• Odds Of Texas Holdem Poker Hands
• Texas Holdem Odds Chart
• Hold Em Odds

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. If
the math shows one player can win more often than another based on the
mathematical and statistical truths about Texas holdem then the game is one of
skill.

Odds Calculator Poker Hand Rankings Starting Hands Texas Hold'em Rules 10 Tips for Winning Odds for Dummies Forum Poker Odds Calculator Best Poker Odds Calculator - Fast, Simple, Free! Texas Hold'em Poker probabilities When calculating probabilities for a card game such as Texas Hold'em, there are two basic approaches. The first approach is to determine the number of outcomes that satisfy the condition being evaluated and divide this by the total number of possible outcomes. Texas Holdem Heads-Up Preflop Odds. This table was created by enumerating through every possible board and opponent hole card combination for each of the 169 texas holdem preflop starting hands.

Let’s look at a few facts before moving on.

• Fact 1

  Texas holdem is played with a deck of 52 playing cards, consisting of
  the same four suits, and 13 ranks in every deck. You know each deck has an
  ace of spades, and ace of hearts, an ace of clubs, and an ace of diamonds.
  The same is true for kings, queens, and all of the ranks down through twos.

• Fact 2

  Over a long period of time each player will play from each position at
  the table an equal number of times. In other words, each player will play in
  the small blind, the big blind, under the gun, on the button, etc. an equal
  number of times as other players. If you take two individual players it
  might not be 100% the same, but it’ll be close. When you take thousands of
  players and average their times played in each position mathematically they
  each play the different positions an equal number of times.

• Fact 3

  The rules in each game are the same for every player at the table.

• Fact 4

  The player that starts the hand with a better two card starting hand
  wins the hand more often than the player with a worse hand. This has been
  proven by computer simulations that run millions of hands and consider every
  possible outcome.

Why Is This Important?

The reason all of this is important to Texas holdem players is that you can
use all of this math to help you win.

Though there are thousands of possibilities on every hand of Texas holdem,
you can use the fact that everything is based on a set of 52 cards to predict
outcomes and possibilities at every stage for every hand.

If you start the hand with two aces as your hole cards, you know that the
remaining 50 cards in the deck only have two aces. The remaining 48 cards
consist of four of each rank below the aces. At the beginning of the hand you
don’t know where any of the other cards are located, but as the hand progresses
you learn where some of them are located.

Continuing with the example, if the flop has an ace and two fours, you hold a
full house. You also know the only hand at this time that can beat you is four
fours. Because two fours are on the flop, the number of times a single opponent
has the other two fours is 1 in 1,326 hands. This is such a small percentage of
the time that you always play the full house in this example as if it’s the best
hand.

How do we know the number of times the opponent has the other two fours?

Because two fours are on the flop, let’s say the four of hearts and the four
of diamonds, so you know that your opponent has to have the four of clubs and
the four of spades. The chances of the first card in their hand being one of
these two cards are two out of 52. If they get one of them as the first card
that leaves the single other card they need out of 51 unseen cards, or one out
of 51.

You multiply two over 52 times one over 51 and this gives us the 1 out of
1,326 hands.

Basic Texas Holdem Math

Some of the math we discuss on this page can be complicated and the truth is
some players won’t be able to use it all. But that doesn’t mean they can’t be
winning Texas holdem players. The math covered in this section forms the
building blocks for the advanced math covered lower on the page.

Every Texas holdem player can use the basic math included in this section,
and if you aren’t using it yet you need to start right away.

Starting Hands

At the most basic level of Texas holdem everything starts with your starting
hand. As we mentioned above, mathematically the player who stars the hand with
the better starting hand wins more than the player with the inferior hand.

This means the first math lesson you need to learn and start using is to play
better starting hand on average than your opponents. While this can get
complicated, especially in games with many multi way pots, you still need to
learn how to play better starting hands.

If you take nothing else from this page, if you simply tighten up your
starting hand selection it’ll immediately improve your results.

Position

It’s difficult to directly relate position to mathematics, but the main thin
to know is the later your position, the better your chances to play in a
positive expectation situation. We’ll discuss expectation in a later section,
but it’s important to understand that having position on an opponent is a strong
advantage that equates to a mathematical advantage over the long run.

Outs

One of the most important skills Texas holdem players need to develop is the
ability to determine the number of outs, or cards remaining in the deck that can
complete the hand they’re drawing to. You use this information to determine your
chances of winning the hand as well as to determine the pot odds. Pot odds are
discussed in the next section, but they show you whether or not a call is
profitable in the long run when an opponent makes a bet.

