Texas Holdem - Odds and Probabilities It can be handy to know the odds and probabilities of being dealt various card combinations in texas hold'em. Learning the odds so that you know when and how much to bet, is probably one of the most important lessons in poker. Texas Holdem takes a minute to learn and a lifetime to master. Learn how to calculate your pot odds and becoming a winning player.

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.

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.

## 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.

Siege social distribution casino france. 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.

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.

### Related Lessons

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.

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If you want to learn how to play Texas hold'em games, then you need to start from the basic rules and hands. That's exactly what you'll find on this beginner's guide to the game.

Texas hold'em is a simple poker game, but it can be daunting to get to grips with.

But don't let that put you off. By the time you are down with this beginner's guide to Texas hold'em, you will know:

## 1. What Is Texas Hold'em Poker?

Texas Hold'em is the most popular of all poker variations.

All of the marquee tournaments around the world (including those played at the World Series of Poker, the World Poker Tour, the and the European Poker Tour) feature the no-limit variation of this game.

Texas hold'em is so popular that is the only poker game many players will ever learn.

It takes a moment to learn, but a lifetime to master.

Discovering how to play Texas hold'em poker is not difficult and the simplicity of its rules, gameplay, and hand-ranking all contribute to the popularity of the game.

However, don't let the simplicity of the game mislead you.

The number of possible situations and combinations is so vast that Texas hold'em can be an extremely complex game when you play at the highest levels.

If you are approaching the game of Texas hold'em for the first time, starting from the basic rules of the game is key. Not only these are the easiest ones to learn, but they are also essential to understand the gameplay and, later on, the game's basic strategy.

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## 2. Texas Hold'em Rules

So how do you play Texas hold'em?

The goal of a Texas hold'em game is to use your hole card and in combination with the community cards to make the best possible five-card poker hand.

Hold'em is not unlike other poker games like five-card draw.

However, the way players construct their hands in Texas hold'em is a little different than in draw poker.

It's always possible a player can 'bluff' and get others to fold better hands.

• In a game of Texas hold'em, each player is dealt two cards face down (the 'hole cards')
• Throughout several betting rounds, five more cards are (eventually) dealt face up in the middle of the table
• These face-up cards are called the 'community cards.' Each player is free to use the community cards in combination with their hole cards to build a five-card poker hand.

While we will see each betting round and different phase that forms a full hand of a Texas hold'em game, you should know that the five community cards are dealt in three stages:

• The Flop: the first three community cards.
• The Turn: the fourth community card.
• The River:The fifth and final community card.

Your mission is to construct your five-card poker hands using the best available five cards out of the seven total cards (the two hole cards and the five community cards).

You can do that by using both your hole cards in combination with three community cards, one hole card in combination with four community cards, or no hole cards.

If the cards on the table lead to a better combination, you can also play all five community cards and forget about yours.

In a game of Texas hold'em you can do whatever works to make the best five-card hand.

If the betting causes all but one player to fold, the lone remaining player wins the pot without having to show any cards.

For that reason, players don't always have to hold the best hand to win the pot. It's always possible a player can 'bluff' and get others to fold better hands.

If two or more players make it all of the way to the showdown after the last community card is dealt and all betting is complete, the only way to win the pot is to have the highest-ranking five-card poker hand.

Now that you know the basics of Texas hold'em and you start to begin gaining an understanding of how the game works, it's time to get into some specifics.

These include how to deal Texas hold'em and how the betting works.

Basic Rules Key Takeaways:

• A game of Texas hold'em feature several betting rounds
• Players get two private and up to five community cards
• Unless all players abandon the game before the showdown, you need the highest poker hand to win

## How to Play

Let's have a look at all the different key aspects of a Texas hold'em game, including the different positions at the table and the betting rounds featured in the game.

### The Button

The play moves clockwise around the table, starting with action to the left of the dealer button.

The 'button' is a round disc that sits in front of a player and is rotated one seat to the left every hand.

When playing in casinos and poker rooms, the player with the dealer button doesn't deal the cards (the poker room hires someone to do that).

In when you play poker home games with friends the player with the button usually deals the hands.

The button determines which player at the table is the acting dealer.

The first two players sitting to the immediate left of the button are required to post a 'small blind' and a 'big blind' to initiate the betting.

From there, the action occurs on multiple streets:

• Preflop
• Flop
• Turn
• River

Each one of these moments (or 'streets' in the game's lingo) is explained further below.

The button determines which player at the table is the acting dealer.

In Texas hold'em, the player on button, or last active player closest to the button receives the last action on all post-flop streets of play.

While the dealer button dictates which players have to post the small and big blinds, it also determines where the dealing of the cards begin.

The player to the immediate left of the dealer button in the small blind receives the first card and then the dealer pitches cards around the table in a clockwise motion from player to player until each has received two starting cards.

READ ALSO: Poker Positions Explained: the Importance of Position in Poker

### The Blinds

Before every new hand begins, two players at the table are obligated to post small and big blinds.

The blinds are forced bets that begin the wagering.

Without these blinds, the game would be very boring because no one would be required to put any money into the pot and players could just wait around until they are dealt pocket aces (AA) and only play then.

The blinds ensure there will be some level of 'action' on every hand.

In tournaments, the blinds are raised at regular intervals. In cash games, the blinds always stay the same.

In tournaments, the blinds are raised at regular intervals.

• As the number of players keeps decreasing and the stacks of the remaining players keep getting bigger, it is a necessity that the blinds keep increasing throughout a tournament. [*]In cash games, the blinds always stay the same.

