Important Concepts in Limit Holdem Part I

By Anthony Bee (a.k.a. ‘Tony’ on the Low Limit Poker Forum).

At it’s heart, limit Hold’em is a technical game.  The fixed betting structure means that it isn’t possible to make huge bluff bets to scare your opponents out of the pot.  You will often have to play all three streets, and play them well.  This means being able to recognize profitable situations and exploit them to the full.  It also means avoiding unprofitable situations and therefore costly mistakes.

There’s no big secret to becoming a winner.  Winning players recognize profitable opportunities and avoid costly mistakes.  They make more money on their winning hands than their opponents, and they lose less money on their losing hands.  And they do this consistently.

But how exactly does one recognize a profitable opportunity?  More importantly perhaps, how does one avoid making costly mistakes?

Luckily, there are a number of fundamental concepts which can guide us in making these decisions.  Some of these concepts are closely related, and I’ve tried to highlight where this is the case.  WARNING: What follows will involve a small amount of arithmetic.  Deep breaths… Let’s start then, with:

Domination

You’ll often see it said that Hold’em is a game of domination.  What is meant by this?

A hand is said to be dominated by another when the dominated hand can make a pair, but still be losing to the dominating hand.  When this is the case it is difficult for the dominated hand to overtake the stronger one.  For this reason it’s VERY important to avoid situations where you are isolated with a dominated hand.

For example, let’s consider the hand

Hole Cards

One hand that dominates KT is

Hole Cards

This is because if a king flops, then KT will be losing and can only win by catching one of the remaining three tens (or an unlikely straight or flush).  In other words, KT will almost always lose to AK.  If these hands were played out to the river heads-up the chances are approximately 74%-26% in favour of AK.  NOT good.

When you are dominated you may well think you are ahead, and feel obliged to ‘pay off’ your opponent to the river.  In other words these kind of situations can prove expensive.  Also, the possibility of domination often means it’s difficult to know ‘where you stand’ if you do happen to flop a pair.  This means you’re unlikely to make much money even if you do happen upon a favourable flop, particularly when playing out of position.  The fear of being ‘outkicked’ for example, can put a break on your ambitions and will limit the amount you can win.

Even when you hit what looks like a ‘dream’ flop, things can go very wrong.  For example, you limp with KT offsuit in early position.  A middle player raises and it’s heads-up on the flop.  The flop comes KKT.  Wow, you’ve flopped a full-house!  But if the turn brings a J or a Q you’ll be in deep trouble if your opponent holds KJ or KQ.

Many players will play a hand like KT offsuit every time they receive it, regardless of their position at the table or the number of bets required to play.  Let’s look in more detail at why this is such a big mistake.

KT is in fact dominated by nine hands in total.  They are:

AK, AT, KQ, KJ, AA, KK, QQ, JJ and TT.

This means that if you hold KT, there are 72 hands that dominate yours.  (I’ll let you check this yourself).  Since there are 1326 possible two-card combinations, the probability of any single player being dealt one of these hands is:

, roughly 5%.

Now, let’s suppose you limp UTG in a ten-handed game with KT offsuit.  What is the probability that someone behind holds a hand that dominates yours? 

The easiest way of finding this is to calculate the probability that no one yet to act holds a hand that dominates yours, and then subtract this probability from 1:

So with nine players yet to act there is around a 40% chance that your hand will be dominated!  Clearly, in a typical game limping here is a bad idea.  A likely scenario is that you will limp, someone with a hand that dominates yours will raise, and you will have to play a dominated hand out of position against just one or two other players.

Don’t fall into the trap of thinking that 40% doesn’t sound too bad.  Doesn’t that mean that you WON’T be dominated most of the time?  Well, yes it does.  BUT the point is, that being dominated is so expensive in the long run that even a 30% or 40% chance of this happening is enough to render a hand unprofitable out of position.  This is particularly true if the hand has little else going for it which will make it easier to play after the flop.  A hand like KT offsuit has only moderate high-card strength and makes relatively few straights.  So if it is dominated it has limited possibilities to improve and is often difficult to play after the flop.

Does this mean that you should never play a hand like KT offsuit?  No, of course not, but the conditions have to be just right.

For instance, if it’s folded to you on the button the probability of being dominated drops to only 11%, and raising becomes an option.  In this case against only two opponents you may win the blinds without seeing a flop, and even if you do you’ll be in position for the rest of the hand.  This illustrates that hand strength is not fixed in Hold’em, and emphasises the importance of position.  The threat of domination means you are FORCED to play more tightly (at least the vast majority of the time) in earlier positions than in later positions.  This is also the reason that most hands should be folded to a raise.

But what if the hand is suited?  Is it OK to limp UTG with KT suited, for example?  Well, it depends.  It can be profitable to limp with a suited hand that may be dominated, but the conditions have to be favourable.  To see why, we need to understand another important concept.  That is, POT EQUITY.

Pot Equity

Your pot equity is simply the percentage of the time your hand will win in a showdown.  For example, if the pot contains $20 and you have a 50% chance of winning if the hand was dealt to the river, your pot equity is 50% or $10.  It’s effectively what the pot is ‘worth’ to you.

Note that this doesn’t necessarily mean you have a 50% of winning this particular pot.  If you choose to bet then your opponents may fold, thinking they are beat.  Pot equity doesn’t take this kind of thing into account.  Also, if you do win, you won’t typically win $10.  You’ll usually either win the whole pot (in this example $20) or win nothing.  Nevertheless, a consideration of pot equity can be very useful for informing correct strategy at the table.