We can determine how many outs you have because we know what’s in the deck
and what we need to improve our hand. If you have a king, queen, jack, and 10
after the turn you know any of the four aces or four nines complete your
straight.

This means you have eight outs. You’ve seen six cards, so the deck has 46
cards remaining in it. Don’t make the mistake of thinking about the cards that
have been folded or your opponent holds. You haven’t seen these cards so any
unseen card is still considered a possible river card.

In other words, on average, if you play this situation 46 times you’re going
to complete your straight eight times and not complete it 38 times.

You should always consider how many outs you have in every situation while
playing. B knowing your outs you have another piece of information that can help
you make profitable decisions throughout the hand.

Pot Odds

The next question many players ask after they learn how to determine their
out sis how they can use this information to make more money at the table. This
is where pot odds come into play.

Pot odds are simply a ratio or comparison between the money in the pot and
the chances you have of completing your hand. You use this ratio to determine if
a call or fold is the best play based on the information you currently have.

If you consider the example in the last section concerning the straight draw,
you know that the deck holds eight cards that complete your straight and 38
cards that don’t. This creates a ratio of 38 to 8, which reduces to 4.75 to 1.
You reduce by dividing 38 by 8.

The way you use this ratio is by comparing it to the amount of money in the
pot and how much you have to put into the pot. If the pot odds are in your favor
it’s profitable to call and if not you should fold.

If the pot has $100 in it and you have to make a $10 call the pot is offering
10 to 1 odds. You determine this the same way as above, by dividing $100 by $10.

If you’re in the situation described above of drawing to a straight on the
river you can see that a call is correct because the pot is offering 10 to 1 and
you have a 4.75 to 1 chance of winning.

On the other hand of the pot has $100 in it and you have to put $40 in to see
the river the pot is only offering 2.5 to 1 odds and your chances of hitting
your straight are still 4.75 to 1 so you should fold.

Pot odds can get complicated, especially when you start considering how they
work when you’re determining the correct play with both the turn and river to
come.

Fortunately charts are available to quickly check the odds of hitting your
hand based on how many outs you have. We’ve included one next so all you have to
do is determine your outs and compute the odds the pot is offering. Then compare
the two to see if it’s profitable to call or fold.

Expand Shrink

When you’re determining your pot odds for the turn and river you determine
them on the turn and then if you don’t hit your draw you determine them again on
the river. This often happens, especially in limit Texas holdem. But if an
opponent moves all in on the turn you simply use the turn and river combined
odds in your decision.

Advanced Texas Holdem Math

Odds Of Texas Holdem Poker Hands

Many beginning Texas holdem players look at a discussion about expectation
and instantly decide it’s too hard and ignore it. When they do this they
severely hurt their long term chances at being a profitable player.

We’ve broken down how to look at situations while playing poker in a simple
manner that almost any player can use below. Do yourself a favor and go into
this with an open mind. Once you understand it at a simple level you can learn
more as you gain experience. You may be surprised at just how easy it gets to
determine positive and negative expectation with a little practice.

Expectation

Expectation is what the average outcome will be if you play the same
situation hundreds or thousands of times. Once you determine the expectation you
know if a situation offers positive or negative results on average.

Your goal as a Texas holdem player is to play in as many positive expectation
situations as possible and avoid as many negative expectation situations as
possible.

You need to understand that expectation is something that can be applied to
almost any situation in poker, but it’s also subjective in many areas.

• If you play at a table where every opponent is better than you in the long
  run you’re going to lose money. This is a negative expectation situation.
• If you play at a table where every opponent is a worse
  player than you it’s a positive expectation situation because you’re going to
  win in the long run.

The problem is determining whether a situation is positive or negative
expectation when you sit down at a table with some players who are better than
you and some who are worse.

You can find many situations where it’s easier to determine expectation
mathematically, and we’ll teach you how to do this now. While this may seem
overly complicated at first, especially to do at the table while playing, you
don’t need to know exactly how negative or positive a situation is, you only
need to know if it’s positive or negative.

Once you determine if a situation is positive expectation or negative
expectation you simply remember the next time you’re in a similar situation.
Once you start determining expectation you’ll find that you learn mist
situations quickly and only have to think through an occasional situation at the
table.

The best way to see how to determine expectation is by running through a
couple examples.

