• Poker Flop
• Poker Rules River Flop Shoes
• Flop River Poker Order
• Poker Odds On Flop

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%.

Playing after the river Your options on the turn After the flop, there are two more community cards to play – the turn and the river, each with a round of betting in between. Before you put more money in the pot, ask yourself: is it worth your while to see these cards or not? The river or river card is the final card dealt in a poker hand, to be followed by a final round of betting and, if necessary, a showdown. In Texas hold 'em and Omaha hold'em, the river is the fifth and last card to be dealt to the community card board, after the flop and turn.

The River – The Rules of the Poker River The river is the final round of the hand and the last chance for players to improve and do some betting. The dealer places one last card face up, the river card, in the middle of the table. On the flop, the dealer deals three community cards. On the turn and river, only one card is dealt per each street for a total of five cards by the end of the hand. To deal the cards properly on the flop, turn, or river the dealer has to follow the burn and turn rules of the game. First, before the community cards (or card) can be dealt, a. Poker Rules Flop Turn River will to get you back. Sometimes this is no registration free spins for existing players or just Poker Rules Flop Turn River a simple free cash bonus. Best way to find this bonuses is to look at our daily campaigns or keep an eye on your email inbox in case the casino send you bonus offers.

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.

The game of Texas Holdem is by far the most popular form of poker being played today. Its popularity is due in large part to its exposure on T.V. with the World Series of Poker being televised on ESPN. And ever since Chris Moneymaker won the Main Event for over $1 million back in 2003 playing Texas Hold Em, its popularity skyrocketed

But, the main reason people love playing Texas Hold Em, is the fact that it’s one of the easier games to learn and play. There’s a saying in the poker community that says Texas Hold Em takes a minute to learn, but a lifetime to master. This statement is very true and one of the reasons why I love it. While it only takes a few minutes to learn the rules, the game is always throwing a curve ball at you and you never stop learning new strategies.

While this article won’t make you a master at playing Texas Holdem online, it will teach everything you need to know about how to play the game. By the end of this reading, you will know exactly how to play hold Em and can start playing online, in a casino or start throwing your own home games.

The Goal

The general goal behind Texas Hold Em is to either showdown the best hand and beat your opponents, or to bluff them off the pot in order to win. Bluffing and stealing pots is a more advanced concept that will be discussed in further articles. For now, let’s just focus on the rules and how to play. We don’t want to get too far ahead of ourselves.

The overall plan is to use the 2 cards you are dealt in connection with the cards that are dealt face up in the middle to make the best5 card hand. You will see a total of 7 cards including the 2 in your hand, but may only use 5 of them. Don’t worry; well cover all this in more detail in just a few, so bear with us.

The basics

The beginning of a hand of Hold Em starts with everyone getting dealt 2 cards. These cards are face down so that no one can see them but you. The deal goes clockwise with each player getting one card at a time.

To determine who the dealer is a disc called the button, will be what determines who is dealer. The dealer will switch after every hand and the button disc will move clockwise to the next person.

When you play online or in a casino, this will be done automatically for you. There is no need to keep track of who deals next and who gets a card, everything is done. The only time you will need to keep track of all this is when you play a home game, but this will be easy after a round or 2.

The button will also dictate who becomes the small and big blind. These blinds are forced bets that the 2 players to immediate left of the button must place. The big blind will be the size of the table stakes and the small blind will be half the size. For example:

If the blinds are $1-$2, the big blind would be $2 and the small blind, $1.

Before any cards are dealt out, the blinds must be placed. Again, when playing online the software will do this for you.

A hand of Hold Em is broken down into sections that have names. There are as follows.

• Pre-flop
• Flop
• Turn
• River

You may hear these referred to as other names such as 4^th street, 5^th street and so on, but they all mean the same thing.

The pre-flop term refers to the action before any cards are dealt out.

The flop will be the first 3 cards dealt out by the dealer face up that are all community cards. These cards that are dealt face up can be used by all the players in the hand.

The turn is the next card dealt after the flop face up as well. Again, all players can use the turn card, along with the 3 on the flop to make the best hand with the 2 in their hand.

If you decide to raise, you must raise at least double the big blind. And, depending on what type of Hold Em you are playing will determine how much you can raise.

Betting Styles

There are 3 types of betting structures in Texas Holdem Poker: no limit, pot limit and limit. No limit is the most common and allows you to bet as much as you want so long as it’s on the table. If you have $100 in your stack, you can bet the full $100 at any given point in the hand.

Pot limit only lets you bet up to the amount in the pot. If the pot only has $10 in it, you can bet between $1 and $10. The amount you can bet will change as the pot grows, but as long as you don’t bet over the amount in the pot, you’ll be fine.

Limit Holdem has a fixed amount to bet during the hand based on the blinds. If the blinds are $1 and $2, you can bet $1 during the pre-flop and flop betting rounds. Then you must bet $2 on the turn and river.

Betting

Once all the cards dealt, players have their choice to bet, raise, or fold when it is their turn.

The player who is immediately to the right of the big blind will be first to act. This position is called under the gun or early position. This player may elect to fold their hand, call the amount of the big blind or raise.

