In the previous article on working out preflop hand probability, we worked out the likelihood of being dealt different combinations of starting hands before the flop.

- Poker Odds Before The Flop Rule
- Poker Odds Before The Flop Season
- Poker Odds Before The Flop Game
- Poker Odds Before The Flop End
- Poker Odds Before Flop

In this article, I will cover the **basics of working out the probabilities behind various possible flops.** I'll go ahead and cover the probability basics first in case you missed it in the preflop probability article.

Texas Hold'em Cheat SheetOdds Based on Outs after the Flop. If after the flop, you have: Two outs: Your odds are 11 to 1 (about 8.5 percent) A common scenario would be when you have a pair and you are hoping your pair becomes a three-of-a-kind (a set). Poker is gambling and you make your own desicions as to how to play the game regardless of what you read here or anywhere else and you are responsible for checking your own facts before getting in over your head. A bet after the flop by a player who did not take the lead in betting before the flop (and when the player that did take the lead in betting before the flop declined to act). Compare with continuation bet prop, proposition player A player who gets paid an hourly rate to start poker games or to help them stay active. Your Texas Hold'em poker odds are given below for hitting a draw by the river with a given number of outs after the flop and turn, and examples of draws with specified numbers of poker outs given. Example: if you hold 22 and the flop does not contain a 2, the odds of hitting a 2 on the turn is 22:1 (4%).

### Poker Odds Before The Flop Rule

- Probability calculations quick links.

## A few probability basics.

When working out flop probabilities, the main probabilities we will work with are **the number of cards left in the deck** and **the number of cards we want to be dealt on the flop**. So for example, if we were going to deal out 1 card:

- The probability of dealing a 7 would be 1/52 - There is one 7 in a deck of 52 cards.
- The probability of dealing any Ace would be 4/52 - There four Aces in a deck of 52 cards.
- The probability of dealing any would be 13/52 - There are 13 s in a deck of 52 cards.

In fact, the probability of being dealt any random card (not just the 7) would be 1/52. This also applies to the probability being dealt any random value of card like Kings, tens, fours, whatever (4/52) and the probability of being dealt any random suit (13/52).

Each card is just as likely to be dealt as any other - no special priorities in this game!

### The numbers change for future cards.

A quick example... let's say we want to work out the probability of being dealt a pair of sevens.

- The probability of being dealt a 7 for the first card will be 4/52.
- The probability of being dealt a 7 for the second card will be 3/51.

Notice how the probability changes for the second card? After we have been dealt the first card, there is now 1 less card in the deck making it 51 cards in total. Also, after already being dealt a 7, there are now only three 7s left in the deck.

Always try and take care with the numbers for future cards. The numbers will change slightly as you go along.

### Working out probabilities.

- Whenever the word 'and' is used, it will usually mean multiply.
- Whenever the word 'or' is used, it will usually mean add.

This won't make much sense for now, but it will make a lot of sense a little further on in the article. Trust me.

## Total number of flop combinations.

First of all, lets work out the total number of possible flop combinations. In other words, we will just be working out the probability of 'any random flop'.

To work out this probability we simply multiply the probability of 3 individual cards being dealt.

- (random card) * (random card) * (random card)
- (1/52) * (1/51) * (1/50) = 132,600 possible flops.

Pretty big combination of cards huh? However, we've omitted the fact that we know our 2 holecards, so there will be two less known cards in the deck when we are dealing the flop. So if we amend this calculation by starting at 50 instead of 52:

P = (1/50) * (1/49) * (1/48)

P = 1/117,600.

Better, but this 1/117,600 probability is with exact cards in order. In Texas Hold'em it does not make a difference whether the flop comes A K Q or A Q K. So to account for this we multiply this fraction by 6 (1*2*3 = 6).

P = 1/117,600 * 6

P = 1/19,600.

The order of cards on the flop makes no difference, so multiply the probability by 6 to account for this (1 * 2 * 3 = 6 - this is math probability stuff). Don't worry if you don't know why we do this, just take it as it is.