Example 1

You’re facing a bet after the turn and you have four to a flush.
The pot had $400 in it and your opponent bet $100. You’re certain that if you
miss your flush draw you’ll lose and when you hit your flush draw you’ll win.

In order to see the river you have to call the $100 bet. When you lose you
lose $100, and when you win you get back $600. You get your $100 back plus the
$400 that was in the pot plus the $100 bet your opponent made.

Many players claim that part of the money already in the pot is theirs, but
once you put money into the pot it isn’t yours. The only way to get it back is
to win the pot. So you can’t consider it in any other way when determining
expectation.

The way to see if it’s positive or negative to call is to determine what will
happen on average if you play the same situation many times. Most players find
it easiest to determine by pretending to play the hand 100 times.

In this example you’re going to hit your flush 9 out of 46 times. This means
19.56% of the time you’re going to win and 80.44% of the time you’re going to
lose. To make this simple we’ll round these numbers off to 20% and 80%.

If you have to put $100 in the pot 100 times your total investment is
$10,000. The 80 times you lose you get nothing back. The 20 times you win you
get $600. 20 times $600 is $12,000. When you take the $12,000 you win and
subtract the $10,000 you lose when you play the situation 100 times, you see
that you win $2,000 overall.

To determine how much you win on average per hand simply divide the $2,000 by
100 to get a positive expectation of $20 per hand. This means that every time
you’re in this situation you’ll win on average $20.

The truth is you may win a little more because we’re ignoring the river.
Because you know you can’t win if you miss your flush, you always need to fold on
the river when you miss your draw. Every once in a while you may be able to
extract a small bet from your opponent on the river when you hit your flush,
increasing your average expectation. Sometimes it’s even correct for your
opponent to call on the river in this situation. See the next example to see
why.

Example 2

Let’s say you’re playing the same hand as above but you have a
straight and your opponent appears to be drawing to a flush. You’re on the
river, the pot has $600 in it, and the board has the third suited card hit on the
river.

If your opponent was drawing to the flush, they completed it and you’re going
to lose the hand. In this situation your opponent bets $20.

In this situation you clearly have to call.

The reason you have to call is because you can’t know for certain your
opponent was drawing to the flush. They may be bluffing or have two pair or any
other number of hands that aren’t as good as your straight.

Let’s look at the math behind this decision.

If you play the situation 100 times your total investment is $20 times 100,
or $2,000.

When you win you get $640, consisting of the original $600 pot, your
opponent’s $20 bet, and your $20 call. If you win three hands you get back
$1,920 for a loss of $80, or 80 cents per hand.

If you win at least four times you’re in a positive expectation situation.
Four wins nets $2,560 for an overall win of $560, or $5.60 per hand.

What this means is if your opponent is bluffing or has a weaker hand just
four times out of 100 or more, calling is a positive expectation situation. Four
times out of 100 is only 4%. You’ll win at least 4% of the time in this
situation.

The numbers get closer the more your opponent bets on the river, and the
closer the numbers get the more you’re going to need to use what you know about
your opponent to determine if a situation is positive or not.

Start looking at every decision you make at the Texas holdem tables in terms
of positive and negative expectation.It’s hard at first, but the more you
practice the better you’ll get at predicting if a situation offers positive
expectation.

Summary

Texas holdem math is often the only thing that separates winning and losing
players. Take the time to learn the basics now so you can improve your game in
every way possible as you gain experience. This guide is the perfect place to
start for players of every experience level.

There are 10 different hands ranks in Texas Hold’em – from a Royal Flush to a Straight to a lousy High Card. Here’s a comprehensive list of all Texas Hold’em poker hand rankings:

You can also print and download the Official Texas Hold’em hand ranking as a PDF file.

Chart: Poker Hand Ranking

Download

Download the poker hand ranking charts image or PDF:

• Official Poker Hand Rankings Image
• Print: Poker Hand Rankings PDF

Official Poker Hand Rankings

• Royal flush: A straight from a ten to an ace with all five cards in the same suit.
• Straight Flush: Any straight with all five cards in the same suit.
• Four of a Kind or Poker or Quads: Any four cards of the same rank. If two players share the same four of a kind (on the board), the larger fifth card (the “kicker”) decides who wins the pot.
• Full House or Boat: Three cards of the same rank along with two cards of the same rank. In short: trips and a pair.
• Flush: All five cards of the same suit (not necessarily consecutive). The highest card determines the rank of the flush.
• Straight: Five consecutive cards (not necessarily the same suit). Aces can count as either high or low cards, but not as both at once. Meaning, a straight cannot go “around the corner”.
• Trips: Three cards of the same value. If two players have the same trips the highest kicker decides who wins the pot.
• Two Pair: Any two cards of the same rank together with two other cards of the same rank.
• One Pair: Any two cards of the same rank.
• High Card: Any hand that is none of the above hands.

