ADVANCED FUNDAMENTALS by Christian Drechsler
Since this is the first of a likely series of articles, I'm going to start with the basics. Mastering any skill, requires perfect understanding of the fundamentals and poker is no exception. So lets begin -
 What is the goal of the game and how do you achieve it?
Simple - the goal of the game is to win the biggest amount of money (or simply chips) possible (which also means to lose the least if a positive outcome is impossible). This means that the best player in the world is the one that wins the most money. Even if your goal is not to win money, but to play the game as well as possible, your success is measured by the amount you've won.
So how do you win the money?
There are 2 ways to win the chips in the pot - by forcing your opponents to lay down their hands by betting or by showing down the best hand in the end.
(Usually you'd prefer to take your winning hands to showdown and to bluff your way out with your second-best ones. There are exceptions though- for instance you'd prefer to take the pot down immediately with a vulnerable hand, having no real implied odds)
The way to lose money is to put them in the pot by either calling, betting, raising or posting blind.
So to actually come out ahead, those investments must have a positive expectation. And to play perfect you must always choose the option with the highest expectation. Thus the essential skill in poker is the ability to correctly evaluate all of your options. But you will also need discipline, as having the skill alone won't do you any good if you don't actually use it to its fullest extent. But this will be a topic of another article. So let's focus on...
The essential skill for success
The skill in poker all comes down to correctly evaluating all of your existing options. But make no mistake, this is no simple task. Ideally, you'd like to know with absolute certainty your opponent's holding and how he's going to play it out. With this information, it will always be possible to find the highest EV option. This is why, it's often said that the most important skill in poker (and especially NLHold`em) is hand reading. In reality, usually the best that is humanly possible is to put your opponent on a range of hands and assign some probability on how he's going to play each one of them.
So how are you going to do that?
What you should know for sure is your hand, your position, the board (if there is one), the action until this moment. What you should ideally know though is your opponent's betting patterns, his level of thinking, his perception of your game, even his mood.
Here, I'd like to say that you should never make a play, just because you feel like you have to make it. This is a very common mistake I see over and over again. People feel that they should defend their blinds with marginal hands, so they don't get "run over". Or that they should play more aggressively, as to not be "playing weak". Or that they should never fold a strong hand on principle. This is not the right kind of thinking. You don't have to do anything. What you should do is look for the most profitable option and then take it. If you can't find it - you can (and probably should) always check and fold. Now I'm going to look at...
Poker from a math perspective
I'd like to say that you absolutely must master the math behind poker. I know that some people think poker is not about math, but in reality - it definitely is. I'll try not to go into the more complicated stuff, but you'd do well to pick up a book where the math is explained in detail. (I'd suggest you read Theory of Poker)
So let's take a look at our options. At any given time we have the options to fold, check or bet; fold, call or raise. The expected value of a fold is always exactly zero, as you invest nothing to win nothing. The EV of a check is always >=0,as unless you expect to make EV- decisions you invest nothing, but may still win the pot. So the more interesting decisions involve betting and calling.
The biggest difficulty when evaluating your options is including your future choices into the equation. (For instance, when trying to decide if a turn value call is profitable, you must evaluate the chance of the river going check/check and whether a river call will win you money) It's easier to evaluate our options the closer they are to closing the betting. The easiest to examine would involve pushing or calling an all in bet and the hardest would be preflop in a NL game with deep stacks. Thus when thinking about a hand it would be wise to start from the finish.
I'd guess everyone reading this article knows, that when facing an all in bet, the EV of a call depends on the chance of your hand winning at showdown and to estimate it you have to evaluate your opponents range and your chances of drawing out. If the bet is exactly pot sized, then you'll need to have 1/3 chance of winning to make the call break even. (EV=0)
What's more interesting is how our opponents bet changes the EV of the hand. Let's say the pot is 1000$ and you have exactly 1/3 chance of drawing out. And for this example let's assume that there will be no more betting if you make your hand. So your EV for now is 333$ and your opponents EV is 666$. If your opponent bets exactly 1000$, he changes the EV in the hand so that now, no matter if you call or fold, your EV is always 0 and his is always 1000$. This illustrates the principle that your bets can only increase your equity to the size of the pot, without relying on your opponent to make a mistake. (As if he always chooses an option with EV of at least zero, you cannot gain more than what`s in the pot.) More about that in a minute. Also this illustrates why betting to protect your hand is important, even if you're never called by a worse hand.
