Thursday, October 24, 2002

Essay: Balance

My approach to poker is built on the foundation of "balance." Poker, at its core, is a game about information. Your cards are face down, but with every poker play, every muscle twitch, and every chip placement, you may give away information about your cards. If you give away more information than you perceive, you will be defeated. Balance minimizes information leakage.

Sun Tzu said:

"All warfare is based on deception.

Hence, when able to attack, we must seem unable; when using our forces, we must seem inactive; when we are near, we must make the enemy believe we are far away; when far away, we must make him believe we are near."

Either Sun Tzu was exaggerating or the average Chinese war lord circa 500 B.C. was rather gullible. If you applied those words literally to poker, you would become the type of player I label "tricky to a fault." When such a player bets, he's bluffing. When he checks, he's strong. Such a player can beat only the most gullible and unobservant players.

I would adapt Sun Tzu's words to poker as follows:

"All poker is based on balance.

Hence, when able to raise, we must be unpredictable; when making a play, we must weigh the apparent gain against the leakage of information; when strong, we must seem weaker than we are; when weak, we must seem stronger than we are."

When strong, we don't want to consistently act weak, and when weak, we don't want to consistently act strong. We should instead balance our play so that our opponent would usually predict that we are closer to the average in strength.

To study how balanced your strategy is, ask yourself what hands you could hold in a given situation given each of your possible actions. For a hold'em example, suppose you open-raised late, the big blind defends, the flop comes something like Q75, and he checks. What hands could you hold if you bet, and what hands could you hold if you check? How similar in average strength are those two sets of hands? If you're only strong when you bet and only weak when you check, you'll be too predictable. If you're only weak when you bet and only strong when you check, you'll be too predictable. If you always bet in this type of spot, you'll be too predictable, as your opponent can reliably check-raise you.

How can you achieve balance with minimal local sacrifice? Obviously, you can mix in some of your strongest hands with your weakest (e.g., check some sets along with weak hands), and you can mix in some of your weaker hands with your stronger hands (e.g., semi-bluff bet along with value betting.) Your checks/calls then indicate extreme weakness or extreme strength, and your bets/raises indicate moderate strength or draw potential. Your opponent does not gain much useful information from that alone, and most hands are played without great local sacrifice.

Limit hold'em is a bit different from most other poker games, in that your strongest hands are very strong indeed, since the board is shared and players get only two cards, making it harder for your opponent to suck out. And with it being limit, your opponents have a lower pay-off when they suck out. And yet, the odds due to the betting structure encourage them to try to suck out. This allows a different approach to balancing, namely the "Pound-Pound-Pound" school of balancing. Here the idea is that once you take the initiative in a hand, you bet and raise with almost everything, representing no less than AA. By playing your strong and weak hands hard, your opponents will pay more to your strong hands and fold more to your weak hands.

Start by always raising when opening preflop, never limping when the first to enter the pot. (This works best in games that are not loose.) This gives away very little information, as given that you raised, your opponents only know that you have a playable hand, instead of splitting your hands in two right off the bat. When you get to the flop, you continue pounding if possible. Once you figure out you're beat and don't have odds to draw, you fold. Raise or fold, that's the mantra, with just enough checks and calls to keep your betting from being too predictable. With really strong hands, it actually can be advantageous to show strength on the flop anyway, putting your opponents into "check-call" mode instead of their possibly escaping on the turn if you slow-play the flop and raise on the turn. Given that you also play aggressively with draws on the flop, your opponents cannot escape from your strong hands without cost.

Obviously, there are times that you realize you are beat and cannot steal and yet you have odds to draw. So, you must sometimes go into passive drawing mode, or sometimes do free card plays. To the extent that you go passive or do free card plays with drawing hands, you should balance that by mimicking the same with strong hands. And to the extent that later in a hand you shed the draw mimicry with strong hands and raise for value, you should also toss in some bluff raises later in a hand with draws or missed draws. Bluffs force your opponent to pay you off more when you raise for value, and value bets and raises force your opponent to fold more when you bluff.

If you do not wish to attend Pound-Pound-Pound University (PPPU), that's fine. However, if you do not balance your play in some manner, you will be but chum in shark-infested waters.

Everything depends on everything else. How you play postflop depends on how you play preflop, and how you play preflop depends on how you play postflop. How you play with a given hand in a given situation depends, in part, on what other hands you could hold there and how you would play them. Missing a profitable thin value bet on the river is more costly than the immediate value lost, if it is a consistent mistake; you lose not only the profit from such bets, but also your bluffs become less profitable, and you allow your opponents to take shots earlier in the hand or call you down without being punished to the maximum.

