In Texas Holdem, it is important to have good starting hand selection. This is important as it prevents you from entering pots with sub-standard hands, which could eventually lead to you losing a lot of money in the process.

"Starting hand selection" is simply choosing the good hands over the bad, and thus folding the bad hands when you get them.

It is true that any hand can win in Texas Holdem (or poker in general for that matter), but the fact of the matter is that some hands will win more than others. So if we stick with the good hands, then we should see better results in the long run.

Basic starting hand selection.

Top tier starting hands - top 2% of starting hands.

Good Texas Holdem starting hands are typically hands like big pocket pairs and big connecting cards. So some of the top starting hands would be:

• AA
• KK
• QQ
• AKs

The little ’s’ indicates that the cards are suited, which will increase the value of the cards because it makes it more likely that they will be able to make a flush compared to if the cards were not suited.

This is obviously the top tier when it comes to starting hands, and if we were to only ever be dealt these starting hands we would be making a lot of money. In fact, if we folded every other hand that we were dealt and only played these hands, there is a fair chance that we would be winning money in the long run. But this would only work at the lower limits where other players probably wouldn’t be aware that we only play premium hands.

Second tier starting hands.

If we only ever played with this elite group of cards, we would be folding numerous hands along the way and missing out on other opportunities to win money. Even though these are the cream of the crop when it comes to starting hands, there are still other great hands out there that can win us a lot of money in the long run if we play them.

Such hands are:

• AK
• AQs
• AJs
• KQs
• JJ
• TT

This gives us another 6 starting hands that we can play with, increasing the number of pots that we will be entering. Although these are not as good as the first set of premium hands mentioned, they are still great starting hands that should help us to win money.

Top 10 Texas Hold’em starting hands.

Now if we stick with this set of 10 starting hands we should definitely by on the right track to winning some money from poker. So for any player new to the game you should try your best to stick to the following top 10 hands (also throwing in some of top 20 hands if you have good position):

1. A A
2. K K
3. Q Q
4. A K (suited)
5. A Q (suited)
6. J J
7. K Q (suited)
8. A J (suited)
9. A K
10. T T

As your game improves, you can look to open up your starting hand requirements and require more marginal hands like suited connectors. However, if you’re new to the game you are better off sticking with the big cards that hit bigger flops and make post-flop play a hell of a lot easier for you.

Starting hand selection and table position.

Your table position should always play a big role in determining the range of hands that you choose to play with.

You should stick to playing much stronger hands from early position than you would from late position.

This means that if you are in one of the early position seats, you should stick to playing the top two tiers of hands and avoid lesser hands like; AQo, AJs, AT, KQs and so on. Conversely, if you are in late position and there has been little action before you, you can afford to play these sort of hands far more comfortably.

Why is table position important in starting hand selection?

If you are one of the first to act in a hand, you are going to be at a serious disadvantage to the rest of the players who are acting after you. Therefore, to avoid making things worse, you do not want to be entering a pot with anything less than a premium hand.

Acting first means that you are going to have little information on your opponents. If you are playing with a mediocre hand, it is likely that you are going to be in a spot where you have no idea whether you have the best hand or not. These situations are the ones that lose you the most money in poker, so avoid falling into them by playing stronger hands from early position that will make it easier to determine whether or not you have the best hand.

The importance of starting hand selection.

Starting hand selection is key because it helps to save us from sticky situations post flop, especially if we are new to the game.

Starting hand selection example.

Say for example we are not exercising very good starting hand selection and we decide to call a raise with K T. The flop then comes K 8 2 giving us top pair, which looks like a very strong hand. Our opponent bets into us and we decide to call, because after all we do have top pair.

The turn comes a 4, and our opponent bets once again. We have top pair and we call seeing as we are still happy with the strength of our hand.

The river comes a 7, and our opponent bets into us one final time. We make the call with our top pair thinking we might still have the best hand, but our opponent turns over K Q.

He also has a pair of Kings but he has the higher kicker, so he takes down the pot.

Starting hand selection example evaluation.

This is an all too common problem for poker beginners, and it could have been so easily avoided by being a little stricter with our starting hand selection. Having top pair is great, but all so often an opponent can easily beat it with a better kicker. This is why it is important to have two big cards instead of one, because the size of our kicker can play a vital role in determining who the winner of the pot will be.

You are dealt two cards in Texas Hold’em; make sure that they are both good cards before you enter a pot. An ace with a low kicker is going to lose you more money than it wins.

Don’t be tempted to call raises or enter pots with hands like A4 (rag aces) or K7, because they will just get you into more trouble than they are worth. Make sure that you are the one with the better kicker every time and take the money from the players who are entering the pots with weaker hands than you.

