Analyzing NLHE: TAP Concept 60

This is the final installment of my series looking at the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Soon I can get back to telling stories from the felt, but I also want to revisit some of these concepts, as well as the project as a whole, in future posts.

Concept No. 60: If someone bets into several players, and you have a hand that is somewhat likely to be best, but unlikely to improve, you often have to fold.

Yes. Similar ideas have been discussed in topics a few times before (particularly concepts 18 and 32, and to some extent concept 50, while concept 6 sort of argues the other way). I agree with the author's closing statement that this may be the single most profitable concept in the book for many readers. The reason is that our human nature (mostly due to the regret aversion and confirmation biases) begs us to call in this situation. For example, if we call with top pair and a good kicker and someone raises behind us, or if we have to fold on the turn or the river, this is easily written off as bad luck because we couldn't have anticipated those things, and we don't regret our call; hence, we will probably call again next time. Of course, the fact that there were so many possibilities we could not anticipate is what should have made us decide to fold. On the other hand, if we were to fold and it turns out we would have won the hand, it is psychologically devastating, and we are likely to call in such a situation next time.

With several players yet to act, two cards yet to come, and very little chance to improve our hand, we lack all sorts of crucial information that we would need in order to continue the hand profitably. Certainly, it depends on the situation (perhaps your hand is a big favorite, or your opponents are very passive), but many players call far too liberally in such situations.

Analyzing NLHE: TAP Concept 59

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 59: Don't help your opponents play correctly.

I agree with this one, and it seems incontrovertible, but there is at least one example of advice that suggests you should help your opponents to play correctly. I think it is worth considering.

Barry Greenstein has a total of eight "play lessons" in his book Ace on the River. Lesson 5 says the following: "If your bets define the strength of your hand, it may make decisions easier for you on later streets." The idea is that if you confuse your opponents too much, you will have trouble interpreting their plays later in the hand, and you won't know how to react. I think Dan Harrington may have similar advice in his book, but I can't quite remember. Anyway, I think Sklansky and Miller's concept holds up despite Greenstein's lesson. You can use Greenstein's advice for your made hands but still make it difficult for your opponents to play correctly if you play bluffs in the same way. However, bluffing actually seems to go against Greenstein's Lesson 5. He suggests you let "your bets define the strength of your hand." This implies that you should not let your bets "equivocate" (my word, not his), which is what happens if your bets could mean either a bluff or a made hand. Bluffing occasionally seems to go against Greenstein's Lesson 5, and so it should not be taken too seriously. I have to take Team Sklansky's side on this one.

Okay, just one more concept to go. Hopefully, I'll finish this year after all!

Analyzing NLHE: TAP Concept 58

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 58: Any strategy relatively close to a game theoretical strategy is at least almost as good as the optimal strategy, and sometimes it's better.

Sklansky and Miller are a little messy with their terminology here, but I think they get their point across. The way I interpret this concept, I agree with the authors. Here's my interpretation: even if you don't know precisely what the optimal play is (and you probably don't), it's still worth trying to approximate it. Playing a strategy that is close to "optimal" (that is, unexploitable) is almost always better than playing a strategy that is not close to optimal. Furthermore, if you have identified exploitable weaknesses in your opponents, it can, in fact, be better (in terms of EV) to deviate from the optimal strategy. One problem I have with this idea is that there probably is no mathematically "optimal" strategy in games with more than two players... but I think the main idea still holds up.

I disagree with the last two sentences of the books discussion. It says: "If you plan to make a play that will give away your hand, choose a different play occasionally and make the same play sometimes with a different holding. If you do this consistently as you play, you'll usually do even better than the game theoretical strategy."

First, I don't agree that you should necessarily change anything just because you plan to make a play that will give your hand away. Hopefully, you've chosen this particular play because it maximizes your EV, so changing it can only reduce your EV. S+M suggest either choosing a different play occasionally (but assuming that you've chosen the play that maximizes EV, changing will lose you money), or making the play sometimes with a different holding (I suggest you only do this if you can do so without losing any EV with this other holding). I've discussed before why I don't like the idea of making certain plays "occasionally."

Second, S+M suggest that as long as you think about what your range and your opponent's range is, and you mix up your play, you can do better than the game theoretically optimal strategy. I doubt that this is true unless your opponents are tremendously weak. The problem is that it's impossible to avoid making mistakes, so very few people would ever be able to do better than if they could consistently play an "optimal" strategy. However, if your competetion is weak enough, you can probably find enough opportunities to exploit them to make up for all of your mistakes.

Analyzing NLHE:TAP Concept 57

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 57: Don't be fooled by players who have giant amounts of cash in front of them.

Sklansky and Miller suggest in their discussion that players who buy in for exorbitant amounts often do so in order to trick other players into thinking that they will be willing to lose their entire stacks, thus enticing these other players to play too loosely. This doesn't fit my experience at all. In my experience, players who buy in deep do so either for mundane strategic reasons (they feel they can outplay the other players at the table with deep stacks) or in order to gain a psychological advantage (either they want to intimidate the shorter stacks, or they want to avoid feeling intimidated). I don't think anyone buys in deep in order to trick players into gambling with them more.

The issue of whether it really is strategically advantageous to buy in deep is something I've addressed in posts a few times before. While many people are intimidated by playing against bigger stacks and believe they are at a disadvantage, I believe it is actually an advantage to have a smaller stack at a full table. It's possible that in certain games you will have higher expectation if you have a big stack, but this is only if you are far superior to your opponents. If everyone plays about the same, players with smaller stacks should be expected to do better.

Analyzing NLHE: TAP Concepts 55-56

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 55: Unlike limit, limping first in on the button is frequently correct.

In a pure NL holdem game, I think this is probably right, mostly for the reasons given by the authors. Specifically, I agree that making the blinds fold is not as profitable in NL, because the blinds are much smaller compared to the normal raise size and final pot size. This probably makes some hands worth limping with, but only against certain opponents.

In practice, however, I practically never limp first on the button. This is largely because of the way pots are raked in my normal game (and most other games in Los Angeles). The casino will take out $1 if there is no flop, but they take $6 if there is a flop ($1 of which is for the jackpot drop). Winning the pot after the flop therefore costs me $5, which is a significant amount when we're looking at a profit of only $10 or $20.

Concept No. 56: Pot odds (as opposed to implied odds) matter a lot less in deep stack no limit than in limit.

Yes. This is central to the difference in the strategy for the two games. Bet sizes in no-limit tend to be much larger in proportion to the pot than in limit, so future bets will have a much larger impact. Since pot odds do not take future betting into account, they aren't as relevant in no limit poker. In no-limit, it's important to try to estimate implied odds rather than relying on pot odds to help make your decisions.

Analyzing NLHE:TAP Concept 54

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 54: Checking to induce a bluff is a significantly stronger play in no limit than it is in limit.

Instead of taking this concept's wording completely literally (it's ambiguous how we should define the "strength" of a play), let me rephrase it in a way that I think reflects the authors' point more accurately: "Checking to induce a bluff is the best play much more frequently in no limit than it is in limit." I think this is right.

I should point out that Sklansky and Miller are double-dipping here: we've already discussed this idea in Concept 33. As I implied in that post, I personally don't usually think of checking on the turn with a moderate hand as "inducing a bluff." Rather, I think of checking as moving my hand range toward the weaker end, which then forces me to call on the river if my hand is on the stronger end of my range. I will admit that "induce a bluff" is a simpler way to get this idea across.

Analyzing NLHE:TAP Concept 53

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 53: In heads-up pots, whether you are first or second to act is more likely to affect your decision in no limit than it is in limit.

I think Sklansky and Miller are having another issue with semantics (or perhaps it's my fault for taking them too literally), but any way I look at it, I can't see the use of this concept. It's also quite awkward trying to judge whether it's true. I happen to think it is true as stated, but not for the reasons the authors were probably thinking of. This post is an almost purely academic analysis of this concept's claim, without much poker insight, so let me apologize. I personally think it's rather interesting, though. First, let's look at the example Sklansky and Miller give.

Their example is that if you have the nut flush draw in limit holdem, you will probably want to bet regardless of whether you are in position. In no-limit, though, you should be much more willing to bet if you are first to act. If you check, they say, you are likely to have to face a bet anyway, so by betting out, you can set the bet-size yourself. If you are second to act, you might want to check to give yourself a free card and a chance to win a big pot.