A river bet for value will generally be profitable if after it is called, your hand is best more often than not. Which means, that you should sometimes pass a value bet with the likely best hand, if it is unlikely that you'll get a call by a worse hand. (This gets to be more important against better players.)
A river pot sized bluff will be profitable if it gets more better hands to fold, than those that call it. (It might still be EV+ if this condition is not met, but it will not be superior to a check, with very rare exceptions)
The more complicated decisions require deeper analysis. I'll provide some examples later in this article.
Winning by mistakes
Basically you win when your opponents make EV- decisions against you, and you lose when you make EV- decisions against them. In reality, your opponents mistakes are your main source of profit. Ideally you want to play against bad players and let them make the worst mistakes possible. This will generally mean one thing - value betting the biggest amount your opponent will call incorrectly and not more (as that would allow him to play correctly and would be a huge blunder on your part). Another thing you should generally do against weak players is find folds with marginal to decent hands when facing aggression, as your opponents are bluffing way too little and so the EV of calling them down is terrible. You can occasionally double barrel a decent draw or find a correct call, but those things won't affect your winrate as much. This brings us to a very important concept:
You win the most, by (correctly)making big bets in big pots and the better you can define your opponents hand, the more you will be able to profit from that.
As we said, when playing against bad to mediocre players, you just let them make the biggest mistake possible and try to avoid making big mistakes yourself. But what if your opponents are thinking players and will generally either find an EV+ option or fold?
You cannot force an opponent to make an EV- decision. You can try to manipulate him into doing it and this is an important skill for sure, but ultimately he is the one responsible for his actions and if he's a good player he will be able to find the fold button more often than not (or to find a correct call for that matter).
But what you can do is try and take all of his EV+ options away from him. You do this by employing precise hand reading, thin value betting and bluffing with the optimal frequency, while giving away the least information possible about your hand and hand range. And you generally cannot win money by calling down, when your hand is well defined. You obviously cannot expect your opponent to make mistakes, when he knows your hand (well of course you can, but that is not really the point), but there is more than that.
To illustrate I'll give you several examples.
Let's say you are on the river and your opponent has checked. He's a decent player, but by now his hand is somewhat defined, while yours isn't. Looking at hand ranges, you are going to have his likely holding beat with 30% of your hands. Let's say you check behind when beat and value bet all of your winning hands. Since he's a good player he is going to (correctly) fold every time and you are going to win the pot 30% of the time. So your total EV is 30%xPot. Let's say you bluff way too much - you fire pot on a bluff as often as you have a winning hand. Then 40% of the time you lose the pot by checking and in the 60% of the time you bet pot, your opponent will be correct in calling you down. Your expectation when ahead will be 2xPOT, and when bluffing - (-1xPOT). So your total expectation is still EV=30%xPOT. It could change for the better if your opponent made the mistake to pass a profitable call or make a bad one. But you cannot rely on that. What you should rely on, against good players, is bluffing at the correct frequency.
So what happens if you decide to value bet half the pot with your 30% winning hands and also bluff with and additional 10% of your hands? From your opponent`s point of view the EV of his call is exactly zero. Which means that your EV after making the bet is equal to the amount of the pot, no matter if he decides to call or fold. Which brings your total expectation up to 40%xPOT.
But you can do better than that. Seeing as how every time you bet, you gain, it makes sense to bet more often. So you must bet bigger. If you bet pot with your winning hands and add 15% bluffs, his call will again show an EV of zero and your expectation of the hand has gone up to 45%POT.But why stop here? If your opponents hand is well defined you can overbet the pot as a thin valuebet or as a bluff, without fear of him showing up with a monster and ruining your strategy. If you bet twice the pot with all of your winning hands and bluff with an additional 20% of your hand range, then your opponent is again faced with an EV0 proposition. This brings your EV to 50% of the pot.
