In general there are three types of poker math you may be familiar with. These types are all being used in different ways. For instance the most complex math is being used to study the game of poker, while simplified poker math is being used during the game. The last type of math is statistics. Poker statistics can for instance be used as a blueprint to know what winning players are doing.
Complex poker math
This type of poker math is there to calculate the very fundamentals of poker for instance the amount of starting hands a player could have:
Which could give 3*2*1/1326=0,45% chance of AA for instance (because there are 6 ways AA can be dealth with 4 aces)
The amount of flops can also be calculated in a similar fashion. In this way you can calculate for instance the chances of getting a double ended straigthdraw on the flop or a flushdraw. Or an easier example the chance of hitting a pair on the flop:
These type of chances are important to know, but you don’t have to do this type of poker math during any game. You should just look at a table to know these important types of information.
In order to solve a lot of poker math problems you should use pokersoftware like:
My personal favorite is Equilab, because it has a lot of extra information and charts to look at. In general these types of pokersoftware are being used to study pokerhands. You estimate your opponents preflop handrange, you put in your own hand and the flop and after pushing a button you know exactly how wel your hand is doing on the flop against your opponents handrange. These type of things are important to know for every poker player and i allready did a similar type of study under the following link:
In the same way you can study your equity on the turn and the river. It is also possible to see the chances of your opponent having or getting certian hands. You can find out how big the chance is of your opponent holding a straightdraw on a certain type of flop, or a flushdraw etc. It turns out to be the most important type of study to improve your knowledge about poker.
Simplified poker math
The poker math during the hand is a bit easier to use. Most of the time this type of math has been simplified for public consumption. For instance the usage of counting outs (cards that improve your hand) and multiplying the amount of outs by 4% or 2,2% to estimate the equity on the turn and the river. This type of poker math is simplified to make it easy for use. In reality the calculation should be done as follows:
For instance you are having a flushdraw and 9 outs and you want to know your chance on the turn and the river.
With the 4% rule you would estimate to have 9*4=36%, which is quite decent given the fact that it is very easy to calculate.
Other types of poker math being used are quick calculations of pot odds or more complex equity calculations on the river.
In the case of an equity calculation on the river hand combinatorics are being used. An example of these type of calculations with the use of hand combinatorics is given under the following link:
And this is the way to study the river by the use of equilab (or pokerstove):
An other example of the usage of handcombinatorics is the example of a poker professional folding his pocket kings.
He was holding KK in a very early stage of the tournament while player very deapstacked. After reraising a player who he knows well he decides to fold his hand. He knows that player as a very risk averse player who would never commit his entire stack at the beginning of the tournament with anything less then AA or KK. But because the pro allready has KK himself, he quickly calculates that the chances are as follows:
Ways to deal AA: 6
Ways to deal the second KK: 1
The chance of his opponent holding AA are 6 times as large as him holding KK.
The pokerpro therefore folds his hand to find out later that his opponent was holding KK as well, something that only happens once every 1225 hands ((2/50)*(1/49)).
Poker statistics are being used to estimate how well you are playing compared to the statistics of winning players. Check also the following link:
Other poker statistics can be used to make certain decisions. For instance which tables do you want to play on? There is a chart that shows that it is easier to achieve higher winrates in 1vs1 then it is on 6 handed or 9 handed tables. Besides that the winrates on a 6 handed table are also much better then on a 9- handed table. There is also a difference in winrate if there is an ante. But ofcourse the most important information is ofcourse how often the players are playing a hand. If more then 35% of the hands are being played you know that there is plenty of room to gain an edge.
Other statistics of poker are statistics about the average profits of all the hands. For instance AA has an expected value of 2,32 BB (based on billions of hands played on the internet). Ofcourse this may change based on your position and how you play the hand as well as how others around you play. This can be done for all hands and the winning hands per position can be used to determine which hands you should play in every position. This leads to the standard loose aggressive playing style described under the following link:
In the end the most important statistics in poker are ofcourse your green, blue and red lines:
This graph was made in a poker program called pokertracker. The green line is the profit curve (and the other green line may be the EV- curve). The red line gives your earnings without showdown and the blue line is your profit after the showdown. As you can see on the graph above this player is quite aggressive because he earns most of his money after his opponents fold. Consequently when he goes to the showdown his opponent will usually have a really good hand, which can be seen on the break even nature of the blue line.
Ofcourse pokertracker has much more important information to study. For instance the money you earn per position will show if you are leaking to much on the blinds or if you aren’t stealing enough of the blinds on the button. The entire leaktracker will be plotted to show how your stats are compared to winning players and so on you can even track the amount of rake you paid to the pokersite.
In general you should use the complex poker math to learn general ideas. For instance what the value is of holding a second pair on a certain type of board against your opponents handrange. These type of things can not be calculated on the spot. Simplified poker math is useable while playing poker. For instance the counting of outs or the counting of the amount of hands based on hand combinatorics. In the end most of the information will be visible in the statistics. Which hands to play in certain position is based on statistics, but also the leaktracker that shows you how you are doing compared to winning players.