Well, that is only a specific example. Let's take a step back and try to answer the question: Should your position be more likely to affect your decision in limit or in no limit? Of course, your position is only one of many factors affecting the decision of whether to check or bet. Your hand range, your opponent's range, and your opponent's tendencies are usually the most relevant. Let's imagine holding all of these other factors constant, and distill your "position" down to the following. If you are "first to act" and you check, your opponent has the opportunity to bet. If you are "second to act" and you check, the betting round ends. In either case, if you bet, your opponent has the opportunity to raise. So, in this formulation, you should always (whether you are playing limit or no limit) be more inclined to check if you are second to act, because you gain the added benefit of denying your opponent the opportunity to bet. So, the question simply becomes: Is this added benefit more valuable in no limit or in limit? I think the answer must be "no limit." Giving your opponent the opportunity to bet tends to be much riskier in no limit than in limit, because a bet can be much larger in proportion to the pot. So, denying your opponent this opportunity has greater value in no limit. Thus, I would have to agree with this concept's claim that, in no limit, your position is somewhat more likely to affect your decision than in limit.

In practice, though, we are more likely to bet when we are second to act than when we are first to act. When we are second to act, this means our opponent has checked, which means his range is weaker. When our opponent's range is weaker, we should be more inclined to bet. In my analysis in the previous paragraph, however, we held these hand ranges constant, which led us to the awkward and counter-intuitive conclusion that you would rather check if you are second to act than if you are first to act. This conclusion led me to agree with this concept's claim. However, this is, of course, not the point the authors were trying to make with the concept. This is made abundantly clear from their example about how you would play a nut flush draw, which incorporates plenty of good ideas about poker, but nothing that really addresses the concept's claim. It attempts only to show one specific case where the concept holds, and it fails even that because it does not hold the opponent's ranges constant (the opponent's range weakens after he checks).

I won't address the ideas that Sklansky and Miller were trying to get across in this concept, which they revealed in their example, except to say that I essentially agree with them.

Analyzing NLHE:TAP Concept 52

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 52: The play of check-raising to knock people out, an important tool in limit, should rarely be used in no limit.

I think this is true. Sometimes when I check-raise on the flop in no limit, I do so with the intention of knocking out some middle-position players, but this is almost never the primary objective of my check-raise. I will either have a very strong hand or a semi-bluff.

In limit, it's sometimes better to check with a low or medium pair, and then raise if a late position player bets. This play is very likely to force players who have overcards to your pair to fold, even if they may have called had you bet out instead of check-raising. If the late position player was betting without a pair, getting these players out substantially improves your chances of winning the pot. In limit poker, as we discussed in Concept 9, winning the pot is the main focus.

In no limit holdem, this play makes far less sense. Here, you don't need to count on someone to bet so that you can check-raise in order to confront them with two bets at once. If you want to deny a middle-position opponent the right odds to call, you can just bet more yourself right out of the gate. Also, in no limit, a check-raise tends to be much more expensive in relation to the pot. Defending a relatively small pot with a large bet should not generally be your main objective (concept 9 again). When you do want to knock out middle position players with your check raise, it's either because you are semi-bluffing with a small flush draw and you want possible bigger draws to fold, or you have a made hand and you want strong draws to fold. It's not like in limit where you are hoping to make players with overcards fold. In no limit, these players will already be folding to the original bet (unless the bet is unusually small), and you won't need to raise it.

Analyzing NLHE:TAP Concept 51

If I'm going to get through these by the end of the year, I'd better try to get a few done during the week. So, here is my analysis of the next concept from the end of No Limit Hold 'em: Theory and Practice. Sorry to those of you who are more interested in my narratives from the poker tables! I'll try to get one of those out in the next week.

Concept No. 51: In tournaments, other things being relatively equal, prefer small river value bets that will often be called to large river value bets that will seldom be called. Put another way, if a smaller bet has a bit less EV, it is still right to make it in most tournament situations.

I haven't played tournaments in years, so I'm no expert, but this concept is seems obviously correct. It's a specific example of a more general tournament concept: it can be worth giving up a little bit of EV in exchange for less volatility. The reasoning behind this idea is that since you can get paid in a tournament even if you do not come in first, it's worthwhile to hold on longer than other players even if your chances of coming in first are diminished slightly. This more general idea would have made for a much better concept idea (ie, more insightful, useful, and generalizable), except perhaps that most tournament poker players already understand this idea.

I'm not sure why, but in these concepts, Sklansky and Miller often forgo more general concepts like this in favor of specific examples that the reader might have difficulty generalizing and incorporating into his game. Maybe using specific examples is more effective in marketing poker books; Sklansky is certainly experienced at writing poker books that are popular.

Also, does anyone else find it strange that the authors are bringing up tournaments in this one concept for this rather obscure point? I guess tournaments are fair game since they are a common form of "No Limit Hold 'em," but I had thought they were focusing on cash games.

Analyzing NLHE:TAP Concept 50

In which I analyze the fiftieth concept at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 50: If someone bets the flop and gets two or more calls, anyone who bets a significant amount on the turn should get respect.

This seems to be happening a lot, but once again, I don't like this concept even though I do agree with it. A big bet into a multiway pot after significant action on the flop is a very strong play, and the bettor should have a very strong hand if he expects to make a profit.

I have two main gripes with the way this concept is presented. First, the concept is a very specific example of a more general idea, which is that when someone bets with the expectation of being raised or called, his hand range must be very strong. I think the book's "concepts" are more useful when they are more general, because they can be applied to various situations.

Second, the example in the discussion is very unconvincing, a sort of "straw man" argument. If the authors felt confident in the generality of their concept, they would set up an example where all factors would suggest that you should not respect the bettor's bet, except for the reason given in the concept. On the contrary, in the example in the book there are many reasons why you should respect the bettor's bet. Sklansky and Miller try to use this to their advantage, saying, "you are out of position with a hand that is unlikely to improve..." However, this just muddles their argument. Thus, their conclusion that "you ... should frequently fold" to the bet on the turn is true, but it doesn't bolster their main argument in the least. They have completely failed to make a logical argument in support of their concept.

Recently, I haven't been doing EV evaluations like I did at the beginning of this project, and that is partly do to my own laziness. However, I think Sklansky and Miller also were lazy in formulating these concepts and discussions. It's frustrating, but enough of them are thought-provoking that I think this is still a worthwhile project. Only ten more to go!

Analyzing NLHE:TAP Concept 49

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 49: If someone makes a big bet into multiple players, typically he will have a good, but not great, hand.

This is very similar to concept 35, and once again, I don't have anything very insightful to say. I think the claim made by this concept is usually true, but it's not very reliable. Different people play differently at different times.

Analyzing NLHE:TAP Concept 48

From No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 48: Often make small bluffs (about one-third the size of the pot) in multiway pots when it appears no one has hit the flop. Balance those bluffs by also sometimes making small bets with good hands.

This is too general. It's also rather vague as to how it can "appear" that no one has hit the flop, but I'll take this to mean that most players have checked (as in the discussion in the book).

Yes, there are situations where a small bluff into a multiway pot can be profitable, but you will probably lose money if you apply this advice indiscriminately. Whether such bluffs are profitable depends on your opponents and on the flop texture. There are lots of players who will call small bets with weak hands or will check-call with relatively strong hands when they are out of position. Also, bluffing small on flops with straight draws usually won't work, because people can call a small bet with a gutshot. In general, your best chance will be on boards with the fewest draws, such as paired boards or A- or K-high boards. Boards with these textures are also the best for making small bets with your good hands, so it will be difficult for observant players to exploit you.

You also might want to use your hand as a guide to when you should bluff. If you have a backdoor draw or overcards, your bluff will have some of the benefits of a semi-bluff, since you will have at least a slim chance to outdraw your opponent if you get called.

Analyzing NLHE:TAP Concepts 46-47

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 46: Don't just think about what you put your opponents on. Think about what they put you on also.

Yeah, this is what I'm always talking about. You need to think about what your range is and what your opponent's range is. That is the basis of game theory.

Concept No. 47: If it's clear your opponent has a hand at least worth a call, but he raises instead, it's almost never a bluff.

I think this is an overstatement to the extent that it is misleading. Also, it is very difficult to tell when your opponent has a hand "at least worth a call." However, this does occasionally arise if your opponent played in a way that was probably a made hand but if not, must have been a draw. If the draw comes in, you might want to bet to get value from his previously-made hands, but you'll have to fold if he raises. I would argue that your opponent could still be bluffing in this situation, but it's unlikely enough that you should usually still fold.

Suppose that you identified a situation where your opponent certainly had a hand that was at least worth a call, and he has raised you. Sklansky and Miller say it is almost never a bluff. However, it could still be a bluff if your opponent is overly aggressive. He would likely be making a mistake, but mistakes like this are not that rare. Moreover, if he knows you will fold to this bluff (which S+M are recommending to you), it means his bluff was actually the correct play after all.

This last idea is a bit convoluted, but I have used this against my more astute opponents. For example, I played a hand that went something like this: suppose you have AsJh and the board comes Jd 5s 4s. There is a lot of action on the flop. The turn is the Ace of clubs and you get check-raised. I think you are probably behind here, but you might still want to call because you might be ahead, and you do have four outs against a small set. If the river is a spade and your opponent bets, you can raise as a bluff. Your opponent will figure you would only do this with a flush, and fold his set. He might even fold a small flush or straight.