Let’s take the question we posed above.  Is it a good idea to limp UTG with a hand like KT suited?  Aren’t we just as likely to be dominated as we were with KT offsuit?  Well yes, we are.  But it turns out that provided the pot is multiway (that is, contested by three or more players), then suited hands become more valuable and domination is not as important a factor.  We can use the concept of preflop pot equity to see why this is the case.

Suited hands have certain advantages postflop which unsuited hands don’t. A flush is generally a very strong hand.  If you make a flush you will win the pot the majority of the time, regardless of the number of players.  For this reason flush draws are relatively easy to play after the flop.  This is often not the case for hands like KT offsuit, as we looked at earlier.

Being suited also adds, on average, about 4% to your preflop pot equity.  This is because there is approximately a 6% chance of catching a flush by the river card, but for example you’ll sometimes lose to a better hand or have to fold on the flop (when you don’t flop a flush draw).

As more opponents enter the pot your preflop pot equity will be reduced, but the (approximate) 4% advantage of being suited remains the same.  Therefore the RELATIVE increase in pot equity as a result of being suited is greater in a multiway pot.  When you add to this the postflop strategic advantages we’ve already mentioned, the result is that in the long run even relatively weak suited hands like KTs can be played profitably even out of position.

Notice that although offsuit hands like KT do have straight possibilities and will therefore also benefit from a multiway pot, the effect is not as pronounced as with suited cards.  This is because hands like KT offsuit have limited straight value, and even if they happen to make a straight they can still lose to flushes, or be beaten by a higher straight.  A flush is a much more robust hand and flush over flush is relatively rare.  Flush draws are also often easier to play after the flop than straight draws.

Let’s look at a specific example.  You are dealt KsTc UTG in a ten-handed $1/$2 game, and you decide to limp in (almost always a bad idea, as we know).  It’s folded to a late position player who raises with KhQd.  Everyone else folds so you’re heads-up.  The pot contains $5.50.  As we saw above, your pot equity in this situation is around 27%, or $1.49.  Your opponent has the other 73% of the equity in the pot.  You’re dominated and It’s a bad spot to find yourself in.

Now let’s look at the same situation, but this time you hold KsTs, a suited hand.  In this case your pot equity is around 31%, or $1.71.  Your pot equity has increased from 1.49 to 1.71, a relative increase of about 15% (). This may sound like a lot, but your opponent is still a clear favourite to beat you.  The fact that your hand is suited is not worth much in these circumstances, and you’re primarily playing your hand for it’s high card value.

Now let’s see what happens if three players limp in after you with Ac3c, 5d5s and Qd9c.  Everyone calls the button’s raise and the pot now contains $11.50.  If you hold unsuited cards KsTc, your pot equity is around 15%, or $1.73.  The pot equity of the KQ hand is about 20%.

But if we now assume you hold the suited cards, KsTs, you’re in much better shape. It turns out your pot equity is around 18%, or about $2.07.  In absolute terms this increase may not sound like much (it’s only 3% after all), but this is a relative increase of 20%, much better than 15% in the similar situation when played heads-up.

Notice also that in this case the pot equity of the KQ hand is a little less than 19%, not significantly better than your 18%.  The fact your hand is dominated has in a sense become less relevant, and this is increasingly the case the more people who enter the pot.

Of course, this doesn’t mean that you’d be happy to be dominated in this situation.  If the flop comes K72 rainbow then you’re still in big trouble against the KQ hand.  When you play a hand like KT suited in early position you need to be aware of the possibility that you’re dominated if you get a flop like this, particularly if a strong player raises behind you preflop.  Ideally you want to make top pair against a weak player who is willing to call you down with a lower pair, or to flop a flush or flush draw against many players.  If you do happen to flop a flush draw you’ll usually be in good shape.

If you think you may be dominated and you have no other draws you HAVE to fold, otherwise these hands will just cost you money.  This is one reason that beginners are advised to play very tightly in early position.  Often new players will not recognize when the table conditions are conducive to a multiway pot, and they also find it difficult to fold top pair if they are probably dominated.  If this is you, then play VERY tightly in early position until you gain more experience.  Whenever you enter a pot preflop, always consider what you are hoping to achieve.  If that scenario is unlikely, you should probably not be playing the hand in the first place.

So a hand such as KT suited may be playable UTG, provided the game conditions are such that you can ‘expect’ a few players to limp along behind you.  This means you need to be at a table with at least a few players who are willing to limp with weak hands, and most pots are not raised (since raises tend to limit the field).  If your table is tight and aggressive (that is, many pots are contested two or three-handed and are often raised or reraised preflop) then you should probably throw away a hand like KTs in early position (or even better, find an easier table where you can play it).

However, don’t get carried away with suited hands.  KT suited is playable because it is suited AND it has some high card value.  When it isn’t dominated it will often make top pair with a reasonable kicker.  Hands such as T3 suited are still junk.

So we’ve looked at one application of pot equity, but this is not the only one.  Your pot equity will change as each board card is dealt.  Another very common application of pot equity is to determine whether you have a pot equity ‘edge’ after the flop.  For example, against three opponents the average player would ‘expect’ to win 1 time out of 4, or 25% of the time.  If your pot equity is greater than that of the average player, then you are said to have a pot equity edge.  If you have a significant edge then you should consider betting or raising, even if you think you are currently behind. 

HUH?” I hear some of you say.  “How can this be correct?  Surely, if you’re behind you should try to save money until you improve?”

Well actually, no.  If you have a pot equity edge, then betting or raising can often MAKE you money in the long run, even if you currently don’t have the best hand.  In fact as game conditions become looser, what actually constitutes the ‘best’ hand can change.  This brings us to our next important concept.  The VALUE BET.

 I’ll discuss this, and a few more important concepts in my next article.  Until then, good decisions at the tables.