It is actually reasonable to bring down our starting hand requirements if we have good position. Position will give us an advantage over our opponents if we are last to act, so we do not necessarily have to have such a strong hand to play with because will be obtaining information from the way our opponent plays because they will be acting first.

This information and knowledge of our opponent’s hand from the way they play will compensate for the fact that our starting hand is a little weaker than normal. However, we still have to be prepared to fold as having position does not guarantee that we will win the hand, it simply gives an advantage. It is advised that you only enter pots with weaker hands in position once you have become a little more experienced.

Conclusion.

As you continue to play poker and gain experience from the game, it is a good idea to start expanding your starting hand requirements and experimenting here and there. However, if you are new to the game it is strongly advised that you stick to the big cards so that you give yourself the best opportunity to win money from poker.

If you are entering pots with a poor hand, you should be expecting to see poor results.

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On the Value of Suited Connectors

First off, some cold hard truths about suited connectors: They rarely flop a made hand. Since they are usually fairly low in rank, flopping a pair usually gives you 2nd or 3rd pair at best - not something you want to bet a lot of chips on. I wouldn't consider flopping a pair worth much consideration at all, in fact. Thus with these hands we are often looking to flop two pair or better (trips, a made straight, a made flush, a full house, etc). I won't do the math here, but this will happen approximately 5% of the time.

This is why these hands play well in cheap multiway pots. To break even on playing these hands, when we flop our rare hand we need to make 20 times the amount we had to invest. If we limped behind 2 other people, the SB is encouraged to call and the BB will often check. This leaves us with 1BB invested into a 5BB pot. We need that pot to include 20BBs from other people on the times that we hit. With 4 others in the hand, there is a good chance that someone else will hit something as well, making this easier to accomplish. To make the 20BB profit we require can often be achieved via a pot-sized bet (PSB) followed by a 2/3 pot bet (~5BB profit in intial pot + 5BB profit when PSB is called + 10BB when 2/3 PB is called = 20BB). Whatever extra we can make (from bigger bets or profits on the river) is where the actual profit comes from. Another option is to bet 2/3 pot on all three streets (5BB + 3BB + 6BB + 10BB = 24BB). The best choice is probably whichever will get you paid most often. That said, if it will be called, a bigger bet is clearly best.

We've seen then that to make these hands profitable in an "ideal" situation (cheap multiway pot), we must be against opponents who will call bets on multiple streets when we hit. This is fairly unlikely when we hit our flush, and only moderately likely on the other boards we can hit - the only ways 76s gets enough action from someone on a 76x board is 1)x is a high card which an opponent paired (which is fairly likely when a high card hits) 2)x gives their low pair a set (which we don't want, because we're behind when it happens) and 3)we're against an opponent who drastically over-values a straight draw (in which case 25% of the time we still lose!). Things are starting to look pretty grim for suited connectors...

What we didn't consider previously, is that often our opponents will bet/raise some of our power flops, because they look safe and/or draw heavy. AJo definitely wants to bet enough to deny odds for a straight draw on a J67 board. 99 feels similarly on a 762 board. If just one of these raises comes in, we're well on our way to value-town. So things with limping big pots aren't as grim as they appear.

Another argument toward the strength of suited connectors is their value as drawing hands. For instance, when we flop a combo-draw giving us flush and straight outs, or when we flop a pair plus either of our draws, we get enough outs to be only a slight dog against most hands our opponent can call us with (and in many such cases, we are even a favorite on the flop). First, these situations are relatively rare. You'll flop such a combo-draw an additional 5% of the time. Even when you flop them, they aren't as great as they appear. Either our opponent has a hand to go to the felt with us (in which case we're even money, so the situation is around 0 EV) or he doesn't, and we win a small pot that doesn't even make up for the amount we had to invest to play the hand. And situations in which we are flat-called on the flop leave us in a bad spot on the turn when we miss - rather than being 50% to win, we're now down to 25%. Now we definitely want a fold from our opponent, but they are relatively unlikely to grant it; after all, they did call the flop...

What about normal draws, such as a flush draw or an open-ended straight draw? Surely these will occur more often? Of course they will. A bit over 20% of the time you will flop one of these above draws. That's nothing worth getting excited about, however, as again you will either win a small pot, or get into a big pot as a dog (though here you are almost certainly a significant dog when called). With the additions brought by fold equity, we can probably consider this a wash as we did the combo-draw situations. Though at many tables that is a bit of a stretch.

So overall, the expected value of limping suited connectors is dependent on having weak players who will call multiple streets when you hit your hand. That makes limping them in many low stakes games ideal. As you move up in stakes, however, it becomes more and more rare to find enough opponents who will make these calls on multiple streets. Does that mean that at high stakes, suited connectors are worthless? Why do we always see Daniel Negreanu and Brian Townsend playing these hands? Because they are usually playing them differently!

