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OK, it’s time for the answers to the first hand quiz.  I had hoped to produce a little more discussion, but I think making it 7 card stud scared everyone off.  That’s unfortunate, but I’m not easily deterred.  So I’m going to keep doing hand quizzes.  I do think in the future I’ll make most of them holdem hands though.

Now, the answers (out of order): Read the rest of this entry »

Hi Wayne,

I’ve been following your blog for quite some time now. It is on the top of my RSS Reader and I love it because of your very logical way of describing optimal play.

My question is how do you play a low set on such a suited board? Read the rest of this entry »

Here’s a little quiz.  I figure it might get some interesting discussion going.  I realize we haven’t done any stud on cardsharp, but think of it as a chance to broaden your horizons.

Read the rest of this entry »

Certain boards in holdem radically alter the value of your holding and the way typical hands play out.  The most common of these is the three-flush or suited flop where all three cards are of the same suit.  You’ll get such a flop roughly 1 hand in 20.

The reason suited flop are important is that they radically change the value of various made hands and draws. Read the rest of this entry »

I’ve touched on this a little bit before in the previous pot control articles, but it probably bears additional discussion.  In situations where you’re engagin in pot control with a top pair/top kicker type hand, you have a large number of simultaneous goals.  The one we’ve spent the most time on is avoiding going broke to a set or other unlikely flopped hand.  This is very important because the amount of money you stand to lose in such situations is very large.  However, implementing pot control is far from your only goal.  After all, the vast majority of the time when you hold top pair or better your opponent doesn’t flop a set or a fluke two pair.  Instead they flop something you have beat.

In such situations the amount of money you stand to win typically isn’t particularly large unless your opponent is either very unlucky or a bad player.  But that doesn’t mean it’s not important.  Rather it means you need to find a strategy that maximizes your results against weaker hands while simultaneously maintaining pot control.  It turns out, as long as you’re in position, this is typically doable. Read the rest of this entry »

Since I wrote them, I’ve gotten a lot of mail about the articles on set farming, the payoff rule, and the two articles on pot control.  Most of that mail has been very positive, but I want to provide a little bit of extra detail and a slightly different perspective on the subject and clear up a few points of confusion that I’ve seen.  If you haven’t read those four articles yet, I’d suggest you start there. Read the rest of this entry »

“In a hierarchy, every employee tends to rise to his level of incompetence” – Dr. Lawrence Peter, The Peter Principle

“In a cardroom, every player tends to move up until he can no longer beat the game” – me, right now.

Dr. Peter’s observation was originally intended as somewhat of a joke, as is my corollary.  But like many jokes, there is some underlying truth involved.  Peter’s observation was this: if you have an hierarchical organization of people, and each person has a fixed set of skills, and you promote people based on competence you will inevitably promote any given individual to the point where they are not competent, and there they will remain.

It’s not hard to see how the same situation can develop in poker. Read the rest of this entry »

Author: Bob Ciaffone & Jim Brier

Publisher: Self Published

I’ve been playing more limit holdem recently, and I suspect it will be the next “project” on CardSharp once I get more or less finished with NL holdem.  In preparation for that I’ve been going back over all the books I own on the limit version of the game as a means of organizing my thoughts.  When I first read Ciaffone’s book a couple of years ago, I thought it was the stone cold nuts as far as limit holdem goes.  On a second read, with many thousands of hands of mid and high limit holdem under my belt, I still think it’s the best book on the game, but not quite as good as I once believed. Read the rest of this entry »

I just got another question about out-of-position play with big hands related to this post here (this article won’t make sense without reading that one):

The one area that still needs addressing on the subject of premium hands in early position is what to do when the blinds are very deep. If a limp, a normal raise and a normal re-raise won’t get ten percent of the effective stacks in, what do you do? Do you make an oversize re-raise? That would seem logical but it is going to lose you some action.

