The main underpinning of poker is math – it is essential. For every decision you make, while factors such as psychology have a part to play, math is the key element.

• List Of Poker Hands Pdf
• List Of Best Poker Starting Hands
• Order Of Poker Hands
• List Of Poker Hands Printable
• Poker Best Hands In Order

In this lesson we’re going to give an overview of probability and how it relates to poker. This will include the probability of being dealt certain hands and how often they’re likely to win. We’ll also cover how to calculating your odds and outs, in addition to introducing you to the concept of pot odds. And finally we’ll take a look at how an understanding of the math will help you to remain emotional stable at the poker table and why you should focus on decisions, not results.

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What is Probability?

Probability is the branch of mathematics that deals with the likelihood that one outcome or another will occur. For instance, a coin flip has two possible outcomes: heads or tails. The probability that a flipped coin will land heads is 50% (one outcome out of the two); the same goes for tails.

Probability and Cards

When dealing with a deck of cards the number of possible outcomes is clearly much greater than the coin example. Each poker deck has fifty-two cards, each designated by one of four suits (clubs, diamonds, hearts and spades) and one of thirteen ranks (the numbers two through ten, Jack, Queen, King, and Ace). Therefore, the odds of getting any Ace as your first card are 1 in 13 (7.7%), while the odds of getting any spade as your first card are 1 in 4 (25%).

Unlike coins, cards are said to have “memory”: every card dealt changes the makeup of the deck. For example, if you receive an Ace as your first card, only three other Aces are left among the remaining fifty-one cards. Therefore, the odds of receiving another Ace are 3 in 51 (5.9%), much less than the odds were before you received the first Ace.

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Pre-flop Probabilities: Pocket Pairs

In order to find the odds of getting dealt a pair of Aces, we multiply the probabilities of receiving each card:

(4/52) x (3/51) = (12/2652) = (1/221) ≈ 0.45%.

To put this in perspective, if you’re playing poker at your local casino and are dealt 30 hands per hour, you can expect to receive pocket Aces an average of once every 7.5 hours.

The odds of receiving any of the thirteen possible pocket pairs (twos up to Aces) is:

(13/221) = (1/17) ≈ 5.9%.

In contrast, you can expect to receive any pocket pair once every 35 minutes on average.

Pre-Flop Probabilities: Hand vs. Hand

Players don’t play poker in a vacuum; each player’s hand must measure up against his opponent’s, especially if a player goes all-in before the flop.

Here are some sample probabilities for most pre-flop situations:

Post-Flop Probabilities: Improving Your Hand

Now let’s look at the chances of certain events occurring when playing certain starting hands. The following table lists some interesting and valuable hold’em math:

Many beginners to poker overvalue certain starting hands, such as suited cards. As you can see, suited cards don’t make flushes very often. Likewise, pairs only make a set on the flop 12% of the time, which is why small pairs are not always profitable.

PDF Chart

We have created a poker math and probability PDF chart (link opens in a new window) which lists a variety of probabilities and odds for many of the common events in Texas hold ‘em. This chart includes the two tables above in addition to various starting hand probabilities and common pre-flop match-ups. You’ll need to have Adobe Acrobat installed to be able to view the chart, but this is freely installed on most computers by default. We recommend you print the chart and use it as a source of reference.

Odds and Outs

If you do see a flop, you will also need to know what the odds are of either you or your opponent improving a hand. In poker terminology, an “out” is any card that will improve a player’s hand after the flop.

One common occurrence is when a player holds two suited cards and two cards of the same suit appear on the flop. The player has four cards to a flush and needs one of the remaining nine cards of that suit to complete the hand. In the case of a “four-flush”, the player has nine “outs” to make his flush.

A useful shortcut to calculating the odds of completing a hand from a number of outs is the “rule of four and two”. The player counts the number of cards that will improve his hand, and then multiplies that number by four to calculate his probability of catching that card on either the turn or the river. If the player misses his draw on the turn, he multiplies his outs by two to find his probability of filling his hand on the river.

