Introduction
Poker is a simple game, that is difficult to play well. That is the beauty of poker. Because the rules are so simple, people are quickly fooled into thinking they can play the game well just after a few hours of learning. From the expert’s point of view, the very fact that people think they can play well is what makes it profitable for the real professionals.
Certainly, every player can get unlucky in any given session. An expert player will have people draw out on them much more as people will have the worst hand against the expert much more than not.
Over the long run everyone gets an equal share of good cards and bad cards. So experts are at war with luck and use their skills to minimize their losses on bad hands and maximize profits on the good hands. Whereas beginners rely on big hands and lucky draws.
If you want to get good at playing poker, you have to remember that it is a game of skill, not luck. And skill, is a learnable trait.
There are many varieties of poker – high, low, stud, draw, limit and no-limit. However, there is an undercurrent of the same logic that runs thought all of these games. Certain concepts and theories apply to them all. However, experienced a player may be with a particular game, only by understanding the underlying logic, can he quickly transfer his skills to other game types and become adept.
Poker logic is not about tricks and ploys. In weaker games these strategies may work, but any player thinking this is the way to plan and win the game is deeply misguided and will never rise to the higher games. Neither is poker completely mathematical. Understanding the mathematics of poker will certainly help you play better but that is just a small part of the logic of the game. Understanding the precepts and underlying concepts of poker is much more important.
The object of the game is to make money. Irrespective of the game type, place or opponents. Even if your grandmother is playing against you, your goal is to wipe her clean and if you are not comfortable doing that, you have no business being at a poker table.
While the objective is to make money, that doesn’t translate to a strategy of trying to win all the pots. Of course you should win as many pots as possible, but trying to win all or too many pots is a bad strategy because the bets you save are as important as the bets you win. Good players reduce losses by not making calls that a weaker player would have made.
The next realization that good players have understood is not to put good money after bad money. This means not to chase the money you have contributed to an individual pot. It is crucial to realize that each individual game is a part of one big poker game. You are never playing one game, you are always playing one of many.
All that matters is what was your net profit (or loss) at the end of the month or year. The only criteria to remain in a game is whether you are a favorite or an underdog. Never quit a good game as a small winner just to make sure you have a winning session. On the other hand, never keep playing a bad hand just to get even. Never let your losses disgruntle you.
Expectation and Hourly Rate
An extremely important factor for good poker play is mathematical expectation. This is the amount a bet will average winning or losing. Let me explain mathematical expectation through examples.
Let’s say you are betting $1 on the flip of a coin and will win every time the coin turns heads. Here the mathematical expectation is precisely Zero because the odds of heads coming up are 1-1 and you are also betting $1-$1. Your hourly rate in this case is also zero because even if you are flipping the coin 100 times in an hour, because your mathematical expectation is zero, your hourly expectation of earnings remains zero.
However, let’s say an idiot bets you $2 for your $1. Now your mathematical expectation becomes $0.5. This is because out of every two bets, you expect to win $2 from one and lose $1 on the other. Therefore, netting $1 over 2 bets means per bet your mathematical expectation is $0.5.
Let’s take another slightly more complicated example. A person will write down a number between 1 to 5 and bets $5 against your bet of $1, that you can not guess the number. Should you take the bet? Yes, you should because your mathematical expectation is $0.2 You have 4-1 odds against you guessing correctly but you have a $5-$1 bet ratio. This means, out of 5 bets, you lose $4 and make $5 thus netting you $1 for 5 bets, giving the said mathematical expectation.
At the heart of every gambling situation is mathematical expectation. So in any play, a move which gives you a higher mathematical expectation, or a lower negative mathematical expectation, is the right move.
It is important to note that mathematical expectation has nothing to do with results. In the $2-$1 coin flipping bet, the imbecile could win the first ten coin flips in a row, but getting 2-to-1 odds on an equal-money proposition, you still earn 50 cents per $1 bet. So it does not matter if you win or lose a bet, or even a sequence of bets, as long as you have sufficient bankroll to sustain your losses easily. This way, as long as you continue to bet, you will win and in the end, your winnings will approach the sum of your expectations.
Mathematical Expectation in Poker
Poker play becomes quite interesting from the perspective of mathematical expectation because you may think a particular play is profitable but it may not be the best move since an alternative play is more profitable. To take an example let’s say you have a full house in a five card draw. The player before you bets and you know if you raise then the player will call. So raising seems like the right decision. However, you are also confident that if you raise, the two players behind you will fold. Whereas you are sure that if you call, then the two players behind you will also call. Therefore, by raising you gain one unit but by calling you gain two units and ultimately becomes the better play due to a higher positive expectation.
Mathematical expectation can also be used to determine if one play is less unprofitable than another. Therefore if you think you will lose average $0.75, including the ante, by playing a hand you should keep playing because it is better than folding the hand if the ante is $1.
One more important reason to understand numerical expectations is because it provides you a sense of equanimity when winning or losing a bet. Whenever you make a good bet or a good fold, you will know that you have earned, or saved a specific amount which a lesser player would not have earned or saved respectively. Whereas it would have been much harder to have make that fold if you were upset that you were outdrawn. Eventually, the money you save from good folds instead of calling increases your net earnings for the night, or month.
You should learn to derive satisfaction from losing a good session, knowing that, a weaker player would have lost more.
Hourly Rate
Especially important to the professional poker player is the hourly rate which is the mathematical expectation multiplied by the number of bets taking place in an hour. Therefore, when you go into a game you should know what is your hourly expectation. While experience and judgement will be needed there are certain mathematical guidelines that can be applied.
Let’s take an example. You you’re playing draw lowball and you find three players calling $10 and drawing two cards (which is a very bad play) you know that every time they put $10 they are losing an average of $2. They do this eight times an hour which means three players will lose $48 per hour. You being one of the four players, therefore get a quarter of the $48 i.e. $12 per hour becomes your hourly rate. In this case, your hourly rate is your share of the total loss per hour of the three bad players in the game. Of course, on most situations you cannot be so precise and other variables will affect the hourly rate. Additionally, in public games the rake for the house also needs to be considered.
Once you have calculated your hourly rate you should understand that what you are doing is earning and not gambling in the traditional sense of the word. You should no longer be looking to have a good day or be upset if you have a bad one as if you play regularly, you would know that it is better to play with an hourly rate of $20 than slog an eight-hour shift with a pay of $8 per hour.
You should never glamorize poker play. If you have estimated your hourly rate correctly, then your earnings will be close to your hourly rate multiplied by the number of hours played. The edge you have is not from having better cards, but from situations where other players would have if they had your hand and you theirs. Assuming you play perfectly, your earnings is the total amount of mistakes they make, minus the rake.
It’s a whole different matter to assume that you will play perfectly. More so, it is sometimes wiser to play incorrectly. So you may purposely make an inferior play in order to gain in a future round of betting. Or, you may play less than optimally when playing against weaker players when you have a tight bankroll. In such instances it is better to reduce your hourly rate but simultaneously ensuring a win.
Sometimes you may want to keep playing for political reasons. You don’t want to be known as a player who only plays when he has the best of it, not only will this make enemies, but can even get you banned from various games.
Continued…Part 2 – The Fundamental Theorem of Poker.