Will in New Haven

In reality, in a typical game that doesn’t have extra callers of the initial raise, even a limp-reraise won’t get in more than about 15BB without seriously overbetting the pot.  So in games well over 150B deep you’re not going to be able to get 10% of the stacks in with your huge hands, or even come close to that number.  So what are you going to do?  I have a few suggestions: Read the rest of this entry »

I would venture a guess that even most winning poker players don’t put enough thought into the ultimate effect of their win rate on their gambling career.  Some work I did on sports betting recently went a long ways towards clarifying this for me personally.  I realize this isn’t a sports betting blog, but I want you to follow along anyways because I promise this will get back to poker eventually. Read the rest of this entry »

I just received the following question and it’s an excellent follow-on to the last preflop article:

Hi  Wayne,

I read the following comment in an old post of yours that discussed starting hands:

When intentionally entering the pot out of position, it’s often best not to raise at all under any circumstances, even if you have a premium hand.  If someone raises behind you, you can ditch the non-premium hands if you relative position is bad and re-raise the big pairs (and possibly AK). Often this re-raise will be all-in. (the post)

My question is, at what point should one start to raise from EP preflop with our opening range of hands,  and how much should that raise be?

Clearly in many cash games or tournaments, people have stacks well under 100BB.  And I did read in another article about your scenario of raising with a big pair vs someone else’s SET. There you talked about the importance of raising PF, and also CB.  So at some point, a player needs to stop limping PF and start raising. But what is the factor that decides that point? Do we go by the 5/10 rule and look at effective stack sizes?

Regards,

Adrian

Ok, I can see I created some confusion here, and re-reading the older article I think I see why: Read the rest of this entry »

I try to answer reader questions as they come in, but for the last few months I’ve been really bad about it.  Hopefully over the next week or so I’ll be able to fix that and clear out the backlog.  Here goes!

Hi Wayne,

I found your site the other day and thanks, it has been very thought
provoking. I will be employing some of the insights I gathered to my game.

It would be great to hear your thoughts on the concept of “buying the
button”, eg raising in whole or part out of position to get position,
particularly pre-flop. Given the increase in EV that having position
entails, there would seem to be a method for valuing this benefit, in terms
of the bet/raise you should be willing to make to obtain, and whereby the
inputs to this valuation would obviously include absolute position (relative
to the cut-off). But what other inputs are specific to this valuation?
What would the formula be? An interesting concept that has not yet been
explored very rigorously, from what I have seen.

Cheers, Todd

This is an interesting question, and I spend a lot of time thinking about it before responding.  The short answer is that I don’t have the type of formula he’s looking for, and indeed I’m not sure anyone does.

The long answer is that I think this is sort of the wrong question. Read the rest of this entry »

We’ve previously defined the types of commitment and talked about how to play when weakly and moderately committed.  All that’s left is strong commitment.

Strong “commitment” most closely matches the basic English definition of the word – you are attached to this hand until the end.  That leads to my first strategy pronouncement:

Once you become strongly committed to a hand, you never fold.  Your sole goal is to get your opponent(s) to put as much money in the pot as possible.

This seems like pretty basic advice, but in my experience it’s not something most players handle particularly well. Read the rest of this entry »

In the previous discussions of commitment here, here and here the examples of hands that commit you always were a strong made hand – top pair or better, or in the case of the preflop example an AK.  That’s no accident – the most common way to become committed in NL holdem is when you hold a strong made hand.  What may not be obvious is that commitment can result from a draw or the combination of a draw and and weak made hand that probably isn’t best. Read the rest of this entry »

We’ve been talking about commitment for a couple of articles – most recently playing when weakly committed.  I now want to discuss the next step up the commitment ladder – playing when moderately committed. Read the rest of this entry »

Last time I posted some general information on how game structure influences correct play.  I now want to apply that directly to no limit holdem.