Once the first player makes their decision, the action moves clockwise to the next player. This player will have the same choices depending on what happened before them. If everyone has folded their hand before you, you may still fold, call the big blind or raise.

If someone before you has raised, you must call their bet amount to stay in the hand. Even if the blinds are $1-$2, and a player bets $10, you must call the $100 to stay in the hand. You may still fold as well and of course you can raise the bet made.

Raising another players bet pre-flop is called a 3 bet in the poker world. There are rules as to what you can raise, but it’s simple. You must raise at least amount of the bet that you are raising. If a player bets $10, you must raise at least $10 to a total of $20.

Depending on which limit type you are playing will also decide how much you can raise. This was already covered in the betting structure section. Just to refresh quickly. If you’re playing no-limit, you raise as much as you wish. If it is l, you may only raise a set amount. If its pot limit, you can only raise up to the amount in the pot.

Once all the betting, folding and all players have made their decisions, we will move on to the flop.

I would like to note, that not every hand will make it to the flop. Often times, everyone will fold their hand which awards the player in the big blind, who is last to act, with the money from the blinds.

The Flop

The dealer will deal 3 cards out in the middle all face up that all players still in the hand can use with their own. The player who is closest to the left of the big blind on the flop will act first. If the player in the small blind or big blind is still in the pot, they will go first on the flop.

Whoevers turn it is will have 2 choices-check or bet. To check means that you don’t want to bet, yet you still keep your hand in the pot. You are not folding; you are in sense deferring to the other players left in the pot.

You may also bet if you so choose. The amount you can bet must be at least the amount of the big blind. It’s not recommended to bet so small, but this is a bit advanced to talk about betting strategy, but as a rule of thumb, betting the minimum is usually never a good idea.

If the player first to act bets, then all players in the pot can call this bet, fold or raise. If the first player checks, then all remaining players can check themselves, or bet.

Let’s use an example to clarify this.

Say you are first to act on the flop. You elect to bet and now it’s the other players turn. They must either call this bet to stay in the hand or raise. If they don’t want to stay in the hand, they can fold and you would win the money in the pot.

Now, if you check and the other player decides to bet, the action will be back on you. You must now decide whether or not you want to call or fold. You can also raise which is called check-raising and is considered very powerful.

If everyone in the hand checks, we would move on to the next card. If someone bets and all remaining players fold, the player who bet would win the money in the pot.

That’s the gist of the flop; now let’s move on to the turn.

The Turn

The turn is basically the same as the flop with one exception. Instead of 3 cards dealt out, only 1 is dealt face up. All players may use this card along with the 3 on the flop and the 2 in your hand as well.

The action is once again determined by who is closest to the left of the blinds or the person in the blinds. If the player who acted first on the flop had folded, but 2 players were still in the hand, the first to act on the turn would change to the next person who is closest to the left of the blinds.

The same exact choices you had on the flop will apply on the turn. You can check, bet, raise, check raise or fold.

The River

The final card dealt face up is called the river or sometimes fifth street. The same exact rules that applied to the turn and the flop and turn will apply to the river.

This will be where the winner is determined if no one folds as well. If everyone checks on the river card, players will show their cards, and the one with the best hand will win the pot. If someone bets and gets called, the player who bet must show their hand first and if no one can beat it, they would win.

Some important notes about the river and the showdown. The showdown is just a name used to describe the part where players show their hands.

First, the player who makes the bet and gets called must show their hand first, no ifs ands or buts.

Poker Flop

If everyone has checked, then the player who was first to act on the river will show their hand first and then you go clockwise around the table.

Lastly and probably most important is the rule about showing your hand. If you were the one called the bet and your opponent shows their hand first, you are not obligated to show your hand if you cannot beat it. You can throw your hand away and never have to show. Players may ask you to show or try to bully you into doing so to get some information, but don’t let them fool you.

Quick re-cap

Let’s go over the rules real quick just to refresh in case you forgot anything.

Two players post the big blind and the small blind. Two cards are dealt face down to everyone at the table. Players can choose to bet, fold, call or raise.

The dealer will deal out 3 cards face up in the middle which all players in the hand can use with their own. Players can now check, bet, call fold, or raise.

The 4^th card, or the turn is dealt face up again and players will have the same choices as on the flop-call, fold, check, and raise.

The 5^th and final card is again dealt face up. Once all players check, call, fold, bet or raise, the remaining players will showdown their hands to see who has the best hand.

Poker Rules River Flop Shoes

At any point in the hand if everyone folds, the last remaining player will win the money in the pot. The goal is to either show the best hand using your 2 cards and the 5 in the middle to make the best 5 card combination.

Flop River Poker Order

That’s the short abridged rules just to come back to and refresh if you ever need to.

If you play online, all of this will be taken of for you, so there will be need to pay attention to this. But, if you play in a casino, it’s important to know this rule.

Poker Odds On Flop

That’s the basics of playing Texas Holdem; it’s really not that difficult and easy to learn. Once you start playing, you can begin to learn strategies that will help you to win. You can find a ton of strategy articles right here if you want to get started right away, but we recommend to take it slow at first. Trying to learn too much at once, will likely confuse you.

Good luck and have fun!