A lot of what we said previously goes out the window if you are raising with suited connectors instead of calling. This is because it is much less likely for a caller to put you on the hand you have. Thus you will get paid off more often on boards that you hit - sometimes from players just making bad bluffs at you. Further, because you raised, you can reasonably represent a much bigger hand. You can frequently get credit for having and Ace or King on an Axx/Kxx board, increasing your equity through significantly increased fold equity. Finally, by raising these hands, you provide cover for the legitimate hands you raise. If you only play big hands, good players can easily stay out of your way. By mixing in other hands, they are forced to either let you win extra pots or to play back at you more often, paying off your bigger hands. So in the end, by raising, you get paid off more when you hit these hands, force good players to pay you off more when you have a big hand, and you pick up more of the pots that you shouldn't have won by representing a stronger hand than you have. Sounds great huh? It doesn't work as well at lower stakes where you're more likely to be looked up by someone who doesn't know to fold his A5 against aggression on an AT4 flop.

The ultimate step in misrepresentation then is to three-bet (reraise preflop occasionally with these hands. Again, this will force your opponent to either give up on more hands or to pay you off with more hands. Further, this is one method of reducing the equity a small pair has to play for set odds against hands you raise and reraise, as you are clearly not paying off a set with a suited connector. Again, this is questionable practice at lower stakes, because players are more likely to call with weaker hands while thinking their hand is good.

Now we understand reasons to limp, raise, and even reraise with suited connectors. There's also a murky idea about why to fold (remember, if you're not going to get called on multiple streets, the limp is often not worth it!). Let's expand a bit on the reasons and situations in which we fold:

1) Against loose opponents when you are the first in the pot: Limping is not an option. You will find it very difficult to make the necessary 20xBB from a limped pot that does not benefit from having several extra limps in to build it. Your flop bet will only serve to make it as large as it would have been to start if more players were in; It's as if you were missing an entire street of betting! Further, with only you in the pot, it becomes very easy for someone left to act to raise, putting you in a tough spot and usually resulting in at best a loss of the blind you paid, sometimes much more.

2) When folded to us in the small blind: Again limping is not an option. We won't make enough of a hand to continue very often, and we'll be playing out of position to boot. Raising is not much better, as people expect loose raises in blind versus blind confrontations, so we are not likely to get the level of respect required to make this play +EV. If, however, we have a very tight image, a raise could be a good play.

3) When raised against our blinds: In a raised pot that is not multiway, it is going to be significantly harder to make the required amount for profit (if we have to call 2.5BB, we have to win 50BB - half our opponents stack! - in order to break even on the call). Further, you are not likely to get the respect we want here because we called rather than raised preflop and because if we reraise, we fall back to the loose blind expectation. And once again, we would be playing out of position here, which is bad for suited connectors (as they benefit significantly from pot control capabilities - see upcoming article on positional play).

4) When out of position in general - again, suited connectors benefit drastically from being played in position. This will be covered more in the upcoming article, but positional factors (such as pot control, seeing your opponent's decision, closing the action, and taking a free card) apply very strongly when playing suited connectors.

 

Capped Ranges

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In the May issue of this magazine, I introduced a simplified system of hand-reading that works quite well against the majority of no-limit hold ‘em players. The idea is not to put an opponent on a specific hand but rather to put him on one or two of three possible broad categories of hands: monsters with which he wants to play a big pot, moderate-strength hands that figure to be best but that he will generally try to showdown cheaply, and draws or other weak hands that will rarely win without bluffing.
This month, I want to demonstrate one way of using this information to guide your play. On the turn or river, it is often possible to determine, based on how he has played on earlier streets, that your opponent will rarely or never have a monster hand. This is sometimes called a “capped range”, meaning that there is an upper limit to how strong your opponent’s hand can be. If you are able to determine this limit, you can both value bet all of your better hands strongly and represent better hands when you need to bluff, putting your opponent in a very difficult spot.
Often, there are two ways for a bluff to go wrong. Either your opponent happens to have a very strong hand, maybe even the one you are trying to represent, and can easily call you, or he guesses that you are bluffing and calls you down with a weak hand (or re-bluffs you, for that matter). When you are able to cap his range, though, you can all but eliminate the first possibility and put your opponent in the uncomfortable position of never having cards stronger than those you are representing. The best he can hope to do is guess at your bluffing frequency and call you down accordingly.