In the example of the four-flush, the player’s probability of filling the flush is approximately 36% after the flop (9 outs x 4) and 18% after the turn (9 outs x 2).

Pot Odds

Another important concept in calculating odds and probabilities is pot odds. Pot odds are the proportion of the next bet in relation to the size of the pot.

For instance, if the pot is $90 and the player must call a $10 bet to continue playing the hand, he is getting 9 to 1 (90 to 10) pot odds. If he calls, the new pot is now $100 and his $10 call makes up 10% of the new pot.

Experienced players compare the pot odds to the odds of improving their hand. If the pot odds are higher than the odds of improving the hand, the expert player will call the bet; if not, the player will fold. This calculation ties into the concept of expected value, which we will explore in a later lesson.

Bad Beats

A “bad beat” happens when a player completes a hand that started out with a very low probability of success. Experts in probability understand the idea that, just because an event is highly unlikely, the low likelihood does not make it completely impossible.

A measure of a player’s experience and maturity is how he handles bad beats. In fact, many experienced poker players subscribe to the idea that bad beats are the reason that many inferior players stay in the game. Bad poker players often mistake their good fortune for skill and continue to make the same mistakes, which the more capable players use against them.

Decisions, Not Results

One of the most important reasons that novice players should understand how probability functions at the poker table is so that they can make the best decisions during a hand. While fluctuations in probability (luck) will happen from hand to hand, the best poker players understand that skill, discipline and patience are the keys to success at the tables.

A big part of strong decision making is understanding how often you should be betting, raising, and applying pressure.
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Conclusion

A strong knowledge of poker math and probabilities will help you adjust your strategies and tactics during the game, as well as giving you reasonable expectations of potential outcomes and the emotional stability to keep playing intelligent, aggressive poker.

Remember that the foundation upon which to build an imposing knowledge of hold’em starts and ends with the math. I’ll end this lesson by simply saying…. the math is essential.

By Gerald Hanks

Gerald Hanks is from Houston Texas, and has been playing poker since 2002. He has played cash games and no-limit hold’em tournaments at live venues all over the United States.

Now that you understand the position concept we are going to expand on that by looking at the subject of which starting hands to play and which to throw in the muck.

This is the area where inexperienced players become fish, simply by not having the ability to fold weak hands before the flop. You can save a lot of money at this stage of the hand just by simply choosing not to play.

The Importance of Starting Hand Selection

As you know Poker is a game of maths and probability. It is therefore possible to know which starting hands are most probable to win a hand and this has been statistically proven in many studies. These studies have been able to rank starting hands according to how likely they are to win the hand against a random selection of opponent’s starting hands.

Starting hand

By Starting Hand we mean the two hole cards which are dealt to you at the start of each hand.

Since we now know which are the best starting hands in poker then we can apply this knowledge to our strategy. Remember, when we play a hand, we want to play with the odds in our favour, and by selectively choosing which starting hands we play we can ensure this.

Of course if we just waited for the two or three best poker starting hands then we wouldn’t actually play many hands as the probability of these cards being dealt is only once in a while.

So we combine the position concept with our starting hand concept, to allow us to only play a narrow starting hand selection when out of position and to play a wider range of starting hands when we are in position. Therefore the benefit of playing in position makes up for the weaker starting hands we may play.

Starting Hand Groups

You could look at all the statistical information and studies, but we’ve taken all the work out of it for you. The following section is a key part of your strategy and you should practise choosing the right action before the flop using the poker starting hands chart below.

We have chosen 46 different hands that we will play depending on the position and situation we are in. Those 46 hands have been separated into 8 groups named Group A to H. Group A are the strongest hands in poker based on the statistics and group H are the weakest hands that we are willing to play. Of course there are many more hand combinations weaker than the hands in Group H, but we are not interested in playing with these and they will be folded into the muck straight away.