This means that the probability of the flop being A K Q in any order is 1/19,600 - which is exactly the same probability as the flop coming something like 2 5 9 in any order.

So in total there are 19,600 different possible flops in Texas Hold'em.

## Probability of specific flops.

To work out the probability of specific flops with the cards in any order we simply multiply the probabilities of each of those cards being dealt.

Multiply the 3 probabilities together.

So let's say we want to find **the probability of flopping a heart flush**.

- There are 2 hearts in our hand.
- There are 11 hearts left in a deck of 50.

P = (11/50) * (10/49) * (9/48)

P = 990/117600 = 1/119

In this example we do not need to multiply the final probability by 6. This is because the order of the cards and their probabilities are important, as the overall probabilities decrease as each heart is dealt.

## Overview of working out flop probabilities.

This is a really basic article for working out flop probabilities in Texas Hold'em. Think of it as more of a taster for working out probabilities on the flop to help you get your feet wet.

If I were to continue with probabilities, I would be delving deeper in to mathematics and further away from poker. That wouldn't necessarily be a bad thing, but my maths is a bit rusty and it's not going to directly improve your game, so I'll stop for now. Maybe I'll address it in a future article, but for now this is as far as I'm going to go.

If you're really interested in the mathematics of the game, try the book: The Mathematics of Poker by Bill Chen. It's definitely not a light read, but it's very interesting if you enjoy the maths side of the game. For other books, try the poker books section.

### Other useful articles.

- Poker mathematics.
- Pot odds.
- Equity in poker.

Go back to the poker odds charts.

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Comments

This article covers ways to improve your results after the flop playing Texas holdem, but you can use the same information to improve your play in any poker game with a flop, like Omaha. Many poker strategy articles focus on playing tight before the flop, and playing all of your hands in an aggressive manner.

### Poker Odds Before The Flop Season

But the best Texas holdem players know how to play well after the flop, and this is where they make most of their profits. While playing tight before the flop is very important, it’s only one of many areas you need to do well in if you want to win more playing poker.

Aggressive play is good in many situations, but the best poker players understand when they should be aggressive and when it’s more profitable to back off and let an opponent lead the way. It’s dangerous to blindly follow any piece of poker advice, because there’s almost always an exception.

Here’s a list of four ways you can improve you post flop play in Texas holdem.

## 1 – Fold More Pre Flop Hands

The best way to improve your post flop play in Texas holdem is to put yourself in the best position to win at the start of the hand. This means that you need to stop playing hands that don’t have a good chance to win after the flop.

You’re going to learn more about expectation and expected value in a different section, but you need to look at every starting hand and try to determine if it’s profitable to play it. In other words, if you were in the exact same situation with your current starting hand hundreds of times, would you make more than you lose if you enter the pot every time.

Most poker players don’t look at starting hands this way, but this is actually the exact situation you’re in. Over the course of your life you’re going to play many poker hands. Instead of playing hundreds or thousands of different playing sessions; you’re actually playing one long game of poker that never ends until you die.

This means that you may play the same starting hand hundreds or thousands of times.

Most Texas holdem players know that pocket aces and kings are profitable to play in the long run, and hands like seven two off suit aren’t profitable. But what do you know about pocket sevens? Are they profitable in the long run? Will this effect your casino bankroll management?

In some situations pocket sevens are profitable, and in some situations they aren’t. The key that unlocks your long term profits is learning when questionable hands can be played for a profit and when they can’t.

Many things go into learning this, but for now you can start improving by playing fewer starting hands. Until you start winning consistently, only play your best starting hands, and only play most hands from late position.

By improving the average value of your starting hands, you improve your chances to have a good hand after the flop.

## 2 – Use Your Position Better

The best Texas holdem poker players are always aware of their position and know how to use it to their advantage. Winning poker players know that they can only play their top starting hands in early and middle position, because these positions make you weak and you can be manipulated by players in later positions.