A Simple Example
We’ll start with an example, probably oversimplified, to illustrate the point. Suppose that you are playing in a €5/€10 9-handed NLHE game. The player first to act opens with a €40 raise. He is extremely tight and predictable, and you know that he would only raise from first position with a big pair, probably tens or better, or a big Ace. Because you have such a precise read, and because the effective stacks are €2000, you call on the button with a suited JT. The rest of the table folds.
The flop comes 982, all different suits, giving you an open-ended straight draw. Your opponent bets €70, and you call. The turn is an off-suit 6, and your opponent bets €150. At this point, just based on his very tight pre-flop raising standards, you are able to identify a clear upper limit on your opponent’s range. He cannot have a hand stronger than one pair, albeit a good pair. You, on the other hand, could have a set, two pair, or even a straight. You raise to €500, and your opponent calls.
The river is a 4. Your opponent checks, and you move all in for a little more than the size of the pot. He scowls at you, fiddles with his chips, mutters something about garbage hands and bad beats, and folds.


A Trickier Example
In a 6-handed €5/€10 NLHE game, the player one off the button opens with a €35 raise. The action folds to you in the big blind, and you call with T [spade] 9 [spade]. The effective stacks are €1000. The flop comes 7 [club] 5 [club] 4 [diamond], missing you entirely. You check, prepared to fold, but your opponent checks behind you.
What can you determine about his hand so far? Many players will open a wide range from late position, so you have very little information about his hand pre-flop. When he checks the flop, though, he is telling you a good deal.
This is not a flop that gets slowplayed very often. If your opponent flopped two pair or a set, he has a lot of incentive to bet. For one thing, there are scary cards that could come on the turn. From his perspective, they may improve you to the best hand, and even if they don’t, they may scare you away from paying off with a second-best hand.
Similarly, because of the coordinated nature of the board, there are a lot of ways you could have flopped a second-best hand. Anything from a worse two pair to a pair and a straight draw to overcards and a flush draw will be willing to put a fair bit of money into the pot on this flop. Thus, if your opponent flopped a strong hand, he would have a lot of incentive to bet it. When he checks, you can be fairly sure he does not have two pair or better.
What could he have? Anything from total air (which in most cases will still beat your hand) to something like Ace-high that has a little bit of showdown value to a strong pair that nevertheless fears a check-raise. Significantly, though, he will very rarely have anything stronger than one pair, possibly with a draw to go along with it.
The turn brings the A [spade]. You could bluff now, but even if you follow it up on the river, this will only put so much pressure on your opponent. It wins nothing more from his bluffs, and many players will call down with a pair after checking the flop. Note that your opponent’s pot control line on the flop has made it difficult for you to bluff him in a conventional way.
If you check, though, your opponent will very often bet. If he has nothing, this is a good card for him to represent. If he hit the Ace, he’ll probably bet for the same reasons that a strong hand would want to bet the flop. Even with a weaker pair, he may feel more confident in his hand, now that you have checked twice, and not want to give a free card. Unless he has A4, A5, or A7, though, it is very unlikely that he will have better than one pair.
You check, and your opponent bets €60 into the €75 pot. You can now make a large raise to represent a strong hand that missed a check-raise on the flop and decided to go for one on this turn.
You make a pot-sized raise to €255. This raise will often take the pot down right away, but suppose that this player makes a stubborn call. It is now more likely than ever that he does not have a strong hand. Given the coordinated nature of the board and the fact that you seem to like your cards, a strong hand would almost certainly put the rest of the money in on the turn.
Thus, you can follow up with a big bluff on most if not all rivers. Your opponent’s flop call probably either represents a skeptical pair that needs a little more convincing or a pair with a draw. Another big bet on blank rivers should show a nice profit.
Bluffing at 8′s, 3′s, and clubs will be a higher variance play but will probably still show a profit. Sometimes you will end up bluffing into a rivered monster, but you may also have better fold equity against pairs that fear you hit the draw yourself.
In this case, your opponent calls the turn raise, and the river brings the K [spade]. You bet €450 into the €585 pot, and he folds. Whereas leading out on the turn may have enabled you to steal a small pot, check-raising the turn and following up with a river bluff won you a much larger one. Essentially, you tricked your opponent into putting a lot of money into the pot when you knew he could not defend it.
Your potential fold equity here is so high that you might choose to make this play even when you have some showdown value, such as when you hold 43. Your pair could be best, but often it won’t be, and you may get outplayed on the river anyway. Turning a weak pair into a bluff like this will often prove more profitable than trying to catch bluffs with it.


Defending Against These Plays
If you are in a game with a player who reads hands this well and has the cojones to makes plays like this, you might do well to find another table. But if you do choose to stay, you should know how to protect yourself.
The first and best strategy is to practice avoidance. When playing with a very competent hand reader, you must go to great lengths to disguise your hands and change up your play. This will require some unconventional play, such as occasionally raising 98s in first position at a 9-handed table or checking back a set on a coordinated flop. These are risky plays, but they are safer than enabling a tricky player to eliminate strong hands from your range altogether.
You may also need to resort to game theory and refuse to fold the best hands in your range, even if they are not objectively all that strong. If you were the Villain in the second example, you might have to call down when you turn a pair of Aces. Sure, your opponent could have a stronger hand, but since you very rarely will, folding a pair of Aces is highly exploitable.