Group B

AK

QQ

Group D

AQs

AQ

AJs

99

88

Group F

AT

KQ

KJs

QJs

44

33

22

Group H

KJ

KT

QJ

J8s

T8s

87s

76s

The ‘s’ next to some of the hands stands for Suited, so two cards of the same suit. ‘AJs’ could stand for A J whereas ‘AJ’ could stand for A J

Take a minute just to browse the hands in each group, you don’t need to memorise these, as you can use the chart to refer to, and once you have used it for a while, you will start to remember which hands are in which groups.

Poker Starting Hand Charts

Ok, so now we have our selection of 46 hands, and have split them into 8 groups based on strength, now what? Well we won’t just automatically play any of those 46 hands when they are dealt to us, we will make a decision based on the position we are in, and the situation we are faced with at the table.

When we are in position we will play a wider range of groups and out of position we will only play the stronger groups. Similarly when opponents have shown strength at the table by raising we will only play the better cards against them.

There are three charts, UNRAISED, RAISED and BLINDS. These are our Action charts, and show us what action to take when we have a hand in one of the starting hand groups.

The three charts are:

• UNRAISED – When everybody acting before you has either folded or called the big blind.
• RAISED – When somebody acting before you has raised.
• BLINDS – When you are in either the small blind or the big blind position and somebody acting before you has raised

To use the charts, just follow these steps:

1. What group is your starting hand in? if it isn’t in any group then you Fold.
2. What Situation are you in? Choose one of the three action charts relevant to the situation you are in.
3. What Position are you in? Look at the column in the chart for the position you are in.
4. Starting Hand Group not shown? If your starting hand group is not shown in that column, then you Fold.
5. Starting Hand Group Shown? If your starting hand group letter is shown then take the action the chart is showing you.

The different actions in each of the charts are:

• Opening Raise – Make the first Raise
• Call – Just Call when a person has Raised
• Re-Raise – Re-Raise a person who has Raised
• Call a Re-Raise – Call when someone Re-Raises your original Raise
• Raise a Re-Raise – Re-Raise when somebody has Re-Raised your original Raise
• Call the Big Blind – Just call the big blind amount (also known as ‘limping in’)

Quick Reference

I don’t expect you to memorise all the starting hand groups and action charts. The way to learn them is by putting them into practise and then over time you will start to memorise them. But to start with, you can refer to the charts while you are playing.

You can either just bookmark and pull this page up each time you play or we have a couple of other methods to make your life a bit easier.

Printable Starting Hands Chart

A neat and tidy, A4 size starting hand chart which you can print and keep in front of you for quick reference while you are playing.

To download the Starting Hands Chart right click on the link and select save target as.

It is a PDF file, so to view and print this you will need the free Adobe Acrobat Reader. If you don’t have this you can download it here.

Starting Hands Chart Desktop Wallpaper

Use this as your computer desktop wallpaper. It is designed so that whilst you are playing poker, you can place your poker table window over the Poker Professor logo and all the charts will be visible around the table. Neat huh!

To download the Starting Hands Wallpaper right click on the link and select save target as.

To set as your desktop wallpaper, right click on the file you have just downloaded and select “Set As Desktop Background”.

The wallpaper is optimised for a desktop screen size of 1920×1080 as this is the most common. It should work with most other desktop sizes as well as windows should automatically resize it for you.

Starting Hand Examples

Lets take a look at some example starting hands and walk through what the charts are telling you to do and what thought process to follow.

Example Hand 1

You are sitting in early position and are dealt A J. You are first to act and so nobody has bet before you.

• What group is my hand in – AJ is a Group E hand
• What situation am I in – Nobody has raised before me so UNRAISED
• What position am I in – Early Position

So from the answers to the above questions we look at the UNRAISED Action chart, and look in the column for Early Position. You will see that Group E is not shown in that column so we are not allowed to play a Group E hand in Early position in this situation and so we would fold this hand.

