How To Learn Poker Math

Texas Holdem Math. Is poker a game of skill or chance? This question has been discussed and argued in many places and is the center of the arguments for and against legalizing Texas holdem and other forms of poker in many places, including online. The answer to this question boils down to the mathematics behind the game. Math skills in poker can be used in a variety of situations. However, for the most part, you are likely to make use of poker calculations when you are about to draw a major hand, such as a flush or a straight.

How to Start Learning Poker Math

It is time to begin learning poker math. We will take it slowly. In this Juicy Stakes Poker review, we will talk about odds—the chance that something will happen—and equity. These are not the only concepts involved in poker math but they are a good place to start.

Mathematicians Tend to Be Eggheads

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Sync The Math With Preflop Plays. While much of this workbook focuses on poker math, almost 1/3 of the book focuses on pairing those math skills up with your preflop playbook. This means taking a technical look at everything from open-raising to 3betting to going all-in preflop. If you'd prefer something more tangible, any beginner's poker book (Theory of Poker, Professional No Limit Holdem) will include a chapter on basic poker math. For learning about the next level of poker math (EV, ranges and equity), most introductory poker books will give you a good starting point. Poker Math is 40% of the game (or more). One awesome way to gain a competitive edge is to learn the math and how to apply it effectively with the rest of your game. That is exactly what this course is designed to do. Mastering Poker Math is a Results Based Course that has been created to help Transform Your Game.

This is as cliche-ish as anything about poker! People who try to explain to laypeople the basic math get bogged down very quickly in numbers. So, to simplify things, we need first of all to know how many possible combinations there are on the two cards every player is dealt before the flop.

Start with the ace. There are 12 cards that aren’t an ace so there are 12 non-pair combinations that have an ace per suit. There are, after all, four suits. So, there are 48 non-pair combinations possible to go along with an ace.

Without working this out for every card, we arrive at 1326 total combinations. It is important to divide these combinations into the three categories they fall into.

Pocket Pairs

There will be about 6% pairs. Of those pairs, only about one third will be of a high card—Jack to Ace. A pair of Jacks is the weakest of the high card pairs. The best pairs are aces and Kings and they represent only about one third of one percent of all hands.

Players who never bet in early position unless they get a pair of aces or kings or ace-king suited, will fold almost every hand they are dealt before the flop.

Suited and Non-suited Cards

Let’s say that you don’t have a pocket pair. Then the two cards you do have might be suited and they might be unsuited. Since there are four suits, we can expect that three times as many non-pair combinations will be unsuited and, in fact, that is correct!

You will get a lot more unsuited cards than suited. Now, are all suited cards equal? Are all unsuited cards equal? The answer to both questions is NO!

Suited cards that are consecutive are a lot more valuable than suited cards that for all practical purposes exist on the other side of the planet from each other such as the 2 and the 9!

What are the Odds of Getting a Good Hand before the Flop?

The simplest answer is: Not very good! If that were all that poker math could teach us it wouldn’t be of much use. This is actually just the top layer of what poker math teaches and informs us.

At this stage, we can learn from the odds of getting any given hand that we have to learn to play less than optimum hands! If we always play only top hands, all of our opponents will know that we have a hand in a very narrow range and will probably fold in the face of the strength of our hand.

Poker math at this stage teaches us that fooling our opponents into thinking that we have a stronger hand than we actually do have is very important.

Equity

When most people buy a house, they take out a mortgage. A mortgage is a loan from a bank to a home buyer. The buyer then repays the loan over a very long time—usually from 20 to 30 years.

The house does not actually belong to the buyer! The house actually belongs to the bank but the bank can take the house and sell it to someone else only if the buyer fails to pay the mortgage over a specific period of time.

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In the early years of a mortgage, the monthly payments are almost all interest on the loan. This is how the bank gets its money back as quickly as possible. Some of the monthly payment is called “equity”. It represents the amount of the house that is actually under the ownership of the buyer.