Thin Value Bets
What if your opponent reads this article or just figures out that he’s getting exploited and decides to start calling down with his strong one-pair hands? Believe it or not, you don’t need to stop bluffing him. The occasional tricky play or thin call down are just stop-gap measures that turn an insanely profitable bluff into a marginally profitable bluff. You won’t win nearly as often, but if you can stand the variance, you’ll still show a profit in the long run.
Realize also that capping your opponent’s range will enable you not only to bluff but also to make big, thin value bets. In the second example, if you know your opponent rarely or never has better than one pair, then you could take the same line with a weak two pair hand like 54 or even one strong pair such as AK. There are very few second-best hands that will pay you off, but there are also very few better hands in your opponent’s range. And if he does correctly adapt by occasionally calling down with one pair, he’ll be in for a surprise!


Conclusion
Poker is a battle for information. Any time that you have more information about your opponent’s hand than he has about yours, the potential for profit is there. It is simply a matter of figuring out how to make the most of it. Even many players who read hands well don’t always take full advantage of that information.
Learning to recognize when there is an upper limit on an opponent’s possible hand strength and how you can exploit it can present you with some very profitable opportunities. Hopefully it will also demonstrate the critical importance of mixing up your own play, at least when there are good hand readers at the table, so that no one is able to take advantage of you.