Example Hand 2

You are sitting in early position and are dealt A K. You are first to act and so nobody has bet before you.

List Of Poker Hands Pdf

• What group is my hand in – AK is a Group B hand
• What situation am I in – I am first to act so it is UNRAISED
• What position am I in – Early Position

So from the above we look at the UNRAISED Action chart, and look in the column for Early Position. You will see that with a group B hand we are told to make an opening raise. So we would enter the hand by making a Raise (We will look at details of how much to raise later in the lesson).

Example Hand 3

You are sitting in Mid Position and are dealt A A. A Player in early position has raised the pot up to 3 times the Big Blind.

• What group is my hand in – AA is the best starting hand and therefore a Group A hand
• What situation am I in – There has been a raise by a player in early position, so it has been RAISED
• What position am I in – Mid Position

So, we look at the RAISED Action chart, and look in the column for Mid Position. You will see that with a group A hand we are told to make a Re-Raise. So we would enter the hand by making a Re-Raise. (We will look at details of how much to raise later in the lesson)

Example Hand 4

You are sitting in Mid Position and are dealt 9 9. A Player in early position has raised the pot up to 3 times the Big Blind.

• What group is my hand in – 99 is a Group D hand
• What situation am I in – There has been a raise by a player in early position, so it has been RAISED
• What position am I in – Mid Position

So, again we look at the RAISED Action chart, and look in the column for Mid Position. You will see that we are not allowed to play an already RAISED pot in Mid Position with a group D hand. So we fold this hand.

Example Hand 5

You are sitting in Late Position and are dealt 8 7. Two Players acting before you have limped in and called the big blind.

• What group is my hand in – 87s is a Group H hand
• What situation am I in – There has been two limpers, but no raise, so it is UNRAISED
• What position am I in – Late Position

List Of Best Poker Starting Hands

So, we look at the UNRAISED Action chart, and look in the column for Late Position. You will see that we are allowed to Call a Multi-way pot with a group H hand (multiple players playing the hand). As two people have already called and the blinds will likely also call we can call the big blind and play the hand. So we would call the big blind on this hand.

How much should I Raise?

An opening Raise in general should be between 3 to 4 times the Big Blind. Anywhere in this range is ok, and as guide to start with I would raise the following amounts:

• When you are in EARLY POSITION Raise 4 times the Big Blind
• When you are in MID POSITION Raise 3.5 times the Big Blind
• When you are in LATE POSITION Raise 3 times the Big Blind

You should mix and match the size of your raises to prevent your opponents getting a read on your betting patterns, but the above can act as a general guide whilst you get used to your new strategy.

Order Of Poker Hands

The reason to Raise more in Early position is because we are out of position and want to put as much pressure on our opponents as we can.

How much should I Re-Raise?

A Re-Raise should in general be between 2 – 4 times the original Raise, As a guide:

• When it has been Raised from EARLY POSITION Raise 2 times the Raise
• When it has been Raised from MID POSITION Raise 3 times the Raise
• When it has been Raised from LATE POSITION Raise 4 times the Raise

The reason for this is it is more likely that a player in late position has raised with a weaker hand than a player in Early position.

Practise Time

Well, that was a lengthy lesson and a lot to take in. Don’t worry, with practise it will start to become second nature, and that is exactly what you should do now with the first stage of your bankroll challenge.

Poker Bankroll Challenge: Stage 1

List Of Poker Hands Printable

• Stakes: $0.02/$0.04
• Buy In: $3 (75 x BB)
• Starting Bankroll: $25
• Target: $3 (1 x Buy In)
• Finishing Bankroll: $28
• Estimated Sessions: 1

Poker Best Hands In Order

Use this exercise to get used to selecting which starting hands to play and which not to play according to the Starting Hands chart and get used to understanding what position you are in at the table. Don’t get too carried away at this stage though, play conservatively and be aware that someone may have a better hand than you. We are going to learn in more detail about betting after the flop later in the course.