Analyzing NLHE:TAP Concept 45

After this post, I'll be three-quarters of the way through the concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 45: Know when a hand (even a good one) has more value as a bluff catcher.

This is good advice (after all, it's always good to know things), but the Sklansky and Miller don't give a good explanation of how to identify this type of situation.

The authors merely point out that sometimes you should check with your good hands, especially if you think it's likely that your opponent has a hand that's too weak to call with. This is true, but it's a meager assessment of the circumstances that make it profitable to check-call with good hands rather than to value bet with them. It would be helpful to discuss these circumstances.

For one thing, we need to consider our opponent's style. As I summed up in my analysis of Concept 10, if you've identified any weakness in your opponent's play, try to put him in situations that will allow you to exploit this. There are two types of mistakes your opponents might make that would turn some of your strong hand into bluff-catchers.

The most common weakness that you will be able to exploit is if your opponent bluffs too often. Against such opponents, you should be much more willing to check with your strong hands and use them as bluff-catchers. Another type of opponent is so tight that he will not pay you off if you bet. These players are great to bluff against, but if you hold a strong hand, you want to get him to put more money in the pot. So, it may be better to just check and call against extremely tight players. Often very tight players will be very passive, though, so this opportunity seldom arises.

There are also circumstances that have nothing to do with your opponents weaknesses that can make many of your hands bluff-catchers. Generally, this will occur if your opponent likely knows whether he has your hand beaten. This can happen if your hand-range is extremely narrow (usually because of the type of board and the betting to this point, or maybe you accidentally exposed your cards), or if your opponent's range is polarized (that is, he probably holds either a very strong hand or a very weak one). In such a situation, your only viable options are to check or to put in a small blocking bet. Let's look at some situations where your opponents range might be polarized.

In my discussion of Concept 44, I noted that when your opponent's hand range becomes polarized when he bets on the river: either he has a reasonably strong hand or he is bluffing. If you hold a hand in between these ranges, it doesn't matter much exactly what you hold; all that matters is your opponent's bluffing frequency. If he bluffs too much, all of your hands in this middle range are good to call with. If he bluffs too little, they should all be folded (or, possibly, raised as a bluff).

Another common situation where your opponent's range is polarized is if he is very likely to have had a drawing hand, but you're not sure if he has hit his draw on the river. Your opponent knows if he has you beaten because his hand is polarized. Either he hit his draw or he didn't. Unless you can beat your opponent even if he hit his draw, your hands now turn into bluff-catchers.

There are other probably other situations where your hands might be best used as "bluff-catchers," but these are the most common ones I can think of.

Diane's Final Hand at the Bike?

There have been some complaints that I have been focusing too much on my poker analyses recently and have neglected telling stories about my experiences at the poker tables. So, here's something that happened last night.

In the 5-10 blind $500+ buyin NL game, I was on the button and somebody straddled for $20 (he gets last action, like another big blind). One player limped, and Diane, to my right, raised to $85. Diane is an attractive Asian woman who prides herself on her ability to loosen up a table, encouraging people to gamble with weak hands. Just a few hands earlier, she had executed a successful bluff with a $250 flop bet followed by a $800 turn bet with ten-high, no draw. She had about $5000 in play.

I had about $900 and looked down at AKo, much better than what Diane was likely playing with. I raised to $275.

To my left (in the small blind) was one of the tightest NL players I've played with. He had about $2700 and called my $275 raise. Everyone folded to Diane, who raised to $1000, putting me all-in. I have to call about $625 more. I need about 30% equity to make the call correct. I call. Even against KK I have enough equity here. I'm hoping the tight player to my left will fold, or that he'll push all-in and make Diane fold (in which case there will be more money for me to win, and I'll only need to win 23% of the time).

While the player to my left was deciding what to do, Diane asked me if she could look at my cards. I smiled at her incredulously and shook my head no. She hadn't bothered to wait for my reply, though, and looked at my cards.

The player who had been in the big blind was quite upset by this, and the floorman was called over. It's rather unusual for a player who isn't directly involved in a situation to call the floorman, and some of the other players (most notably Diane and "Corporation" Mike) were quite upset with this guy. However, as the guy said, "I'm not going to just sit here if I see something fishy going on at the table! I'm supposed to just sit back and watch cheating going on?" I'm sure Diane didn't mean to cheat, but I still think it was right for this guy to call the floorman.

Anyway, I think you can see where this is going. The floorman misunderstood the first explanation and said "well, I can't kill her hand just because someone showed his hand to her!" Of course, she had taken it upon herself to look at my hand. Diane started shouting about how this wasn't fair and if they decided to kill her hand, she would never come back to the Bike. The floorman called over the floor supervisor, who, amidst a growing crowd of onlookers, took about two minutes to finally call Diane's hand dead. Her $1000 stayed in the pot. On the verge of tears, Diane left, loudly cursing the floormen and explaining that this is why nobody comes to the Bike anymore.

In my opinion, this was a relatively clear decision for the floormen. Although Diane was not trying to cheat, she did break the rules and give herself an unfair advantage. Technically, her hand would be dead even if she were also all-in already (even though looking at my cards would give her no advantage because she would have had no more decisions to make). However, it's unfortunate to lose a friendly player who was generally very good for the game.

With Diane's hand out of the way and her money in the pot, the tight player made an easy call with QQ and won the whole pot.

Analyzing NLHE:TAP Concepts 42-44

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 42: If you check the river, most players will bet only with very good hands and with bluffs. They'll check down hands that could win a showdown, but that are unlikely to be called by worse hands.

Yup. This is the correct way for your opponents to play the river, and since it's rather basic and intuitive, most players have mastered this strategy. You will see players deviate from this, but it is quite rare. However, I think it is worth noting because you don't want to fall into a pattern where you pay off your opponents if they make huge bets with hands that are only moderately strong.

As Sklansky and Malmuth point out in their discussion, this fact means that a lot of your medium-strength hands become "bluff-catchers." That is, they can only win if your opponent is bluffing. For example, it doesn't matter whether you hold top pair or bottom pair if your opponent will only value bet with two pair or better. Both hands can beat only bluffs. As S+M point out in Concept 44 (which I analyze below), the bigger your opponent's river bet, the less your hand matters; for example, if your opponent is rational and makes a bet of ten times the size of the pot, a wide range of your hands become "bluff-catchers," since your opponent will probably either have the nuts or nothing. On the other hand, if your opponent bets only one-tenth of the pot, the strength of your hand is very relevant.

Concept No. 43: Big bets mean big hands. Don't make or call big bets very often with weak hands.

As uncontroversial as this concept seems, I don't think it's precisely right. Big bets can mean not only big hands; they can also mean big draws or hands worried about draws. When your opponent makes a big bet (or when you make a big bet and get called), his hand range becomes much stronger. Thus, you should only call or make big bets with hands that have the potential to beat your opponent's strong range. This means you should be calling or making big bets only with big hands or big draws.

We can look back at some earlier concepts that touched on this topic to find some more exceptions and possibly gain some interesting insights.

Concept 35 seems to contradict this concept: "Unusually small bets tend to be made either with a big hand ... or with a bluff... With one pair your opponents will usually either check or bet a larger amount." So Concept 35 suggests: Big bets mean one pair.

Concept 40 also somewhat contradicts our current concept. This one suggests: Big bets mean the board has lots of likely draws.

Concept 1: "When in doubt, bet more" suggests: Big bets imply more doubt. Or something. This concept was pretty dumb.

To be fair, several concepts do support our current concept. For example, Concept 11 said "A big bet is the most relevant and accurate information available."

Concept 39 also supports our current concept. This was the one suggesting that you respect bigger bets more than smaller ones.

Concept No. 44: The bigger a bet your opponent makes, the more of your hands that turn into bluff catchers.

As I said above in my Concept 42 analysis, I agree with this one. At least in my games, my opponents are usually smart enough not to bet a huge amount with a hand that is only moderately strong, because they know I will probably only call them with hands that are even stronger.

It occurs to me that if my opponent is especially talented, he might be able to trick me into calling with a weaker hand trying to catch his bluff, but this is a very high-risk maneuver for him if his hand is only moderately strong.

I like to think about these concepts in terms of hand ranges, when possible. When my opponent makes a big bet, his hand range is polarized: usually he'll have near the nuts, sometimes he'll have nothing. My range falls almost entirely between these two poles, so my hands are mostly bluff-catchers. When my opponent makes a small bet, it's usually with a hand that is only somewhat strong, or it could be a bluff. Many of the hands in my range will fall on either side of his value-betting range, so my hand strength is the main factor determining how I react to his bet.

Analyzing NLHE:TAP Concept 41

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 41: When holding a mediocre hand, usually bet enough (but not more) so that a raise means you are almost certainly beaten.