The player directly to the left of the button posts the small blind, and the player to his or her direct left posts the big blind.

The small blind is generally half the amount of the big blind, although this stipulation varies from room to room and can also be dependent on the game being played.

In a '\$1/\$2' Texas holdem game, the small blind is \$1 and the big blind is \$2.

### Probabilidades No Poker Texas Holdem

The first round of betting takes place right after each player has been dealt two hole cards.

The first player to act is the player to the left of the big blind.

This position referred to as 'under the gun' because the player has to act first. The first player has three options:

• Call: match the amount of the big blind
• Raise: increase the bet within the specific limits of the game
• Fold: throw the hand away

If the player chooses to fold, he or she is out of the game and no longer eligible to win the current hand.

Players can bet anywhere from the amount of the big blind (the minimum bet allowed) up to the total amount in the current pot.

The amount a player can raise to depends on the game that is being played.

In a game of no-limit Texas hold'em, the minimum opening raise must be at least twice the big blind, and the maximum raise can be all of the chips a player has in his or her stack (an 'all-in' bet).

There are other betting variations in hold'em poker.

In fixed-limit hold'em (or just 'limit hold'em), a raise is always exactly twice the big blind.

In pot-limit hold'em (played much less often than the other variations), players can bet anywhere from the amount of the big blind (the minimum bet allowed) up to the total amount in the current pot.

After the first player ('under the gun') acts, the play proceeds in a clockwise fashion around the table with each player also having the same three options — to call, to raise, or fold.

Once the last bet is called and the action is 'closed,' the preflop round is over and play moves on to the 'flop.'

### Second Betting Round: The Flop

After the first preflop betting round has been completed, the first three community cards are dealt and a second betting round follows involving only the players who have not folded already.

A check simply means to pass the action to the next player in the hand.

In this betting round (and subsequent ones), the action starts with the first active player to the left of the button.

Along with the options to bet, call, fold, or raise, a player now has the option to 'check' if no betting action has occurred beforehand.

A check simply means to pass the action to the next player in the hand.

Again betting continues until the last bet or raise has been called (which closes the action).

It also can happen that every player simply chooses not to be and checks around the table, which also ends the betting round.

### Third Betting Round: The Turn

Call – match the amount of the big blind

The fourth community card, called the turn, is dealt face-up following all betting action on the flop.

Once this has been completed, another round of betting occurs, similar to that on the previous street of play.

Again players have the option to options to check, bet, call, fold, or raise.

### Final Betting Round: The River

Fold – throw the hand away

The fifth community card, called the river, is dealt face-up following all betting action on the turn.

Once this has been completed, another round of betting occurs, similar to what took play on the previous street of play.

Once more the remaining players have the option to options to check, bet, call, fold, or raise.

After all betting action has been completed, the remaining players in the hand with hole cards now expose their holdings to determine a winner. This is called the showdown.

### The Showdown

Players construct their hands by choosing the five best cards from the seven available

The remaining players show their hole cards, and with the assistance of the dealer, a winning hand is determined.

The player with the best combination of five cards wins the pot according to the official poker hand rankings.

## 3. The Hands in Texas Hold'em

These hand rankings aren't specifically part of Texas hold'em rules, but apply to many different poker games.

• Royal Flush — five cards of the same suit, ranked ace through ten; e.g., AKQJ10
• Straight Flush — five cards of the same suit and consecutively ranked; e.g., 98765
• Four of a Kind — four cards of the same rank; e.g., QQQQ4
• Full House — three cards of the same rank and two more cards of the same rank; e.g., JJJ88
• Flush — any five cards of the same suit; e.g., AJ852
• Straight — any five cards consecutively ranked; e.g., QJ1098
• Three of a Kind — three cards of the same rank; e.g., 888K4
• Two Pair — two cards of the same rank and two more cards of the same rank; e.g., AAJJ7
• One Pair — two cards of the same rank; e.g., 1010942
• High Card — five unmatched cards; e.g., AJ1052 would be called 'ace-high'

Players construct their hands by choosing the five best cards from the seven available (their two hole cards and the five community cards).

If the board is showing 95K3A, a player with the two hole cards 9 would have two pair (aces and nines) and would lose to a player who has 99 for three of a kind (three nines).

Learning hold'em poker begins with understanding how hands are dealt and the order of play as described above.

### Tabla Probabilidades Poker Texas Holdem

Of course, learning Texas hold'em rules is just the beginning, as the next step is to learn strategy which involves understanding what constitutes good starting hand selection, the odds and probabilities associated with the game, the significance of position and getting to act last during those post-flop betting rounds, and many other aspects of the game.

## 4. How to Play Texas Hold'em Games Online

Now that you know how Texas Hold'em works, it's time to put the theory into practice and play your first games.

The best way to start playing Texas Hold'em is to start from these free poker games available online and then move up to the real money action only when you feel comfortable enough to do so.

All the 'must-have poker rooms' below offer free games to practice online.

If you are completely new to the game, you should go for play money options, first. These risk-free games with fake money are an excellent way to familiarise with the different moments of play and the betting rounds.

The play money games are a great way to learn more about the hand rankings and begin to read the board fast enough to take all the right decisions at the right time.

After that, you should more to the poker freerolls. These are free poker tournaments with actual prizes on tap that range from free money to free entries into more expensive real money games.

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### Probabilidades Texas Holdem Poker Wsop

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