Introduction
I had a nightmare last night that I was playing high-stakes heads up no-limit hold ‘em with Phil Ivey himself. I knew he had picked up a tell on me that revealed the approximate strength of my hand as strong, marginal, or weak, but I didn’t know what it was or how to stop doing it.
The river had just completed a possible flush, and the final board read 5 [spade] 8 [diamond] T [spade] Q [heart] 2 [spade]. I was holding A [spade] T [heart] and checked. Phil gave me that look, like he’d just spotted my tell, and then announced, “All in.” The dealer counted the bet down: €14,000 even, into a pot of just €6000. Somehow, I managed to have the Great One covered. But could I call this bet?
Optimal Calling Frequency
OK, I don’t really dream about poker. At least not that vividly. But it’s a good example of a nightmare situation, facing a big bet on the river when your hand is clearly defined as good but not great. Unless you have some exploitable read on your opponent that he either bluffs too much or not enough, then your best defense in a situation like this is to use game theory to make your decision.
Let’s assume that this river overbet represents either a flush or a bluff. The real Ivey is probably good enough that his game can’t be pigeonholed so neatly, but this is my nightmare, and I make the rules. Is he going to bluff all of his air to make me fold one pair? Is he never going to bluff because he knows I know he knows I only have one pair and he expects me to expect him to bluff? He’s Ivey and I’m lowly old me, so I’m going to abandon any pretense of outthinking or outplaying him.
In a situation where I beat all of his bluffs and none of his value hands, I’m going to call with a frequency such that it doesn’t matter what he does. In fact, I could show him my hand, tell him what percentage of the time I’m going to call, and there would still be nothing he could do to take advantage of me. I need to find the calling frequency such that whether he bluffs 100%, 0%, or anywhere in between, it makes no difference to my bottom line.
To do this, I have to figure out what calling frequency will make Ivey indifferent to bluffing with this bet. He is risking €14,000 to win €6000, so his Expected Value (EV) for a bluff is equal to -14000 (x) + 6000 (1-x), where x is my calling frequency. We want to solve for x such that his EV will be 0, so
0 = -14000 (x) + 6000 (1-x)
0 = -14000x + 6000 – 6000x
0 = 6000 – 20000x
20000x = 6000
x = 6000/20000, or 30%.
One way to prevent Ivey from exploiting me with a bluff in this situation is to use a random number generator to call with an arbitrary 30% of my bluff-catching range. Dan Harrington recommends the second hand of a watch for this purpose. Any time I have a hand that can only beat a bluff, I check my watch. If the second hand is at 18 or lower, I call. Otherwise, I fold.
Again, even if Ivey knows that I am doing this, there is nothing he can do to exploit me. If he bluffs more, I catch him just often enough. If he bluffs less, then he misses out on just enough pots that he could have stolen from me.
Blockers
That’s one method, anyway. If I know that I need to call 30% of the time, then I can call with each of my bluff-catchers 30% of the time.
But not all bluff-catchers are created equal. In this example, there is a big difference between my hand, which is A [spade] T [heart], and the nearly identical A [heart] T [heart]. Can you see what it is?
When I have the A [spade], Ivey has fewer flush combinations that he could be value betting. The equation we looked at above is just the EV of Ivey’s bluffs. Since I never have a hand stronger than a flush, his value bets are always going to be profitable. My EV on the river is going to be equal to the amount I win by catching his bluffs minus the amount I lose by calling his value bets.
The A [spade] in my hand removes twelve combinations of flushes from my opponent’s range. When I call with A [spade] T [heart], I will run into a flush a lot less often than when I call with A [heart] T [heart]. Thus, even though both hands beat all bluffs and lose to all flushes, one of them will be shown a flush far less often and is thus a far superior candidate for bluff-catching.
I will have the A [spade] 25% of the time that I have AT. Since it is a better bluff-catcher than my other AT combinations, I want to call with it over the others whenever possible. Thus, I should call 100% of the time that I have A [spade] T and use a random number generator to call 5% of the time that I have any other AT combination, so that I am still catching bluffs 30% of the time but paying off value bets as infrequently as possible.
Hand Strength
This, then, is one of the characteristics of a good bluff-catcher: it has blockers to my opponent’s value betting range.
Another important characteristic is that a bluff-catching hand should be able to beat all of your opponent’s bluffs. That may seem obvious, but I’ve had a river bluff called by a hand that I beat on more than one occasion.
In this example, since we don’t expect Ivey to be value betting one-pair, it may seem like AT and 33 are functionally the same hand. The catch is that Ivey could be bluffing one-pair. What a disaster it would be to “correctly” snap off a bluff only to find that he was turning 66 into a bluff and just took you to Valuetown, completely by accident!
Stronger hands are also better if there’s any chance of beating a hand that your opponent is betting for value. As I said before, Ivey is an extremely good player, so he might try to confound all of this reasoning by betting a hand like KT for value. Even if I don’t think that’s likely, all other things being equal, I might as well call with AT rather than 33 just in case.
Practice Avoidance
The best tactic of all for dealing with a situation like this is to avoid it altogether. You never want to be in a spot where your hand is as clearly defined as mine is in this example. Hopefully you do not regularly compete against opponents with reads as rock-solid as those of Nightmare Phil Ivey, but you should still be careful about avoiding situations where your range contains nothing stronger than bluff-catchers.
We don’t know the action leading up to the river in this hand, but let’s say that I bet the turn with my top pair, top kicker, and then checked the scare card on the river. That’s a fine way to play it as long as I’m also capable of checking a strong hand like the nut flush in the same spot. Doing so won’t prevent Ivey from value betting or bluffing, but it will make both of these plays less profitable.
By the way, if I were capable of showing up with a value hand when Ivey shoves the river, I would need to adjust my bluff-catching frequency accordingly. For example, if 10% of my range were flushes and the rest were AT, then I would only need to call with AT 20% of the time, since my overall calling frequency still needs to be at 30% to prevent exploitation from bluffing. That means I’d never want to call with any non-spade AT, and even with the A [spade], I’d only need to call 89% of the time.
Where did that number come from? When flushes are 10% of my range, AT is the other 90%. One-fourth of those AT combinations include the A [spade], so overall A [spade] T is 22.5% of my range. But I only need another 20% worth of calls, so I don’t want to call every time I have the A [spade], and 20/22.5 is approximately 89%. To translate that into seconds on a wristwatch, multiply by 60 to get approximately 53.
Real-Time Decision Making
You’re probably wondering what good all of these calculations are going to do you at the table. Well, we practice this kind of mathematical precision away from the table so that our understanding and our instincts are better when tough spots arise in live games. Even if we aren’t able to be quite so precise in the real world, we can use our understanding to make good approximations.
If I really found myself in this situation, the first question I’d ask myself is how the hand I’m holding compares to all of the other hands I would have played in the same way. If I rarely or never check a hand stronger than AT on the river, then I know that I have to call sometimes with AT or a comparable bluff-catcher to avoid being exploited by bluffs.
The math behind my optimal bluff-catching frequency isn’t hard: it’s just the size of the pot divided by the sum of the pot plus the river bet, or Pot/ (Bet + Pot). Once I know that I need to call 30% of the time, I think about my range and try to decide what are the best 30% of hands that I could have in this situation for catching a bluff?
Remember our criteria for a good bluff-catcher: (1) able to beat all of the hands he could be bluffing with; (2) blocks some portion of the opponent’s value betting range; (3) possibly even ahead of a thin value bet. If all I can ever have in this spot is AT, then even without doing any math I can recognize that a hand with a spade is a much better bluff-catcher than the alternatives. Calling when I have a spade and folding when I don’t would be a very close approximation to the optimal solution, costing me only about €300 in EV for the 5% of the time that he gets away with stealing a €6000 pot.
Playing high-stakes heads up no-limit hold ‘em with Phil Ivey and losing no more than €300… now that’s a dream come true!