I don't like this one. It falls into the category of advice that stems from the idea that you should avoid putting yourself in a position of having to make a difficult decision. As I've already discussed twice before in this series of concept analyses, I don't buy into this idea. I don't think that you can generally improve your EV by maneuvering like this. However, I have heard that Chris Ferguson espouses this idea in The Full Tilt Poker Strategy Guide, which makes me worry that I might be wrong. A project I'd like to take on when I'm done with these concept analyses is to try to disprove this idea in general (or prove it, as the case may be). I'll have to take a look at what "Jesus" has to say, since he really knows what he's talking about when it comes to game theory.

Analyzing NLHE:TAP Concept 40

After this post, I'll be two-thirds of the way through my analysis of the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 40: Certain flops require certain-size bets. No matter what hand you hold, your flop bets, on average, should be smaller on flops like AhKdKs than they are on flops like Jh9s7h.

I think the authors have overstated the idea here, but I still like this concept. Most players underestimate the importance of flop texture in sizing their bets, but the authors go too far when they imply that flop texture is the only factor worth considering. Also important are position, stack-sizes, number of opponents, your hand, your table image, and your opponents' tendencies. On the AKK flop, for example, the bet should usually be around 1/4 to 1/2 of the pot. Bets outside this range might sometimes be better if stack sizes are quite small or if your opponents are maniacs, but these are unusual circumstances. On the J97 flop, you should almost never bet less than 3/4 of the pot, and sometimes it will be correct to bet 3/2 of the pot.

The reasons for the different bet sizes on different flops are basically those described in the book's discussion. If you are ahead on a AKK flop, your opponents have little chance to outdraw you, and even if they do, they usually won't be able to make much more from you. They have very little implied odds and very little incentive to call a bet of over 1/4 of the pot unless they have you beat. Similarly, your bluffs should be small on this flop to cover your small value bets. On the J97 flop, however, there are all sorts of draws, meaning that your opponent could easily draw to beat your hand, and if he does, he might be able to win quite a bit more from you. Your opponents are likely to have good implied odds in this situation, and so you must bet more to discourage them from calling. Your bluffs must follow suit.

Another way to look at this is that if you have a made hand on the J97 flop, you can make large value bets without worrying about making your opponents fold, but on the AKK flop, the most you can hope to win is a small bet or two.

Analyzing NLHE:TAP Concept 39

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 39: You must adapt your play to different-sized bets. If you will call a twice-pot bet as often as you call a half-pot bet, you're in trouble.

This is correct both in terms of game theory and in practice. There are probably some players against whom you should not take this advice, but they are rare.

Game theory assumes that your opponents play optimally against your strategy. If you call just as often whether the bet is big or small, your opponents can easily exploit this by making their bluff bets small and their value bets big.

In both theory and practice, I think it's true that big bets are more likely to be bluffs than small bets, and this is why some people are inclined to call big bets liberally. The big bets look suspicious. However, this does not mean you can call these big bets more often, because you need to win a higher percentage of the time for you to come out ahead. The fact is that you have to let yourself be bluffed once in a while, especially when your opponent makes a big bet.

As I said, there are probably some players against whom you should call big bets even more liberally than small bets. This situation can arise if you notice that your opponent always makes small value bets but his big bets tend to be bluffs. You still need to be wary, though, because players are liable to change their strategy at any time!

Analyzing NLHE:TAP Concept 38

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 38: Be more apt to semi-bluff when your draw isn't to the nuts than when it is.

Yes. This was discussed indirectly in my analysis of Concept 34. The key point there was "the higher implied odds your draw has, the less attractive semibluffing with it becomes."A draw to the nuts has much better implied odds when it hits than does a non-nut draw, which makes checking or calling with it a more attractive option relative to semibluffing.

Put another way, semibluffing will often win the hand immediately when your opponent folds. This is the ideal result regardless of whether your draw is to the nuts, but it's more beneficial if your draw has meager implied odds. Nut draws usually have strong implied odds, so they are commonly worth just calling with.

As an aside, when semibluffing with a non-nut draw, I try to bet enough to make better draws consider folding. For example, if I have 8h7h and the flop is Ah6h5c, I will make sure to offer my opponent significantly worse than 2-to-1 odds. This way, someone with a better flush draw will have to consider folding, because if I have a pair of aces or better, calling would be incorrect for him.

Analyzing NLHE:TAP Concept 37

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 37: Bets on the turn should, on average, constitute a smaller percentage of the pot than flop bets.

This is probably true for the reason given by the authors in their discussion, but they neglect an opposing factor that could conceivably refute this concept's claim.

There are some obvious differences between the flop and the turn. After the turn betting round, there is only one more card to come and one more betting round. After the flop, there are two more cards and two more betting rounds. As Sklansky and Miller discuss, both of these factors favor the EV of draws on the flop over the turn. It follows that, in order to make it unprofitable for a drawing hand to call, a made hand would need to bet more on the flop than on the turn.

However, there is another obvious difference between the flop and the turn that can have an effect of the EV of draws, and this one favors the EV of the draw on the turn. I am referring to the fact that while there are only three cards on the board after the flop, there are four after the turn. This extra card means that the board has much more potential to threaten multiple draws, which means that it will be less obvious which draw your opponent has. This, in turn, means that each draw has higher implied odds, because (as Sklansky and Miller pointed out in Concept 31) if your opponent hits his draw, it will be very difficult for you to figure it out. To combat this, you will often have to bet extra on the turn if you have a made hand. This factor is completely ignored by S+M.

So, on the flop, draws have the benefit of an extra round of betting to extract value if they hit on the turn, plus the a possibility of getting two tries to hit the card (although they may have to call another bet on the turn in order to see the river). These factors increase the EV of draws on the flop, and thus demand bigger bets from made hands.

On the turn, draws have the benefit of some extra "cover" because there will often be more draws on the board than on the flop. These factors increase the EV of draws on the turn, and thus demand bigger bets from made hands.

Although I suspect the former factor is more significant, which would make this concept's claim correct, it's not entirely clear. What is clear is that the latter factor was ignored by the authors in the book's discussion.

Analyzing NLHE:TAP Concept 36

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 36: Be more apt to slowplay very good hands that aren't quite the nuts than the nuts itself.

This concept seemed wrong to me from the first time I read it, but the authors bring up an interesting point in the discussion. After considering it, I still think the advice is generally wrong.

The point that Sklansky and Miller make is that one of the benefits of slowplaying a hand that is not quite the nuts is that you will potentially save a lot of money if you happen to be up against the nut hand. The example they use is a J66 flop. Here they say you'd rather slowplay with K6 than with JJ, because with K6 you might save money if you are up against JJ, J6, or A6.

Well, this is true, but it's a minor concern because your opponent will so rarely hold one of these hands. In the extremely likely event that your opponent does not hold one of these hands, you should be more apt to slowplay with the nuts (well, JJ is not the nuts, but we can imagine we hold 66). It's possible that there may be some situations where you would save so much money by slowplaying with K6 when you are behind that it actually is correct to slowplay it in a situation where slowplaying with JJ is not correct. However, I think this would be extremely unlikely in practice.

Sklansky and Miller neglect to mention the bad things that can happen when you slowplay. By slowplaying:

1. You don't get as much money in the pot when your opponent would call you.
2. Your opponent might outdraw you with a hand he would have folded.
3. Your opponent might have called on the flop but be scared off by a turn or river card.
4. A turn or river card might scare you enough that you have to stop betting or raising.

Factors 2 and 4 are a much bigger concern if you hold the near-nuts than if you hold the nuts. These problems are relatively common, at least when compared to the likelihood of finding that you're up against JJ when you hold K6 on a J66 flop.

Analyzing NLHE:TAP Concept 35

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 35: Unusually small bets tend to be made either with a big hand (a suck-in bet) or with a bluff (a cheap stab at the pot). With one pair, your opponents will usually either check or bet a larger amount.

This is a strange concept because it contains no advice. I think the information is correct, but, to me, it seems only slightly useful.

In my experience, I think it's true that when someone makes a small bet it means it's slightly more likely that he has a big hand, and slightly less likely that he has one pair, but it's not a very significant difference. Depending on the game you are playing in, this concept could be off the mark for a stereotypical player; different types of plays are more or less popular in different venues, and this can also change over time. Also, once you have figured out what a particular opponent likes to do, the generalization made by this concept will be obsolete for that opponent; this concept applies only to players you do not know much about, and for them, bet-size is only a weak indication of hand-type.

Supposing that your opponent's bet-size really were a strong indicator of the type of hand he held, this information would be quite useful, but not devastatingly so. On the one hand, if you knew your opponent either had a big hand or a bluff, you could decide whether to fold right away or just call; raising would never be a good play in this situation. If, on the other hand, you knew your opponent held a pair, it could be a good play for you to raise either for value or as a bluff, but it would still be unclear how your opponent would react to this raise or if he would continue to bet his pair on future streets.