Equity in Poker

Equity in poker is a lot easier to understand. It is the percentage of the pot that theoretically belongs to any player based on his or her hand and the hand of any opponent who stays in the hand.

This is quite easy to understand with one very important exception. First, look at a pair of twos against a pair of aces. The pair of aces is about five times as strong as the pair of twos. A similar analysis holds for all hands where one player has a low hand and another has a high hand.

The big exception here is that an ace-king combination is a lot stronger than an ace-queen. A lot of players see ace-queen and think that they have a powerhouse. In many hands they do but in another large set of hands, they have a far weaker hand!

The equity of an ace-queen against even an ace-king is about one third. The ace-king is three times as strong as the ace-queen.

Range Based on What We Have Learned

The simplest aspect of range is now available to us. If we have a pair, the chances that any opponent will have the same pair are very low. The chance that an opponent will also have a pair is almost the same as the chance that we would have been dealt a pair.

It is only fractionally less since we have taken out of the deck one of the possible pairs.

What happens when we have the highest pair with cards that are not royals or aces? This is a pair of tens. The only pairs that can defeat this hand in the pre-flop stage are a pair of jacks, queens, kings, or aces and the chances that an opponent will have one of these pairs is only about 7%.

It means that if you know your opponents well, a pair of tens might be a very strong hand before the flop.

What if I have an Ace?

If you have any of the three royals or an ace, even if you don’t have a pair, the chances that an opponent will have a pair that beats you are a lot lower than the chances they have a pair that beats a pair of tens. That’s because you have one of the high cards! If you have two of the high cards, your opponents have even less chance to have a pair that beats you. Therefore, a hand with an ace is a strong hand.

Is it Possible to Make Poker Math Too Complicated?

It is in spades! Some people will shower charts on players and will expect them to learn these charts post haste. We will do our best to make poker math understandable without resorting to a surfeit of complex charts!

You can be certain that Juicy Stakes Poker will do everything we can to make poker as fun as it can be and we’ll also do our best to help you improve your game!

This is a very important lesson and can also be quite intimidating to a lot of people as we are going to discuss Poker Math!

But there is no need for you to be intimidated, Poker Maths is very simple and we will show you a very simple method in this lesson.

You won’t need to carry a calculator around with you or perform any complex mathematical calculations.

What is Poker Math?

As daunting as it sounds, it is simply a tool that we use during the decision making process to calculate the Pot Odds in Poker and the chances of us winning the pot.

Remember, Poker is not based on pure luck, it is a game of probabilities, there are a certain number of cards in the deck and a certain probability that outcomes will occur. So we can use this in our decision making process.

Every time we make a decision in Poker it is a mathematical gamble, what we have to make sure is that we only take the gamble when the odds are on in our favour. As long as we do this, in the long term we will always come out on top.

When to Use Poker Maths

Poker Maths is mainly used when we need to hit a card in order to make our hand into a winning hand, and we have to decide whether it is worth carrying on and chasing that card.

To make this decision we consider two elements:

1. How many “Outs” we have (Cards that will make us a winning hand) and how likely it is that an Out will be dealt.
2. What are our “Pot Odds” – How much money will we win in return for us taking the gamble that our Out will be dealt

We then compare the likelihood of us hitting one of our Outs against the Pot Odds we are getting for our bet and see if mathematically it is a good bet.

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The best way to understand and explain this is by using a hand walk through, looking at each element individually first, then we’ll bring it all together in order to make a decision on whether we should call the bet.

Consider the following situation where you hold A 8 in the big blind. Before the flop everyone folds round to the small blind who calls the extra 5c, to make the Total pot before the Flop 20c (2 players x 10c). The flop comes down K 9 4 and your opponent bets 10c. Let’s use Poker Math to make the decision on whether to call or not.

Poker Outs

When we are counting the number of “Outs” we have, we are looking at how many cards still remain in the deck that could come on the turn or river which we think will make our hand into the winning hand.