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Poker Hand Rankings Explained

• If two players have a Straight or Straight Flush, the higher Straight or Straight Flush wins.
• If two players have a quads, the player with the highest quad wins. If they are identical, the highest kicker wins.
• If two players have a flush, the player with the highest card in the flush wins. If they are identical, the second highest card decides, then the third highest, and so on. The suit of the flush does not matter.
• If two players have a full house, the player with the higher trips wins. If they are identical, the player with the higher pair wins.
• If two players have two pairs, the player with the bigger pair wins. If they are identical, the player with the higher pair wins. If they are also identical, the player with the highest kicker wins.
• If two players have a pair, the player with the higher pair wins. If they are identical, the highest kicker wins, then the second highest, then the third highest.
• If two players have a high card, the highest card wins. If they are identical, the second highest card decides, etc.

How many Poker Hands are there?

There are only 10 distinct poker hand ranks, but if you randomly deal 5 cards from a deck of 52 cards there are exactly 2,598,960 possible card combinations.

Poker Hand Odds for 5-Card-Poker

The poker hand ranking charts are based on the probability for each distinct hand rank. More unlikely combinations are ranked higher. Those are the probabilities and odds for all 5-card poker hands:

Poker Hand Odds for Texas Hold’em

If you’re playing Texas Hold’em, you have 7 cards to chose your hand from. There are 133,784,560 to deal 7 random cards. This changes the odds and probabilities for all poker hands a bit. Those are the probabilities and odds for all Texas Hold’em Poker hands:

Technically it’s more likely that you’re dealt at least a pair in Texas Hold’em than holding only high card. But “High Card” still remains the lowest rank.

FAQ: Poker Hand Rankings

Does 2 pairs beat a straight?

When playing Texas Hold’em (or any other popular poker variant) 2 pairs are always ranked below a straight.

Does 3 Aces beat a straight?

3 Aces are just trips (or three of a kind) in poker. When playing regular Texas Hold’em a straight is ranked above trips. There are however rule variations where trips can bet a straight, namely Short Deck Hold’em, a poker variant where all cards below 5 are removed.

Does 5 of a kind beat a royal flush?

In regular poker variants there are is no 5-of-kind rank. When playing with wildcards (joker) 5 of a kind are possible. In this case 5 of a kind are the highest possible poker hand and beat a royal flush.

Does a full house beat 3 aces?

Every full house always beats trips, no matter the rank of the trips. Even trip aces are always ranked below every possible full house.

Does Royal Straight beat flush?

A Royal Flush is the best possible poker hand and of course always beats any other flush.

Does straight beat a full house?

Every common poker variant, including Texas Hold’em, ranks a Full House above a straight. So no, a Straight never beats a Full House in Poker.

What beats a royal flush?

In all regular modern poker variations (including Texas Hold’em and Omaha) a Royal Flush is always the highest possible hand rank. A higher rank is only possible when playing with a Joker. In this case 5 of a kind (4 Aces plus Joker) beats a Royal Flush.

What can beat a flush in poker?

A Flush is a very strong hand in poker. The only hands that beat a Flush are Full House, Quads, Straight Flush, and Royal Flush.

How rare is a royal flush?

A Royal Flush is extremely rare. When playing Texas Hold’em you’ll only get one every 31,000 hands. And that assumes you never fold. The hand is so rare that most poker players can remember all Royal Flushes they have been dealt in their life time.

What are the odds of hitting a straight flush?

Straight Flushes are almost as rare as Royal Flushes. When playing Texas Hold’em you will hit a Straight Flush roughly every 3,600 hands (assuming you never fold any hand that can make a Straight Flush).

Can you have 3 pairs in poker?

There is no “3 pair” hand rank in poker. When playing Texas Hold’em it’s technically possible to have three pairs, but since a poker hand only consists of 5 cards only the 2 highest pairs are in play. For example, if you hold Q-J and the board reads Q-J-6-A-A you only have two pair: Aces and Queens.

Does Royal Flush have to be spades?

A Royal Flush can be any of the 4 suits, spades, hearts, diamonds, or clubs. It’s just that usually a Royal Flush is depicted in spades or hearts. Nevertheless, it doesn’t matter which suit, a Royal Flush is always the best Texas Hold’em Poker Hand.