With this concept, Sklansky and Miller are pointing out a very marginal interpretation of how to read an opponent's action, and it's dependent (as they admit in their discussion) on who your opponent is. They offer no insight into how to use this information, although I can accept that they probably consider it outside the scope of this concept (or maybe they just think the answer is obvious).

Analyzing NLHE:TAP Concept 34

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 34: If you have a close decision between semibluffing with a draw and checking it, be more inclined to check if you could make your draw with an overcard to the board.

Sklansky and Miller explain that if you make your draw with an overcard to the board, you might be able to win a big pot if your opponent happens to hit this card, too. I agree, but I don't like how this concept is presented. The discussion begins with the observation that "the higher implied odds your draw has, the less attractive semibluffing with it becomes." This is an important idea, and it would have made for a better "concept" than the one the authors chose. By semibluffing, you often eliminate your implied odds by ending the betting right away.

As it stands, Concept 34 describes a specific case of this idea. The authors not only missed this opportunity to put a particularly useful idea in their concepts, but they also failed to emphasize that the reader needs to be careful not to overgeneralize the advice given, which I think only holds in the specific case where you are deciding between semibluffing and checking. If you are deciding between semibluffing and betting, the opposite advice seems to hold: be more inclined to semibluff if you could make your draw with an overcard to the board.

The reason for this subtle distinction is that your implied odds only improve if an overcard is likely to help your opponent. This is generally only the case if your opponent has two overcards, which is unikely if you are thinking about calling (meaning your opponent has bet), because your opponent probably already has a pair. In this case, you would rather your draw be to undercards, because your opponent might be scared away by an overcard, thereby reducing your implied odds. In the case described by S+M, you are considering checking with your draw, meaning your opponent has not bet. So, it's a lot more likely that he his holding two overcards, and indeed it might help your implied odds if your draw included overcards to the board.

This is a little confusing, but I think the important insight is rather clear: "the higher implied odds your draw has, the less attractive semibluffing with it becomes."

Analyzing NLHE:TAP Concepts 32-33

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 32: It can be correct to fold a hand before the river that has a better than 50 percent chance of being the best hand.

This is certainly true, but there are two reasons that each would be sufficient even in the absence of the other. Sklansky and Miller ignore the first of these reasons in their discussion, and only touch on part of the second.

1. It matters how far behind you are when behind, and how far ahead when ahead. For example, TT is ahead 4/7 of the time against a range of AA,KK, or AK, but it only wins about 40% of the time. This is because it is way behind 3/7 of the time and only a little bit ahead 4/7 of the time.

2. With more cards and more betting still to come, other factors come into play when it comes to EV. Your pot equity can take a back seat to the power of having more information about your opponent's hand than he has about yours. The obvious example is that if you are out of position, you will have to act first in later rounds, and thus you will give your opponent information about your hand before each of his actions. Also, if you are a tight player, your opponent will have a better idea of what sort of hand you are likely to be holding. Furthermore, drawing hands have an information advantage on later streets; whether the draw is hit or missed, the player who was drawing can be fairly certain of whether he has the best hand or the worst hand. All of these factors are more important in NL holdem than in Limit, because players can make larger bets after accumulating the new information.

Sklansky and Malmuth are right about this concept, but their analysis neglects all these factors except that position becomes more important in NL, and that "vulnerable" hands (ie, moderately strong hands that can lose to many draws) lose some value in NL.

Concept No. 33: Be willing to risk free cards to manage the pot size and induce bluffs.

This is good advice. With certain types of hands (in particular, "vulnerable" hands), you would prefer to play a small pot. I've never had much use for the concept of "pot control" or "managing pot size," but it's not really such a bad way to conceptualize why it's best not to bet with certain moderately strong hands. I'm not in the habit of using these ideas; I always just think about it in terms of managing my range and trying to maximize my EV. If I bet with a medium-strength hand on a drawish flop, I will tend to be called mostly by better hands than mine or draws; I will lose a lot against the stronger hands, but gain only a little against the draws. Making matters worse, players holding draws will sometimes raise as a bluff, forcing me to fold. If I do decide to bet the flop despite all these dangers, I will probably check on the turn, regardless of whether the draw comes in. If I bet, I will have problems similar to those I had on the flop, only worse. I will have shown strength by betting, but my hand will be among the weakest in my betting range, and I will have to consider folding if there is a substantial bet on the river. If instead I check and show weakness, my hand will be among the strongest in my checking range, and I can pick off lots of bluffs on the next street.

There is way too much information to process exhaustively at a poker table. Even when I sit at home and analyze hands, I often have to generalize and guess at EV in certain situations, because it's just too complicated to approach it more thoroughly. So, it's necessary to conceptualize poker and use principles or heuristics to simplify decisions. The way I think about the game lends itself much better to the EV and hand ranges conceptualization, but there is value in using a higher-level conceptualization such as pot control and bluff-inducing, as Sklansky and Miller recommend. In future analyses, I might try occasionally to approach problems with both conceptualizations if I think there is a chance they will be at odds.

Poker Riddle

Yesterday, a guy named Jesse, his friend (can't remember his name), and the actor Michael Muhney were in the 500 NL game discussing probabilities and IQs and other nerdy things. I learned that Michael is in MENSA (actually I knew this from his IMDb page), Jesse has a 168 IQ, and his friend went to a school that required an IQ of at least 150. They had a discussion of how many times you'd need to double up to get $1 million if you started with $3. Jesse concluded that the probability was 1-(1/2)^18. He was emphatic on this point for a while even after it was suggested to him that the real answer was more likely (1/2)^18.

Anyway, Jesse had a riddle that he was sure nobody could figure out: you are heads-up in a holdem game, and you're ahead preflop, on the flop, and on the turn, but you have no chance to win on the river (only fold or chop). Jesse offered Michael 3-1 odds on a bet that he couldn't figure it out in 15 minutes, but Michael refused because, as Jesse put it, he is a "life nit," meaning that he is unwilling to gamble on things outside of poker. (A "nit" in poker is someone who is unwilling to gamble much, mostly only playing the nuts.) Michael confirmed that yes, he is a "life nit," if, by that, Jesse meant "a responsible person with two kids who doesn't want to have to explain to his wife in 15 years that he can't pay for their kids to go to college because he gambled all his money away to some guy at the casino with a 168 IQ who can't even do simple algebra."

I asked Jesse's friend, who had heard the riddle and was sitting next to me, how they define "being ahead on the turn." My definition would be that "being ahead" means you have the best chance to win the pot. Clearly, they had a different definition, since the problem is set up such that the hand that is "ahead" supposedly has no chance to win the pot. Jesse's friend said that a hand was defined as being "ahead" if it would win without any more cards coming. Jesse offered me the deal as well ($25 to $75), but, being a life nit myself, I turned him down.

I thought about the problem for a minute but did not figure it out. I eliminated the possibility that the answer involved flushes, and decided that it probably involved low cards. With low cards, it's much easier for kickers to get counterfeited on the river. Anyway, after playing for another half hour, I asked Jesse's friend what the answer was.

"You have to figure it out for yourself, man. Jesse! He wants us to just tell him the answer!"
"Okay, let me think about it," I said.

I thought about 32 against 42, but it didn't quite work. I thought about 43 against 42, with a flop of QQ4. Then a 2 on the turn. So far, so good. 43 is ahead preflop, on the flop, and on the turn, but I can't think of any river card that would result in a win for 43. If the river is a 2, then 42 wins with a full house. Any X higher than 2, and both players have QQ44 with a X kicker. Any Q or 4 and both players have the same full house. After about 1 minute, I told Jesse's friend I thought I figured it out.

"Did you think through all the possibilities? Just think about it." Jesse told me he still wanted to bet me 3-1, and he would give me twelve minutes and let me discuss it with anyone in the casino except his friend, who knew the answer. I hesitated, partly due to his confidence (although he had been similarly confident about the 1-(1/2)^18 formulation), but mostly just because I do not like making proposition bets, especially at poker tables. After a minute, I took the bet anyway. I asked Tony, another prop at the 500NL table, to confirm my answer. We discussed it for about five minutes, and he thought it looked good. Meanwhile, Jesse, having heard my discussion with Tony, proclaimed that I was "a million miles off" and wanted to double the stakes and give me a hint and let me call someone on the phone. I didn't want to escalate the situation any further, so I declined. I gave him my answer. After studying it incredulously for ten or fifteen minutes (and briefly trying to argue that 43 was not "ahead" on the turn), he conceded that it looked right and gave me my $75. I gave $15 to Tony for helping. Jesse said he had seen this question in a magazine and thought there was only one answer, which he told me. He said he had been asking that question at poker tables for five years and nobody had figured it out. I suspect he left something important out of the question, but I can't think what it would be. Anyway, Tony now thinks I'm a genius.