I have focused on balance in basic betting actions, but balance applies elsewhere too. For example, if sometimes you pause when considering a borderline raise, you either need to eliminate those pauses or add balancing pauses with strong hands. Identify your information leaks and plug them.

Sun Tzu said:

"The good fighters of old first put themselves beyond the possibility of defeat, and then waited for an opportunity of defeating the enemy.

To secure ourselves against defeat lies in our own hands, but the opportunity of defeating the enemy is provided by the enemy himself.

Thus the good fighter is able to secure himself against defeat, but cannot make certain of defeating the enemy.

Hence the saying: One may know how to conquer without being able to do it."

That's some 2500 year old game theory. The strategy I've outlined is largely defensive, which should not be confused with passive. To win, one must first avoid losing. Some poker players adopt the opposite stance, trying at all times exploit the mistakes of their opponents. In tough games, either such players may not know how to play or they may try foolishly to exploit holes that are only imagined, thus playing suboptimally and defeating themselves. Play good solid poker and wait for your opponent to defeat himself. When there is a real opening, it's usually obvious how to take advantage to make your opponent pay the maximum. That is just the icing on the cake.

Wednesday, September 04, 2002

Some blinds questions.

I have only a vague sense of the value of hands like 67s on the blinds.

76s is on par with KQ for blind defense versus a lone middle raiser. That is, it's definitely playable, but towards the low end of playable hands. 76s has the advantages of extra draw outs (valuable when you're getting odds like here) and less chance of being dominated, which offset its baby card problem.

How many callers would you need to call a raise in the BB with this hand ?

zero versus a middle raiser.

I have a hard time judging the value of the blind discount.

For example, say the button steal-raises and I have AA.

Would it be a good idea, assuming info-leak and discouraging stealing are not issues, to smooth-call to let the BB in? Or would the BB actually be making money at my expense? Of course I can see how this depends on the other players, but in general is this a terrible idea, a decent idea, or a good idea ?

Assuming info leak is not a problem, then AA definitely wants to give the big blind a cheap shot. You might try looking for a tell from the big blind - if he has a "fold tell", then your smooth calling won't bring him in and you might as well 3-bet.

If this might be +EV with AA, what about KK? QQ? JJ? Surely TT is to vulnerable to let a random hand in cheaply?

KK probably, but probably nothing else.

Also, though I understand the concept of dominance well enough, I think, I have a hard time balancing it against pot odds.

For example, say a tight UTG player raises, but then 8 people cold-call. I have A2 in the BB. I play... right? Even though dominance is likely from UTG, the pot odds are excellent.

What is the chance that not one of the other players has an ace? Pretty much zero in a fairly sane game. So, you're playing for trip deuces or a wheel or a split pot with aces, mostly. In a more normal situation, like a raise and two or three cold callers, A2 would be a clear fold. The pot in your example is 19 small bets, and my mind boggles at such odds. My guess is that you should call, but this bloated pot is giving a disproportionate reward for splitting the pot with aces up, so the normal rules don't apply.

What about same situation but I have KQ? KJ? K7 ? J9?

If you're in a game where you are in fact getting in this situation repeatedly, then I suggest calling with all these, as your opponents are horrible and don't have much better than random cards! Knowing the answers to these questions won't make you a better player for most games.

What about one tight UTG raiser, one random cold-caller, and me in the BB. How weak could I go here with offsuits?

I've done a careful study of heads up in the big blind against a tight UTG raiser (alone), and my conclusion there is that you need a minimum of AQ, and even AQ needs to be played with great care postflop. With the extra player in there, you could add KQ, but you could also muck it if the raiser is a rock or the cold caller likely has a strong hand.

The basic idea is to look at the effective odds for the whole hand, not the immediate odds you're getting now. For the best odds, you want to flop hard and win the pot, no problemo. That's why 55 is so good for blind defense. On the other hand, when you flop something like top pair and put in a bunch of bets before you find out you're beat, then your odds are much reduced. That's why A2 is not normally a good blind defense hand even with fairly big odds. Another kind of hand is one that can flop a draw. That's not nearly as good as the near "auto-win" situation of flopping a set, of course, as you are now fairly likely to put in a bunch of bets and lose, so that reduces your effective odds. Still, lots of times you will flop nothing and fold, so that improves your effective odds. Drawing hands become better exponentially the more ways they have to draw, as you can back into a hand when you were drawing for another, again reducing the chance of putting in lots of losing bets. 76s is much more than twice as good as 72s and 76, for example. That's why 76s is usually somewhere between marginal and very profitable for blind defense.
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