The only way your opponent can prevent you from employing this strategy is by misrepresenting his hand, which would limit the size of your bet. If there is even a small chance of him slowplaying a better hand, the size of your bets must go down as well. And if you're totally wrong in your read and he will show up with a better hand often, then this kind of betting will be a disaster. What allows you to outplay him is your knowledge of his hand. So yeah - knowledge is power.
Against inferiour players though you're infinitely better just bluffing when you think they're likely to fold. It makes no sense to use game theory to outplay them, when you'll win more if you exploit their weaknesses to the fullest.
Another example - this time to illustrate why calling down cannot win you much money against really good players. Let's say you have position with a decent, somewhat defined hand (ignoring the chance to improve) and your opponent fires a pot bet. Assuming he'll bet pot with a perfect frequency on river and we will always win when it gets checked down, we have to estimate how often he does actually check the river. As we are investing X=POT, to win 2X when the action goes check check and to win absolutely nothing when he bets. Well if he checks the river less than 50% of the time we should have just folded on the turn. Which leads us to the interesting conclusion that if he fires turn having a better hand 33% of the time and plays perfectly on the river we cannot win money even though 2 times out of 3 we have the better hand. He can also fire the turn with a lot of draws in his range, but finally have the winning hand 33% of the time.
So you have to remember - you should never play in a way that defines your hand against perceptive opponents as this allows them to play perfectly against you. Playing your hand in an obvious way and calling rather than betting will not win you money against decent players. Instead of doing that, you should stay on the aggressive side and put pressure on them and ideally make them define their hand, without exposing your own.
So finally, let's see what can we make of all this.
- Your goal in poker is to find and choose the highest EV option in every single hand.
- Which means poker success requires the ability to correctly evaluate the situation and the discipline to always make the best use of that
- Since the EV of check/fold is always at least neutral, this should always be your choice when you're unable to find a profitable option. Don't ever feel like you have to do anything else. In fact if you folded 100 hands in a row, because you couldn't find an EV+ option, that is perfectly fine as long as you were looking for it. What's not fine is knowing the best option and not taking it.
- To evaluate an earlier street decision, you must be able to predict how the hand will play out and know in advance how you're going to play it out.
- Your main weapons in poker and hand reading and deception
- To become the best player you can be, you need to know the math behind poker. There is no going around that. So open PokerStove a notepad and a calculator and get to work.
- Generally you profit from your opponents mistakes and by not making them yourself. Knowing your opponent will help you a great deal in this case. You want to play in such a way that magnifies his weaknesses and doesn't justify them in any way.
- However, when playing against really good players you don't rely as much on them taking EV- choices, instead you try to bring down the EV of their decisions to zero.
- You win the most, by (correctly) making big bets in big pots and the better you can define your opponents hand, the more you will be able to profit from that.
- Thus - playing deeper increases your edge as you have the opportunity to extract precise information about your opponents hand and act on it with a big bet with a big expectation.
- You cannot expect to win much by calling down against a good opponent, especially if your hand is exactly what it looks like. That's the main reason you avoid playing marginal hands out of position.
- You must play in such a way that gives out as little information about your hand as possible to prevent your thinking opponents from playing well against you. This works both ways - if you can provoke them into exposing their own hand, you will benefit greatly.
I intended to write about some common misconceptions, but I think it'd be better to devote an entire article to that. I'd appreciate any feedback on this first attempt of mine and I'd like to know what you want me to write about.
To see if you have fully understood what you just read I'd like you to do a little homework. Try and construct a hand in which the correct play is to bluff with a marginal hand to prevent a bluff, even though your hand figures to be best at least half the time. This was mentioned in "Theory and Practice", but no example was given. It's a pretty hard thing to do!
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Bulgaria. Dec 21 2007 09:50. Posts 2586