My answer can actually be generalized quite a bit. Instead of 43 and 42, I think any X3 and X2 will work, except X=2 or 3. Similarly, in addition to QQ on the flop, any YYX flop will work, unless it gives X3 a backdoor straight draw. So, X=Ace and Y=4 does not work, but X=7 and Y=4 does. The key is that a 2 has to come on the turn in all cases.

Jesse's answer does not fall into this category. Can you think of it? I'll give clues in the comments if anyone asks. I haven't thought of any solutions besides Jesse's answer and mine.

Analyzing NLHE:TAP Concepts 30-31

After this post, I'll be more than half-way through my analysis of the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 30: Implied odds are a critically important decision-making tool, but always be aware that different opponents offer different odds.

I like this one. Players often overestimate their implied odds by assuming they will win their opponent's entire stack if they make their hand. In reality, of course, sometimes the other player will fold. Other times, you will make your hand only to see it lose to a better one. The probability of either of these two things happening can be approximated without any knowledge of your opponent. However, as Sklansky and Miller point out, if you do have any prior knowledge about your opponent, you'd better take it into account. It can make the difference when deciding whether to call with a drawing hand.

I also like the authors' observation (in their discussion) that the players who offer the least implied odds (because they will fold if you hit your draw) will also be the easiest to bluff. This slightly increases the EV of calling a player who offers low implied odds, but it also influences how you should play your draws and the types of draws you should be calling with. First of all, against such players you should be much more inclined to raise as a semi-bluff. Not only are they more likely to fold, but you're also giving up less in the way of implied odds had you just called. Second of all, you'll want to look for opportunities disguise one draw as another. For example, if you're heads-up against such a player on a board of Ad Th 8d, it's probably better to have the 97 straight draw than the diamond flush draw. You have fewer "outs," but with the straight draw, you not only have decent implied odds for the times you hit your straight, but you'll also probably win the pot by bluffing if another diamond comes. On the other hand, if you have the flush draw, your only chance to win is probably to make your flush, and if you do, your draw is so obvious that you have little chance of getting paid off. This leads directly to the next concept, so let's move right along...

Concept No. 31: Your implied odds with any draw will be better the less obvious the draw is.

Since you just read my analysis of Concept 30, you can guess that I agree with this one. If your opponents are worried about a particular draw and it comes in, they are not likely to pay you off if you hit it. Against some players, you'll probably want to make only a tiny bet if you hit such a draw, because that is your only hope to get paid. In other words, if your draw is obvious, you have very little implied odds. S+M use the example of the nut flush draw on a flop of three diamonds. Everyone is worried about the flush. On the other hand, if you decided to play 53 and the flop comes K42 rainbow, you will have very good implied odds for drawing to your straight.

Analyzing NLHE:TAP Concept 29

I'm working my way through the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Almost halfway done!

Concept No. 29: It's okay to make small raises (2-3x the big blind) to build the pot or to set up a future play.

My standard raises are already rather small, about 3-4x the big blind, so I have to agree that there's probably nothing wrong with raising only 2-3x the big blind instead. In fact, I will sometimes raise as little as 2x the blind, but this is almost always in order to deal with awkward stack-sizes. For example, if the effective stack sizes are around 8-12 times the big blind, I think 3-4x raises will commit me to the pot, but going all-in is too much to risk for just the blinds. In this scenario, I might make a tiny raise pre-flop. Another conceivable reason for a minimum-raise would be to manipulate your opponents to either reraise you or just call you (as S+M suggest in Concept 24), but unless you are extremely attuned to your opponents, it will be hard to convince them to react exactly how you intended. I don't think I personallyhave the talent to make this play work. In any case, Sklansky and Miller have an entirely different reason for making these small raises, and I am not impressed with it.

The authors say, "often you should make this sort of raise with 'brave' hands - pocket pairs, suited connectors, and suited aces - hands that play well after the flop." While I do like calling such hands "brave," I think it's because they are capable of going up against bigger hands and beating them for a big pot. You can be "brave" and call a raise with 98s because you have a chance of winning a big pot with a small investment. However, intentionally increasing the size of this initial investment defeats the whole purpose! By doubling the bet, you are essentially cutting your implied odds in half. If the effective stack size was 100 times the big blind, a 2x raise means you can now only win 50 times your investment if you get lucky and hit your straight. Usually all that will happen is you will fold on the flop and lose two blinds instead of one.

Note that I'm not suggesting that you should never raise with "brave" hands. In fact, I think raising with them is an important part of a balanced strategy. However, that doesn't work if you raise an abnormally small amount with them. You need to raise your normal 3-4x amount in order to disguise your hand.

Analyzing NLHE:TAP Concept 28

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 28: With strong hands, generally raise either a small, pot-building amount or a large, hand-defining amount. Don't raise an amount in the middle that both tells your opponents that you have a good hand and offers them the right implied odds to try to beat you.

I think it's better to just always bet a normal amount. I don't think you should you ever raise a "hand-defining amount." This will enable good players to play correctly against you, which means they will probably just fold unless they have you beat. This is clearly a terrible scenario for your strong hands. Bad players might call you with worse hands, but they even bad players are usually more likely to call a smaller bet. Then you can outplay them post-flop.

I'm also not a fan of "pot-building" bets, but these could conceivably work. Personally, I'd rather bet a little more and risk making a few players fold. Usually the result will be a pot of around the same size with fewer opponents, meaning you have a better chance to win.

Analyzing NLHE:TAP Concepts 26-27

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 26: When there's an ante, your opening raises should be larger than if there were no ante. But they shouldn't be larger in the same proportion that the size of the initial pot increases; they should be somewhat smaller than that.

I don't know of any NL Holdem cash games that actually use an ante, but in theory I think Sklansky and Miller are right that this would be the correct way to adjust. With more money in the pot, it becomes more profitable to "steal"pots, and it becomes correct for you and your opponents to play looser because you have better pot odds. This involves not only raising more, but also widening your raising and calling ranges.

Concept No. 27: When semi-bluffing before the flop, usually do it those times you have one of the best hands that you'd otherwise fold. However, when you are in the blinds in an unraised pot, you should usually do it when you have one of your worst hands.

This one is complicated. I used to like this strategy, but now I think it's probably wrong. I now think the best hands to "semi-bluff" with are the hands that play the best against your opponent's likely calling hands. These include primarily suited aces, but also pocket pairs and suited connectors. Note that I don't think it is relevant whether you would "otherwise fold" with these hands, as Sklansky and Miller suggest. Many of these "semi-bluffing" hands are hands that you would likely have otherwise called with.

Sklansky and Miller's advice seems to be based on game-theoretically optimal river strategy, when there are no cards left to come. On the river, your bluff bets should indeed be with your worst possible hands, and your bluff raises should be with the best of the hands you would otherwise fold. This mirrors S+M's advice that you should bluff when "you have one of your worst hands" from the blinds, and that if you are not in the blinds you should bluff when "you have one of the best hands that you would otherwise fold."

The problem is that this optimal river bluffing strategy does not apply preflop. Preflop, the logic is much different because there are such things as drawing hands and semibluffs. Preflop, you do not need to bluff with terrible hands in order to induce your opponents to play hands weaker than your range; they will already be calling with some hands that they know are behind your range because they are "drawing hands." Instead, you should be bluffing with moderately strong hands as "semibluffs." The best hands to semibluff with preflop have two qualities. 1. They contain an ace, thereby reducing the chances you are up against AA. 2. They have a decent chance of making a big hand like a flush or a set. If your opponent is very tight, or if there have already been a couple of raises, point 1 is reasonably important. Otherwise, point 2 is much more important, because your opponent is unlikely to have AA anyway. In any case, this is why I suggested that the best hands to semibluff with preflop are suited aces, suited connectors, and pocket pairs.

Besides these types of hands, if you want to add some "bluffs" to your range, I think the best approach is to add some more hands that you would otherwise have called with. For example, try reraising with AJ or 77 on the button if you feel the need to bluff. Although these hands do have a lot of equity in just calling, they will also fare okay when your bluff is called. In the end, it's just my opinion, but I think this is a better approach than taking S+M's advice and raising with hands you would otherwise with fold, such as K7s. Although you are not losing any "calling equity" with K7s (since you would be folding otherwise), against normal opponents, these hands are just too unlikely to win if you are called preflop.

Analyzing NLHE:TAP Concept 25

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 25: The button is the true bread and butter position in no limit. In many games you can play an extremely wide range of hands from the button, even for a raise.

Sklansky and Miller say that if effective stack sizes are at least 200 times the big blind, then, as long as you have at least one opponent who plays too loose after the flop, it is correct to limp on the button with over 50% of hands ("probably any two suited cards, any big offsuit cards, any ace, and any offsuit connector down to at least five-four"), and possibly with 100%. They also suggest that you call with over 30% of hands "if the raise represents only a few percent of the stacks (e.g., no more than maybe $50 with $1000 stacks)."