In our example hand you have a flush draw needing only one more Club to make the Nut Flush (highest possible). You also hold an overcard, meaning that if you pair your Ace then you would beat anyone who has already hit a single pair on the flop.

From the looks of that flop we can confidently assume that if you complete your Flush or Pair your Ace then you will hold the leading hand. So how many cards are left in the deck that can turn our hand into the leading hand?

• Flush – There are a total of 13 clubs in the deck, of which we can see 4 clubs already (2 in our hand and 2 on the flop) that means there are a further 9 club cards that we cannot see, so we have 9 Outs here.
• Ace Pair – There are 4 Ace’s in the deck of which we are holding one in our hand, so that leaves a further 3 Aces that we haven’t seen yet, so this creates a further 3 Outs.

So we have 9 outs that will give us a flush and a further 3 outs that will give us Top Pair, so we have a total of 12 outs that we think will give us the winning hand.

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So what is the likelihood of one of those 12 outs coming on the Turn or River?

Professor’s Rule of 4 and 2

An easy and quick way to calculate this is by using the Professor’s rule of 4 and 2. This way we can forget about complex calculations and quickly calculate the probability of hitting one of our outs.

The Professor’s Rule of 4 and 2

• After the Flop (2 cards still to come… Turn + River)
  Probability we will hit our Outs = Number of Outs x 4
• After the Turn (1 card to come.. River)
  Probability we will hit our Outs – Number of Outs x 2

So after the flop we have 12 outs which using the Rule of 4 and 2 we can calculate very quickly that the probability of hitting one of our outs is 12 x 4 = 48%. The exact % actually works out to 46.7%, but the rule of 4 and 2 gives us a close enough answer for the purposes we need it for.

If we don’t hit one of our Outs on the Turn then with only the River left to come the probability that we will hit one of our 12 Outs drops to 12 x 2 = 24% (again the exact % works out at 27.3%)

To compare this to the exact percentages lets take a look at our poker outs chart:

As you can see the Rule of 4 and 2 does not give us the exact %, but it is pretty close and a nice quick and easy way to do the math in your head.

Now lets summarise what we have calculated so far:

• We estimate that to win the hand you have 12 Outs
• We have calculated that after the flop with 2 cards still to come there is approximately a 48% chance you will hit one of your outs.

Now we know the Odds of us winning, we need to look at the return we will get for our gamble, or in other words the Pot Odds.

Pot Odds

When we calculate the Pot Odds we are simply looking to see how much money we will win in return for our bet. Again it’s a very simple calculation…

Pot Odds Formula

Pot Odds = Total Pot divided by the Bet I would have to call

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What are the pot odds after the flop with our opponent having bet 10c?

• Total Pot = 20c + 10c bet = 30 cents
• Total Bet I would have to make = 10 cents
• Therefore the pot odds are 30 cents divided by 10 cents or 3 to 1.

What does this mean? It means that in order to break even we would need to win once for every 3 times we lose. The amount we would win would be the Total Pot + the bet we make = 30 cents + 10 cents = 40 cents.

Break Even Percentage

Now that we have worked out the Pot Odds we need to convert this into a Break Even Percentage so that we can use it to make our decision. Again it’s another simple calculation that you can do in your head.

Break Even Percentage

Break Even Percentage = 100% divided by (Pot odds added together)

Let me explain a bit further. Pot Odds added together means replace the “to” with a plus sign eg: 3 to 1 becomes 3+1 = 4. So in the example above our pot odds are 3 to 1 so our Break Even Percentage = 100% divided by 4 = 25%

Note – This only works if you express your pot odds against a factor of 1 eg: “3 to 1” or “5 to 1” etc. It will not work if you express the pot odds as any other factor eg: 3 to 2 etc.

So… Should You call?

So lets bring the two elements together in our example hand and see how we can use the new poker math techniques you have learned to arrive at a decision of whether to continue in the hand or whether to fold.