Poker - Slow playing

Slowplaying

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1. You must have a very strong hand.
2. The free card or cheap card you are allowing other players to get must have good possibilities of making them a second best hand.
3. That same free card must have little chance of making someone a better hand than yours or even giving that person a draw to a better hand than yours on the next round with sufficient odds to justify a call.
4. You must be sure you will drive other players out by showing aggression, but you have a good chance of winning a big pot if you don’t.
5. The pot must not yet be very large.

It is a testament to the quality of this book that, though Sklansky was writing primarily in the context of games with a fixed betting structure, his advice here is largely applicable to the big bet games like No-Limit Hold ‘em (NLHE) and Pot Limit Omaha (PLO) that are most popular these days. The only thing I’d add to Sklansky’s list to make it more applicable to big bet games is that you must weigh the advantages of slowplaying against what you would have won from second-best hands that would have paid you off on three streets but end up losing a smaller pot because of your slowplay. In a fixed limit game, this usually costs you just one small bet if you slowplay the flop.
In a big bet game, it costs you a lot more, because pot and bet sizes grows geometrically. In other words, a bigger pot on the flop means a bigger pot on the turn means a much bigger pot, and therefore a much bigger bet, on the river. Thus, slowplaying in big bet games carries a much larger cost than it does in fixed limit games. As we’ll see, it can still be correct, but the conditions must be even more ideal than those Sklansky allows in Theory of Poker.
Demonstration
Suppose that you flop the nuts and the pot is currently €100. When you value bet, you decide that you are going to bet about 80% of pot. First, though, you have a decision about whether to bet three streets or to check the flop and then bet the turn and river.
If your flop bet of €80 is called, there will be €260 in the pot on the turn. Eighty percent of €260 is about €210, which if called will mean a €670 pot on the river. Thus your river bet would be €536, and if your opponent called, you would win a total of €826 after flopping a monster.
If you instead check the flop, then you only win the first two bets of €80 and €210, for a total of €290. Slowplaying would have to triple your chances of getting those first two bets paid off to justify your failure to build the pot from the flop.
Example
You are playing €5/€10 NLHE with €1,000 stacks. You open to €45 UTG+1 with 77, a loose-passive player calls in the SB, and everyone else folds. The flop comes K 7 2.
If your opponent holds a pocket pair higher than your 7′s, he has a 4% chance of turning a hand better than yours. Otherwise, there is no way for the turn card to cost you the pot. Even if your opponent turns a draw, you can size your turn bet such that he will not have the correct odds to call you, which alleviates another of Sklansky’s concerns about slowplaying.
Despite the near-invulnerability of your hand, you should bet. There is an obvious second-best hand for your opponent to pay you off with: a pair of Kings. You want to start building the pot right away so that you can win a big one from a pair of Kings, even if this means you win a little bet less from a hand like QJ that might turn a pair if you slowplay.
To see why, suppose that this player will never bet himself but will also not fold a pair for bets of up to 80% of pot. As we saw above, fast-playing your set will win you €826 if your opponent paired the flop. Checking the flop and then betting the turn and river will win you €290 when your opponent has a pair on the turn.
Two unpaired hole cards will turn a pair about 12% of the time. Thus, if your opponent does not yet have a pair, there is a 12% chance that you will win €290 by checking the flop, which makes checking worth €34.80.
When your opponent has a pair, slowplaying the flop costs you €536. Thus, he needs to hold a pair on the flop just 16% of the time to make fast-playing superior to slowplaying.
Shallower Stacks
This assumes that stacks are deep enough for you to get three streets of value from your hand. Slowplaying is far safer if one or two bets will be enough to get all the money in anyway, as checking one street will not cost you a big bet on the river.
In this example, slowplaying would be correct if the effective stacks were €300-€400. In that case, you would not cost yourself much when your opponent flops a pair. Even if you do check the flop, you will get most of his stack, so you might as well give him a chance to turn a pair before you start building the pot.
Aggressive Opponents
There is more value in slowplaying against opponents who will make big bluffs and thin value bets. Suppose that in the above example, you were out of position and believed that your opponent would bet 80% of pot with top pair on all three streets if you kept checking and calling.
In that case, slowplaying would be correct. Not only would you give him a chance to turn a pair if he doesn’t already have one, but you could also potentially win even more money from his top pair by check-raising the river. Even if he doesn’t call, you haven’t lost anything relative to betting the flop.
Note that if you are in position, you would still need to bet the flop. This is because your aggressive opponent would not have the opportunity to bet his top pair even if he wanted to, as your check closes the action.
Crushing the Deck
Just because you flop a huge hand does not necessarily mean that you have all of the cards that connect well with the flop. In our example, your opponent could easily have top pair, a strong hand with which he will be willing to play a big pot, despite the fact that you have trips.