On the other hand, when you play most of your hands with position on your opponents you can manipulate them and use your position to your advantage. Consider all of the advantages that having position at the poker table gives you.

The largest advantage of having position is that you have more information than your opponent or opponents have when you have to act. You already know what your opponents did before you have to act, so you have additional information. This is a strong advantage that winning poker players understand.

Another advantage is when you’re the last to act; you have more control over the pot size.

Learn how position changes the value of your starting hands and it makes it easier to decide which hands to see the flop with and which hands you should fold early.

## 3 – Pot Odds and Expectation

The most profitable tools in every poker player’s belt if they want to win more are pot odds and expectation. And these tools are of the most value after the flop.

When you see the flop, you know the value of five out of the seven total cards that you’re going to use to make your best five card hand. You also know how your opponents have played the hand up to this point, so you have a large amount of information.

With this information you can start formulating the odds of winning the hand, make correct decisions based on pot odds when one of your opponents makes a bet, and use expectation, or expected value, to make all of your decisions.

Pot odds are a simple way to determine if you should call a bet. You compare the odds of winning the hand, either with your current hand or improving to a better hand, with the size of the bet against the size of the pot. Every winning Texas holdem player uses pot odds to some degree, so if you’re not using them now the best way to improve is to learn how to use pot odds.

Expectation or expected value is the most important concept you need to learn. Expected value can be assigned to every decision you make at the Texas holdem tables. It starts before you receive your starting hand, and runs throughout each hand until the showdown.

Every decision you make at the poker table is either profitable or unprofitable. When you raise with pocket aces before the flop it’s profitable because in the long run you’re going to make more than you lose. If you limp into the pot with two seven, it’s a negative expectation play because you’re going to lose more than you win in the long run.

When you make decisions based on pot odds after the flop, you’re using expected value. If the pot odds are correct, it’s profitable to stay in the hand. When the pot odds aren’t correct, the most profitable long term play is to fold.

The odds are high that you’re not currently using expectation and expected value as well as you can. Learn how to improve your use of expectation and it automatically improves your post flop results at the Texas holdem tables.

## 4 – Bluff and Fold Less

If you only see the flop with hands that show a long term profit, use your position at the table correctly, and use pot odds and expectation, most of the hard work to becoming a profitable post flop Texas holdem player is done. The only two things you need to know to complete your transformation are you need to bluff less and fold less after the flop.

The reason I include both of these things in the same section is because they’re closely related.

### Poker Odds Before The Flop Game

As it turns out, if you play your hand correctly through the turn, your decision on whether to fold on the river should almost always be made before you see the river. If you know you’re behind and have received the correct pot odds to stay in the hand, you either hit your hand and bet or miss your hand and fold.

If you reach the river and have a decent hand, it’s rarely correct to fold to a reasonable sized bet. You only have to catch your opponent bluffing a small percentage of the time when you have a decent hand to make a call profitable.

This is also why you need to bluff less after the turn. Your opponent or opponents only need to catch you bluffing a small percentage of the time in order for bluffing to be a bad play. Of course, there’s a big difference between making a semi bluff on the flop or turn and making a naked bluff on the river.

Semi bluffs are often profitable, but naked bluffs are dangerous. The only time you should consider making a naked bluff is when it has a very high chance of success.

When it comes to folding on the river, if you find that you have to make this decision often, you need to consider what you’re doing before the river that’s creating the issue. This is almost always an indication that you’re making mistakes earlier in the hand.

## Conclusion

### Poker Odds Before The Flop End

The best place to start improving your post flop results at the Texas holdem tables is to stop playing weak starting hands. Learn how to use your table position to increase your chances to win, fold less on the river, and bluff less after the flop and your results will also improve.

### Poker Odds Before Flop

Finally, learn how to use pot odds and expectation and you’re going to see immediate improvements. Few poker players use pot odds and expectation; and few poker players win in the long run. These two things are related, and if you want to win you’re going to need to start doing what winning players are doing.