To do this we compare the percentage probability that we are going to hit one of our Outs and win the hand, with the Break Even Percentage.

Should I Call?

• Call if…… Probability of Hitting an Out is greater than Pot Odds Break Even Percentage
• Fold if…… Probability of Hitting an Out is less than Pot Odds Break Even Percentage

Our calculations above were as follows:

• Probability of Hitting an Out = 48%
• Break Even Percentage = 25%

If our Probability of hitting an out is higher than the Break Even percentage then this represents a good bet – the odds are in our favour. Why? Because what we are saying above is that we are going to get the winning hand 48% of the time, yet in order to break even we only need to hit the winning hand 25% of the time, so over the long run making this bet will be profitable because we will win the hand more times that we need to in order to just break even.

Hand Walk Through #2

Lets look at another hand example to see poker mathematics in action again.

Before the Flop:

• Blinds: 5 cents / 10 cents
• Your Position: Big Blind
• Your Hand: K 10
• Before Flop Action: Everyone folds to the dealer who calls and the small blind calls, you check.

Two people have called and per the Starting hand chart you should just check here, so the Total Pot before the flop = 30 cents.

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Flop comes down Q J 6 and the Dealer bets 10c, the small blind folds.

Do we call? Lets go through the thought process:

How has the Flop helped my hand?
It hasn’t but we do have some draws as we have an open ended straight draw (any Ace or 9 will give us a straight) We also have an overcard with the King.

How has the Flop helped my opponent?
The Dealer did not raise before the flop so it is unlikely he is holding a really strong hand. He may have limped in with high cards or suited connectors. At this stage our best guess is to assume that he has hit top pair and holds a pair of Queens. It’s possible that he hit 2 pair with Q J or he holds a small pair like 6’s and now has a set, but we come to the conclusion that this is unlikely.

How many Outs do we have?
So we conclude that we are facing top pair, in which case we need to hit our straight or a King to make top pair to hold the winning hand.

• Open Ended Straight Draw = 8 Outs (4 Aces and 4 Nines)
• King Top Pair = 3 Outs (4 Kings less the King in our hand)
• Total Outs = 11 Probability of Winning = 11 x 4 = 44%

What are the Pot Odds?
Total Pot is now 40 cents and we are asked to call 10 cents so our Pot odds are 4 to 1 and our break even % = 100% divided by 5 = 20%.

Decision
So now we have quickly run the numbers it is clear that this is a good bet for us (44% vs 20%), and we make the call – Total Pot now equals 50 cents.

Turn Card

Turn Card = 3 and our opponent makes a bet of 25 cents.

After the Turn Card
This card has not helped us and it is unlikely that it has helped our opponent, so at this point we still estimate that our opponent is still in the lead with top pair.

Outs
We still need to hit one of our 11 Outs and now with only the River card to come our Probability of Winning has reduced and is now = 11 x 2 = 22%

Pot Odds
The Total Pot is now 75 cents and our Pot odds are 75 divided by 25 = 3 to 1. This makes our Break Even percentage = 100% divided by 4 = 25%

Decision
So now we have the situation where our probability of winning is less than the break even percentage and so at this point we would fold, even though it is a close call.

Summary

Well that was a very heavy lesson, but I hope you can see how Poker Maths doesn’t have to be intimidating, and really they are just some simple calculations that you can do in your head. The numbers never lie, and you can use them to make decisions very easy in Poker.

You’ve learnt some important new skills and it’s time to practise them and get back to the tables with the next stage of the Poker Bankroll Challenge.

Poker Bankroll Challenge: Stage 3

• Stakes: $0.02/$0.04
• Buy In: $3 (75 x BB)
• Starting Bankroll: $34
• Target: $9 (3 x Buy In)
• Finishing Bankroll: $43
• Estimated Sessions: 3

Use this exercise to start to consider your Outs and Pot Odds in your decision making process, and add this tool to the other tools you have already put into practice such as the starting hands chart.