If you instead held KK on this same flop, however, checking would make a lot more sense. There is only one K left for your opponent to have, and if he has anything less, even a pair of 7′s, he isn’t likely to be too excited about it.
Importantly, there are no scary turn cards for you. Literally the only way in which the turn could give your opponent a better hand is if he has AA and turns an Ace, a rather unlikely prospect. Far more likely is that if an Ace turns, a hand like AJ that looked weak on the flop will suddenly be strong enough to pay off two bets.
Underbetting
A small bet of 1/4 to 1/2 of the pot is an underutilized alternative to checking when you want to slowplay a strong hand. Suppose that you are playing €5/€10 NLHE with €1,000 stacks. Your opponent opens to €30 UTG, you call UTG+1 with 77, the SB calls, and everyone else folds. The flop comes T 7 5, and both players check to you.
On the one hand, this is a dangerous flop to slowplay. There are quite a few turn cards that, even if they do not give your opponents a better hand, could at least kill your action and make it difficult for your opponents to put money into the pot with hands worse than yours. Plus, in the event that someone is playing for pot control with a hand like T9 or JJ, you’d like to start building the pot.
On the other hand, it seems unlikely that either player has anything particularly good. For the same reasons that you are reluctant to slowplay, your opponents should be, too. A big bet will very often result in two folds, which is a shame when you have such a strong hand.
A small bet of €33 offers enticing but incorrect odds for most draws to see one more card. A bare flush draw or open-ended straight draw has 8 outs, giving them a 16% chance to hit on the turn. They can probably count on some implied odds if they get there, but then again so can you. One of the reasons you’d like to keep a draw in the pot is that every once in a while, the draw will get there but you will improve to a full house and be in a position to stack your opponent.
A small bet may also be misinterpreted as weakness, enticing an opponent to raise you with a draw (or less). It also may entice an opponent to call or raise with overcards like AK that he was planning on folding to a larger bet. An underbet can therefore be a viable option when you believe your opponent to be weak but your hand is strong enough to start building a pot on the flop.
Moderately Strong Hands
Good but not great hands like top pair are often better candidates for slowplaying than are really huge hands like sets or straights. If you believe that your hand is not strong enough to value bet on three streets, then you do not cost yourself money by checking the flop or turn in the same way that you do with a stronger hand. To see why, let’s look at a slight variation on the example we’ve been considering:
You are playing €5/€10 NLHE with €1,000 stacks. The UTG player limps, you raise to €45 with KJo on the BTN, and everyone else folds. The flop comes K7 2.
You believe that UTG’s limp-calling range consists almost entirely of pocket pairs and suited connectors with which he is trying to see a cheap flop. He is really aiming to make two-pair or better, so while he’ll try to pick off bluffs when he has just one pair, he’s only going to play a big pot with a hand that beats yours.
You should plan to check either the flop or the turn. There is no way for your opponent to have a draw on the flop, so he can have at best five outs if he holds a suited connector like 76 or 87. With a pocket pair he has just two outs, and with an unpaired suited connector he cannot outdraw you on the turn at all.
Your opponent is not likely to turn a strong second-best hand, but he could easily turn a pair or draw that will be good enough for one or maybe two bets. Given that you weren’t going to try to get three streets of value out of your top pair anyway, you have little to lose by checking an early street.
Against straight-forward opponents who are mostly playing their own hand, I would check the flop and then either call bets on the turn and on most rivers or bet the turn and river if my opponent checked.
More sophisticated opponents might expect a continuation bet on the flop and therefore be suspicious of your check. They would correctly read your check to mean that you have a hand that does not need to bluff, and consequently they would not make a big mistake on future streets. Against such players, it is better to give them the bet that they expect on the flop and then plan on checking most turns and going for more value on the river.
Balance
So far, we have considered the merits of slowplaying “in a vacuum”, i.e. without consideration for how you would play others hands in your range. There exist circumstances you might choose to slowplay a very strong hand in order to give your checks or calls more credibility and make you less susceptible bluffs when you play weaker hands in the same way.
For instance, if KK is the only strong hand that you ever check on a K72 flop, then other players can exploit you by bluffing the turn and river. Even if they occasionally run into top set, you’ll fold far more often.
The lesson here is that you need to check hands good enough to call bets on the turn and river, but those don’t necessarily need to be the strongest hands in your range. The moderately strong hands discussed above are generally better candidates for a “balance check” than a set of 7′s. This is again because the price that you pay for putting AK in your flop checking range is much lower than the price that you pay for putting 77 in your flop checking range.
Conclusion
When your hand is strong enough to bet three times for value, you take a big risk by slowplaying in a big bet game. Such a play can still be justified, but it requires more specific circumstances than in fixed limit games.

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Article original written by David Sklansky. Read more articles at http://www.thinkingpoker.net.