How many kickers can you have in poker?

A poker hand can consist of up to 5 kickers. A player with no pair only has kickers. A player with one pair has 3 kickers, a player with trips has 2 kickers, and a player with 2 pair or quads has 1 kicker.

Is Ace a 1 in poker?

When building a straight an Ace can be used as a virtual “1” in poker. Meaning, A-2-3-4-5 is a straight. There are also lowball poker variations where the Ace counts as the lowest card.

Is an Ace 2 3 4 5 a straight?

Yes, the ace can count as the lowest card in a straight and function as a “1” when combined with 2-3-4-5.

Is JQKA 2 a straight?

A straight cannot go “around the corner”, the Ace can only be either the highest or the lowest card, not a card in the middle. So no, J-Q-K-A-2 is no straight in poker.

Is Queen King Ace 2 3 a straight?

A straight cannot go “around the corner”, the Ace can only be either the highest or the lowest card, not a card in the middle. So no, Q-K-A-2-3 is no straight in poker.

Is there a kicker on a straight?

For a straight you need to use all 5 cards. There are no cards left for a kicker. The rank of the straight is determined by the highest card. E.g. an ace-high straight beats a queen-high straight.

What is a flush in poker?

A flush in poker is hand which consists of 5 cards of the same suit. The same color (red or black) is not enough. It has to 5 spades, hearts, diamonds, or clubs.

What is the highest royal flush in poker?

There are no distinctions between the 4 possible Royal Flushes in poker. A Royal Flush in spades is as good as a Royal Flush in hearts, diamonds, or clubs.

What is the highest suit in Texas Hold’em poker?

Only in very rare occasions (for example when dealing for the button) the suits are ranked in poker. In this case the ranking is: 1. spades, 2. hearts, 3. diamonds, 4. clubs. Suits are otherwise generally not ranked in poker. A Flush in spades is as good as a flush in any other suit, only the ranks of the cards matter.

What is the lowest pair in a game of poker?

In poker the lowest possible pair is a pair of Deuces (twos).

How do you win bad beat jackpots in poker?

Texas Holdem Odds Chart

To win a bad beat jackpot in poker you need to lose with a very strong hand, usually a strong Full House (Aces Full). It’s also necessary that both, the winning hand losing player, user both of their hole cards. E.g. losing with quads on the board does not count.

What are the odds of hitting a bad beat jackpot in poker?

The odds of hitting a bad beat jackpot in poker depend on the rules for the jackpot. If you have to lose with Aces Full or better your odds of hitting the bad beat jackpot are 1:58,948. If you have to lose with quads or better your odds are 1:624,609 (assuming a 10 player table where nobody ever folds).

What is a bad beat in poker?

If you lose with a very strong hand against an even stronger hand this is called a “bad beat”. It is also a bad beat if you lose an all-in while being far ahead and you opponent wins by catching some miracle cards.

How many 5 stud poker hands are there?

5 Card Stud is one of the oldest poker variants where each player is dealt 5 cards. There are exactly 2,598,960 different 5 stud poker hands possible.

Hold Em Odds

How many poker hands are there?

There are only 10 distinct poker hand ranks, but if you randomly deal 5 cards from a deck of 52 cards there are exactly 2,598,960 possible card combinations. If you’re playing Texas Hold’em, you have 7 cards to chose your hand from. There are 133,784,560 to deal 7 random cards.

What happens if two hands tie in poker?

It’s possible (and not too uncommon) for two players to have the same hand in poker. In this case the pot is split and both players receive half the pot.

What happens if two people have a royal flush?

When playing Texas Hold’em it’s almost impossible for two players to have a Royal Flush. For that to happen the 5 community cards need to form a Royal Flush. In that case all players in the hand win and split the pot.

What happens if two poker hands are the same?

If two players have the same hand, the pot is split and both players win half of it. This can happen for example if both players have the same cards (e.g. Ace-King) and nobody makes a Flush.

How do you hit a royal flush on video poker?

In Video Poker you can win the jackpot when you hit a Royal Flush. To maximize your chances you should always keep all suited cards 10 or above (if you have at least 2) and discard the rest. You will see a Royal Flush roughly once every 40,000 spins.

What are the odds of hitting a royal flush on a video poker machine?

The odds of hitting a royal flush directly are only 1 in 649,739. But since you can draw one time your odds increase. If you play perfectly your odds of hitting a royal flush are roughly 1 in 40,000.