would happen. Here are the major problems as I see them:

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In the last game theory column, I presented a real-world poker problem, and started through the process of figuring out the equilibrium solution. As you probably noticed, I simply told you what the solution was without explaining how I got that solution. Now I owe it to you to explain how I did it.

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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.

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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

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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 togeather 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.

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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.

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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?

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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:

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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.

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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.

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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:

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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’:

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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:

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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