This is another one that is tough to analyze precisely, but in general, I think this advice is encouraging the reader to play too loosely. Unless you are much, much better than your opponents, this advice is probably -EV. I would be especially wary of the advice to call a raise to $50 with KTo in a $2-5 blind game, even if the stacks are over $1000. First of all, this advice completely neglects to consider whether the raise is coming from early or late position, which can have a drastic effect on your opponent's range. Even if the player is in late position and is rather aggressive, though, I would not be happy calling with KTo in this spot. You need to flop a straight or have the flop to contain KT or TT in order to be confident with your hand in there is a lot of action. Otherwise, a hand like this is going to have no implied odds, or worse, negative implied odds.

I do think the general idea that the button is a powerful position is correct, and indeed there are a lot more hands that can be played profitably from here than any other position (except the BB with no raise). However, in my humble opinion, S+M take the idea a bit to far here. If I were an online player, or if I took careful track of my results during poker sessions, such data might be helpful in coming to a well-informed conclusion. As it stands, all I (and also S+M, I suspect) can really do is guess.

Analyzing NLHE:TAP Concept 24

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 24: If you have a hand that you would limp with in a passive game, consider making a small raise (two to three times the big blind) in an aggressive game instead of limping.

The idea here is that by raising, you reduce the chances an aggressive player will put in a big raise because he will be afraid of you. As long as your raise is rather small, this should allow you to see a flop more cheaply than if you just limp.

In my experience, this doesn't really work. After I first read this concept, I tried this strategy a few times with no success. I found that if I was in a game that was so aggressive that I felt like trying this strategy, I very often found myself facing a large reraise. Players who are hyper-aggressive preflop tend to be interested in gambling, and they will not be satisfied with your 2-3x raise. They will reraise you. Some players will even (correctly) see your abnormally small raise as a sign of weakness and raise with hands with which they may otherwise have limped or folded. In fact, in such situations you might want to consider making these small raises when you have strong preflop hand in order to trap your aggressive opponents when they reraise you.

If you are in a game where the aggressive players are not maniacs, this "blocking raise" strategy could conceivably work, but this is rarely the case. As I said, I personally have never utilized the strategy successfully, but I've only tried it a few times. If you do find yourself in this situation and want to try this "blocking raise" strategy, it's probably a good idea to also make small raises with big hands like JJ+ in order to balance your range, as S+M suggest in the discussion of this concept. Without at least some balance, a strong, aggressive opponent won't take long to figure out that your small raises indicate weakness.

Analyzing NLHE:TAP Concept 23

From No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 23: It's ok to limp in, planning to fold to a raise. It's sometimes ok even when you think a raise is likely.

This piece of advice is meant for limit players, who are used to automatically calling a raise after they limp in. I certainly agree with this advice; the only thing possibly controversial is that some would argue that you should never limp in, you should always open with a raise. I think limping is fine, though, and I do it often.

Sklansky and Miller give a good, simple example to support their stronger claim that limp-folding is "sometimes ok even when you think a raise is likely." Basically, the example says that if you think your limp for $2 will return $6 on average when nobody raises, then even if there is a 60% chance someone will make a raise and you fold, it's still profitable to limp. EV= (.6)*(-$2) + (.4)*($4) = $0.40. Although this ignores the possibility that raising could be even more profitable than limping, it proves their point that limping can be better than just folding even if you are likely going to fold anyway.

Analyzing NLHE:TAP Concept 22

Another installment in my analysis of the concepts at the end of No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 22: Ace-king is a powerful "move-in" hand and frequently moving in preflop is by far the best play with it.

I think this is a powerful idea that is underutilized by many of the good players I play with. Sklansky won me over to this idea when he introduced it in Tournament Poker for Advanced Players.

AK has a negative reputation as being kind of a "sucker" hand, since it is rarely the favorite if another player puts lots of chips in before the flop, because the other player usually has a pair or another AK. I think this reputation is undeserved. While it's true that AK has less than 50% chance against many other strong hands, it is only a big underdog against AA (6.5%-12%) and, to a lesser extent, KK (~30%). Against other pairs, AK has 43%-50%. There are three points that I think are misunderstood by players who think it's a sucker play to move all-in with AK preflop.

1. Players put way too much emphasis on having 50% equity when all-in. Whether a play is "correct" is determined by calculating (or guessing at) the play's expected value (EV). Actually heads-up winning percentage is only one factor in an EV calculation. When you are raising all-in, your EV depends only on the size of your raise, your pot equity (the amount in the pot after your raise is called times the probability you will win), and your fold equity (the amount in the pot before your raise times the probability your opponents will fold). Because fold equity is always positive, the required equity (when you are called) to make raising better than folding is always less than 50%. Having a higher probability of winning when you are all-in is nice, but it is only one factor to consider, and the difference between 50% equity and 43% equity is pretty small. Using the criterion of having a 50% or better chance against a certain hand or range of hands is wrong. It misleads people into thinking AK is worse than it really is because AK often falls just below this threshhold.

2. If you hold AK, this reduces the likelihood an opponent could hold AA or KK, which are really the only two hands you need to worry about. Players do understand this, but I think the effect is underrated. There are only half as many ways to make AA or KK when only three of each are left in the deck. If you hold AK and your opponent's range is AA-JJ, there is only a 1/3 chance he holds AA or KK, and your equity is about 35% (38% with AK suited). Note that when your opponent's range is this small, your fold equity is likely quite large.

3. Many players tend to view a big preflop raise by a good player as AA. They will often fold JJ or QQ, and some will even fold KK in certain situations. Although this means you are usually way behind when you are called, your fold equity is enormous.

Good players tend to play very tight ranges when there is a lot of action preflop and not much money left to play with after the flop. Players often fall into the habit of playing only AA or KK in these situations, sometimes QQ. AK is the perfect hand with which to balance your big-pot play before the flop. In some situations where your opponent's range is especially strong, it can certainly be correct to fold AK before the flop, but I think this is done way too often. Players are missing out on lots of situations where moving all-in with AK (and especially AK suited) is a +EV play.

Standard Work Week

Starting this coming week, I'll be working Monday-Friday for the first time since I started playing poker professionally. This isn't much of a shift; I was already working 11AM-7pm Tuesday-Friday and noon-8pm on Saturday. It used to be the case that poker games were juicier on the weekends, but for some reason, things have been slower recently on Saturdays than the rest of the week. Today, the $500+ NL game never even got started. This is not uncommon, which is the reason my supervisor decided to change my schedule.

I noticed last week that a local bar has poker every Saturday. I might check it out, but I doubt it will be worth my time. They have some sort of point system and at the end of the year someone gets a prize. I was also invited to a house game supposedly run by Koreans in downtown LA. I'm told it runs 8pm-4am on Tuesdays and Thursdays and that there are incredible amounts of money to be won. I don't think I'll go. Even if it felt safe to me, I have to work both those days, and I would find it difficult to play for 8 hours at the Bike and then head off to another game.

I've been seeing and meeting some actors and other entertainment industry types recently at the Bike. One of the producers of Zombieland plays the $500NL sometimes. Teri Hatcher came and played the $300-$500 NL game at least twice this month. Michael Muhney, who was in Veronica Mars and now stars in The Young and the Restless played $500NL with us for a few hours yesterday. There was a guy who claimed to have been a drummer for Parliament Funkadelic, but I forgot his name. He bragged of a patent he has for some denim jeans design. Bo Koster of the band My Morning Jacket plays quite often. He's a good guy and a good player. I've chatted with him quite a bit, but I haven't seen him at the Bike for the past couple weeks.

Analyzing NLHE:TAP Concept 21

Here's my analysis of the next concept from No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 21: Sometimes you can try for a deep check-raise with the nuts (or close to it).

By "deep" the authors mean that you are in middle-late position in a large field. I have seen it recommended that you not try a check-raise in such a situation, because some of the reasons for a check-raise are diminished in a large field, while the risk of being outdrawn is greatly increased. Still, I think Sklansky and Miller are right about this, and I would actually say you often should try for a deep check-raise with the nuts. It's very difficult to do a proper EV analysis of this situation, but here's my subjective opinion, for what it's worth.

In a small field, check-raising with a strong hand is standard (although there are situations where you would want to bet out even with the nuts). One reason for this is that a late position player is more likely to bet behind you if he is facing a small field. It's very common for the player in last position to bet if the first player or two check, because he will often be able to take the pot with a bet in this situation. A second reason is that the downside risk of checking is not as great when there is a small field; even if nobody bets on the flop, it's very unlikely that anyone will outdraw you, because you only have one or two opponents. A third reason to check-raise with strong hands when there is a small field is that it disguises your checks when you miss a flop. If your opponent knows you might check-raise, he'll be slightly more likely to check the flop and let you see the turn for free.

