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.
Sunday, November 29, 2009
Wednesday, November 25, 2009
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.
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.
Sunday, November 22, 2009
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.
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!
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!
Saturday, November 21, 2009
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.
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.
Wednesday, November 18, 2009
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.
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.
Sunday, November 15, 2009
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.
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.
Saturday, November 14, 2009
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).
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).
Monday, November 09, 2009
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."
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."
Sunday, November 08, 2009
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.
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.
Saturday, November 07, 2009
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.
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.
Friday, November 06, 2009
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.
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.
Thursday, November 05, 2009
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.
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.
Wednesday, November 04, 2009
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.
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.
Monday, November 02, 2009
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.
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.
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