I identified two factors about a game that influence how eager you should be to voluntarily enter the pot preflop.  The first was the size of the antes and forced bets.  It’s relevant to ask, especially in a NL game, “size relative to what?”.  That’s a good question.  I think for purposes of discussion, it’s reasonable to discuss their size relative to a reasonable 100 big blind buyin.  Obviously many games are played with larger or smaller buyins, but 100 big blinds is a good place to start discussion. Read the rest of this entry »

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 »

If you can’t evade a tax, pay a little too much to confuse their computers.

-Friday, Robert Heinlein

Here’s a funny little story.  A few years ago I was playing a 1/2 NL home game.  It was my first time there, and we were playing somewhat deep for a small game – I think I had 150BB and several people had me covered.  Anyways, because of the stack depths and general table atmosphere I was using a slightly oversized preflop raise – I was thinking something like 4.5BB+1BB/limper would be about right (3 to 3.5BB +1BB/limper is more standard).  Anyways, just for shits and giggles, I decided to do 4+1/limp half the time and 5+1/limp half the time. Read the rest of this entry »

Last time I went to some length to define three different types of pot commitment.  This wasn’t just a ploy to fill space – you should care about the distinction for a very simple reason: correct play is different depending on how committed you are.  Put another way, all situations at the same level of commitment will share major similarities.

So let’s get started with weak commitment 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 »

There are some things about specific forms of poker that just don’t become obvious until you compare them to other forms, so for my holdem-only readers this statement may come as a surprise.  But holdem (both limit and no limit) has the least information contained in the mechanical play of the cards of any form of poker.  Simply put, when a new board card is dealt, especially on the turn and river, it often tells you very little that you didn’t already know. Read the rest of this entry »

I don’t play in Vegas all that often, so when I do make it out to the desert there’s always something new going on.  This time it was a new way of taking your first hand when sitting down at the table. Read the rest of this entry »

I’ve seen this happen a million times:

Beginner Bob has just absorbed the sage wisdom of Play Holdem Pretty Darn Good, NL Edition and sits down at a small stakes NL game to try out his newfound knowledge.  He knows his opponents will be playing far too loose at these stakes, and as such resolves to wait for big hands he wants to show down and then bet them for value.  Sure enough, 30 minutes into his session he flops a set, bets it, gets called down, and stacks someone.  Now Bob is sitting in front of a nice big doubled stack.  Then something funny happens an orbit later: Bob enters the pot by calling an under the gun raise with an AQ, hits an ace, gets check-raised on the flop, pays off the whole way to the river, and loses to AK.  Suddenly Bob is worse off in terms of money than he was before he hit the set.  Bummer.

I swear this happens FAR too often to be coincidence. Read the rest of this entry »

Subtitle: How to Win at No-Limit Hold’em Money Games

Author: Dan Harrington & Bill Robertie

Publisher: 2+2

This is the follow-on to the excellent Harrington on Cash Games Volume I.  The two volumes are in essence one book, and should be treated as such.  Volume one deals primarily with basic concepts and play before and after the flop, and volume II deals mostly with play on the turn and river.  Since turn and river play are more essential to winning at NL, this could in some ways be considered the more important volume.  That said, don’t consider buying only one of the two volumes – they really are just one book split in half, and having one but not the other doesn’t make much sense.  So if you’re going to buy one, buy both.

Like the previous volume, the advice in this volume is of high quality and strikes me as sound on a number of theoretical levels. 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.

Maybe you’ve had this experience –  I know I have.  You’re studying some form of math, and you’re not quite clear on why it works the way it does or what it has to do with anything – someone’s just stuck this formula in front of you.   And then you go back and read about why it was invented in the first place, and suddenly you realize you’re holding the answer to everything, or at least a much bigger chunk of everything than you originally thought. Read the rest of this entry »

One of my readers sent in the following question which I think deserves discussion:

Wayne,

I have stumbled across your website and I think your articles are excellent. I am writing to request your insight about split 2 pair. An article or an email would be much appreciated. I have heard it referred to as a trap hand and I can see why. As I understand it Mark Twain once said “That knowing how to play two pair correctly is worth a college education and costs about as much to learn how to do so”. I am paraphrasing but you get the point. The heart of my dilemma is this: I do not know if I should play all split two pair hands as drawing hands hoping to fill up or play them strongly knowing I will have to win with just two pair. Two pair (especially top two pair ) seems to be too strong a had to play as what amounts to a gun shot draw but more often than I like I seem to be toast to a set on the flop or beat by the river. I know board coordination plays a role but I REALLY hate getting my money in when I am beat to a set on an uncoordinated flop board. Is this just a cooler like set over set. What is a poker player to do? In my mind there is a big difference between 3 types of split two pair you can have and thus there should an equally big difference in how you play the hand. But I am not sure how to work this all out or if I am on the right track. Any advice you can give or articles you will write are much appreciated! I look forward to reading more of your poker insights in the future. Thanks.

This is a good question. Mark Twain’s comment about two pair certainly refers to draw poker. While draw poker is essentially a dead game in this day and age, it’s worth looking at what happens there as background for thinking about 2 pair in holdem. Read the rest of this entry »

One of the advantages I have when playing in Vegas is that almost nobody knows who I am.  I don’t play there enough to be a “regular” and I don’t volunteer my name at the table so it’s unlikely anyone would connect me with CardSharp.

At first look, this might actually seem to be a disadvantage.  While my opponents generally know little to nothing about me, the reverse is also true.  I know little to nothing about them.  If we assume I’m a better player than the majority of my opponents, then it stands to reason that I would make more effective use of information about how they play than they would of information about how I play.  So the mutual lack of information would in theory puts me at a disadvantage.  I believe that effect is real, and does hurt me slightly.

However, there’s a more dramatic effect at work that I believe gives me a huge edge.  There is a basic principle of psychology that it’s easier to deceive people on a subject they’re trying to gather information than it is to deceive them on a subject they’ve already made up their minds about. Read the rest of this entry »

OK, it’s been WAY too long since I’ve posted.  Sometimes I just go through periods where poker doesn’t interest me much.  That said, I’ve got a burst of motivation so I’m going to get some new content up here.  Here’s what’s on the agenda for the next few weeks:

• A bunch of “CardSharp Mailbag” features based on all the mail I got and didn’t answer the last few months
• Some more postflop material for NL holdem
• Beginner strategy articles for limit holdem and Omaha 8
• A review of Cogert’s Play Razz Poker To Win – he was nice enough to send me a copy, so I should get my ass in gear and review it.

All that aside, I want to comment on the poker economy a bit.  It’s pretty clearly going through a bit of a downturn at this point, at least in terms of cash game availability (I haven’t been watching the tournament circuit too closely).  There’s probably a lot of reasons for this – the NL holdem fad is beginning to wear off, for starters.  The slower economy also means there’s not as much loose cash being dropped by the tourists.  Therefore we can expect the standards of play to rise somewhat at the midstakes and higher as the ratio of pros to fish changes for the worse.  Over time things will even back out as some of the pros quit or move down, but for now, things are IMO a bit ugly out there.  One thing worth noting is that as the NL holdem boom cools off, it’s good to know other games.  These games have the virtue that there was no boom, so there isn’t as much shrinkage when the boom ends.  Also, the average quality of play tends to be worse at the midstakes.

To help CardSharp’s readers cope with this, I’m going to add more content that isn’t NL holdem.  For now I’m going to start with limit holdem and Omaha 8, but PLO is a likely addition in the near future. Hopefully everyone enjoys the new articles.

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. 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 »

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. 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 »

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. Read the rest of this entry »

Last Time we talked about top-pair and overpair type hands, and the desirability of keeping the pot relatively 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: Read the rest of this entry »

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. Read the rest of this entry »

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. 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 »

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: 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 »

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: 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 »

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: Read the rest of this entry »

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. 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 »