These reasons for check-raising do not hold up as well when you are in middle-late position in a large field. You need a stronger hand to check-raise in this situation. Still, with hands that are nearly the nuts, I think it's often correct to try it. A flopped set or straight is only a little vulnerable to being outdrawn, and the reward for a successful check-raise can be quite huge if there are multiple callers. If nobody bets, often another player will make two pair or three of a kind on the turn, which is likely to result in a very big win.

Analyzing NLHE:TAP Concept 20

After this post, I'll be one third of the way through the concepts at the end of No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 20: Sometimes you should limp behind limpers with pocket aces.

I agree with this. It does sound a little like it's recommending that you "randomize" your play, which I've argued against previously. However, this one is a little different for two reasons.

First, Sklansky and Miller are not actually recommending that you apply this advice in a random manner. Instead, they say, "you'd do this if you have opponents yet to act who like to raise a series of limpers with weak hands." I agree, but I think there are also other situations where you may want to limp behind limpers with AA. Basically, any situation where you think it likely that someone behind you will raise is a good time to limp with AA. In fact, sometimes you should be limping with weaker hands, as well. This week I was sitting to the right of a maniac, and I literally stopped raising preflop with any hands because it was so likely that the maniac would reopen the betting for me if I just limped. This was a great situation because I got the best relative position before the flop, meaning I got to see how everyone else reacted to the maniac's raises before I had to decide how to proceed. This is an extreme situation, but even if the player to your left is only somewhat maniacal, limp-raising with JJ+ (or even weaker) may be correct.

Second, although randomizing your play is not usually a good idea, it can be theoretically correct to randomize your play in certain situations with the best possible hand. Before the flop, AA is the best possible hand, and it can be useful to include it in your limp-raising range. Even if you are never in a game with a maniac or with players that like to try to steal before the flop after several limpers, it still might be a good idea to limp randomly sometimes with AA behind other limpers. This play is probably only worthwhile if your opponents do not expect you would try such a thing. If they already do expect you'd try this play, it's probably not worth actually doing; its value is in its deceptiveness.

Analyzing NLHE:TAP Concept 19

Here is another in my series analyzing the concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 19: Don't call in protected pots without a very good hand.

By "protected pot," Sklansky and Miller mean a pot where bluffing will obviously not work. The most common example is when one player is all-in. Then, there is no point in bluffing because the all-in player will probably win the pot even if you get the other player to fold.

I think this should be good advice in theory, but in practice, it is astonishing how often players will bluff into protected pots. I generally follow S+M's advice and fold my moderate hands in such situations, but, in so doing, I've been bluffed out of many pots. In fact, I've recently decided to relax my calling standards slightly except against thoughtful opponents.

Sklansky and Miller extend this advice to pots that are "protected" by a loose player in the field or by a player who is nearly all-in. Unless you know your opponent is an alert and logical player, I would not suggest taking this advice very seriously. Players still sometimes bluff in these situations. Many will fail to notice that these factors are in play, and many who do notice it will still fail to realize that this means the pot is protected and that they should not try bluffing. This is my personal experience, so take it with a grain of salt.

Surprisingly, the seemingly obvious idea that you should not bluff when a player is all-in (and there is no side-pot) is not supported by game theory. Bill Chen and Jerrod Ankenman show in Chapter 29 of The Mathematics of Poker that it actually can be theoretically advantageous to bluff into protected pots. This is basically because it forces your opponent to play much more loosely. In "theory," all players always know the strategy of their opponents. In practice, of course, this is not the case, and your opponent probably will not expect you to bluff into a protected pot. So, bluffing in these situations is probably never a good idea after all. Actually, if you can get your opponent to suspect that you might bluff into a protected pot, you can forgo ever actually making such bluffs and still gain the benefit of making your opponent play too loosely. I'm not sure how you convince your opponents of this. Maybe pretend to be very drunk?

Analyzing NLHE:TAP Concept 18

Continuing my project of analyzing each of the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 18: Don't get trapped with a fourth street top pair in multiway checked pots.

Wow, Sklansky and Miller are really going out on a limb with this one! "Don't get trapped" is pretty hard to argue with. The question is whether this advice is likely to help anyone.

Actually, I think this is marginally good advice, but it's too specific. There are plenty of circumstances where you can get trapped by underestimating the chance that someone in a large field of opponents is lurking with a big hand. For example, top pair is also a treacherous hand to call with in multiways pots on the flop. Still, this doesn't invalidate the more specific point made in this concept.

It's true that you need a much stronger hand to call a bet when there are several players behind you than when you are heads-up, especially if there are various draws on the board. A top pair hand with a decent kicker is much weaker than it looks if you're used to having only one or two opponents on a flop, and thus it's pretty common for players to get trapped with such hands. In their discussion, Sklansky and Miller say "there's a decent chance you have the best hand, yet this isn't reason enough to call." This is a good point. This idea seems paradoxical at first, and it would make for a more interesting Concept topic, in my opinion.

Analyzing NLHE:TAP Concept 17

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 17: If your preflop raise is called behind you, check a lot of flops.

The standard play is to continuation-bet in these situations, in order to maintain the initiative and keep the pressure on your opponent(s). I think this standard c-bet is probably overused, so in this sense Sklansky and Miller's advice to check a lot of flops is good. Still, I disagree with the reasoning they offer in their discussion of this concept. They focus too much on your hand and on randomizing your play, and not enough on the texture of the flop. I think better advice would be, "... often check on certain types of flops." This is mostly based on my intuition, and I won't be presenting any quantitative evidence.

I often do like to continuation bet even if I miss a flop because many players like to call preflop raises with small pocket pairs or suited connectors, hoping to catch a set, two pair, or a big draw and win a big pot against the preflop raiser. Usually, these hands will miss the flop, and they will fold to a continuation bet. For example, if I have AT and the flop comes Q43, I have a decent chance to win with a continuation bet even though my opponents often have a small pair or a healthy six outs. On this flop it's also a good idea to bet with many of your other likely preflop raising hands for similar reasons. With a good hand like KK, you can bet for value to balance all your weaker hands. However, there are certain types of flops where the continuation bet seems counter-productive. Generally, the flops where you don't want to bet are ones where there's a good chance you have the best hand and not too much risk of being outdrawn. For example, I think KK on a board of A92 rainbow is often better off just checking. On this flop, you're probably okay checking lots of your other likely hands, too. This includes strong hands such as AT. By waiting until the turn to bet with these hands, you are probably more likely to get called by a small pocket pair.

There are also more extreme examples of flops that don't have many draws, such as AA6 rainbow, or, to a lesser extent, 66T. On paired flop such as these I will often make a small bet. If my opponent has something, they'll call or raise, and I can react according to the strength of my hand. Often, my opponents will have completely missed these flops and just fold.

This seems like it could make for a bigger project if I want to come back to it later and do more quantitative analysis. For example, I'd like to test whether it's better to just alter my bet-sizes based on the texture of a flop rather than changing my betting frequency.

Analyzing NLHE:TAP Concept 16

Okay, let's keep the ball rolling. Here's the next installment in my analysis of the concepts at the end of No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 16: Occasionally overbet with moderate hands to disguise your overbets with excellent hands.

No; this seems like terrible advice. By "occasionally," I think Sklansky and Miller mean something like "randomly," and I've already discussed in my Concept 3 analysis why I think this idea is vastly overrated. In their discussion, S+M say "as long as you don't do it too often, these overbets won't cost you too much, and they will support you those times you make big bets with excellent hands." I think this is wrong. If a play costs you anything in the long run, it should be considered "too much," because you can just fold and lose nothing more. If you determine that a certain play is +EV, you should do it every time, not just occasionally. If it's -EV, never do it (except maybe in some extremely rare instances if you really know what you're doing). Something I forgot to mention about randomizing your play in my Concept 3 analysis is that if you ever make mistakes when you play poker (ie, make a play that is -EV), you are already randomizing your play. Don't make matters worse by adding extra mistakes to your game! Of course, I assume everyone makes mistakes, so this advice should apply to everyone; to some extent, human error automatically disguises your hands.

There's another, more obvious, explanation for why this concept's advice is bad. If you want to "disguise your overbets with excellent hands," the best way to do this is by overbetting with draws as semibluffs. The example in the book suggests occasionally overbetting with KQ on a board of Ks9s7c. This is going to force your opponent to fold most of the hands you can beat. When you are behind, you will be called or raised and have only about three outs. I would suggest simply value-betting KQ while overbetting with hands like T8 or flush draws as well as with your monster hands. Semibluffs are great because your opponents are likely to fold better hands than yours, but you have lots of outs if you get called. Neither of these advantages exist when you overbet with mediocre hand like KQ on this flop. Moreover, semibluffs actually do a better job of "supporting" your overbets with excellent hands, because if your opponent has KJ or KT, he might think about calling if he suspects you are on a draw. If he thinks you have at worst KQ, he will fold right away.