Texas Hold Em Probability
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- Poker Texas Hold 'em Probability Calculator / Simulator. Poker Texas Hold 'em Probability Calculator / Simulator. Click 'edit' on a card to assign a value to that card. Cards with no value assigned are treated as being face down with unknown values. Type the following letters.
- 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.
.beside these unique secret features PreFlopper is also an Online Pre Flop Calculator Poker App that calculates the exact winning probability of any Texas Hold'em Poker Starting Hand in Real Time - so you'll always know whether you should call a bet by knowing your probabilty of winning the hand. Probability of making a specific hand (7 out of 52) The following chart shows the probability of getting a certain hand. Whereas a pair floats by often enough, getting a straight or royal flush is less likely. 7 out of 52 means, that although you build your hand using 5 cards, you still have 7.
Introduction to Probability with Texas Hold’em Examplesillustrates both standard and advanced probability topics using the popular poker game of Texas Hold’em, rather than the typical balls in urns. The author uses students’ natural interest in poker to teach important concepts in probability.
Holdem Calculator. The Holdem Calculator library calculates the probability that a certain Texas Hold'em hand will win. This probability is approximated by running a Monte Carlo method or calculated exactly by simulating the set of all possible hands. The Holdem Calculator also shows how likely each set of hole cards is to make a certain poker hand. Welcome to the free online texas hold 'em poker odds calculator. Simulate texas holdem poker situations and see the odds of a winning hand. The poker odds calculator is a useful tool in the study of hold 'em odds. Use the tool to calculate odds for any possible combination of known cards and unknown cards. The most advanced Poker Odds Calculator on the web. Know your probability of having a winning hand against one or many opponents in Texas Hold'em. Sep 18, 2019 This poker calculator will give you the odds of a win, loss, and tie for each player. Click on any card and it will be used in the position indicated by the yellow frame. You may click on any valid card to move the frame there. Check 'folded hand' to indicate the given player is out of the hand. 21, favor, 20, If you flop an open-ended straight draw this gives you eight outs (eight possible cards that will complete the hand), so you'll hit your hand by the river Texas Hold'em Poker Odds & Probabilities.You can refer to my section on probabilities in poker to see the probability is The odds are the same in both Texas hold 'em and 7-card.
Texas Holdem Hand Probability Calculator Free
Just plug in your cards, the other hold cards, and the community cards. Then, let our poker probability calculator crunch the numbers. You'll find out what the chances of winning, losing, and tying are.
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Designed to provide a mathematical breakdown of every possible match-up and showdown you’ll face at the table, the Poker Sites calculator is the perfect tool for players of all persuasions. Whether you’re a seasoned grinder reviewing a tough session or a novice looking to improve your understanding of the game, our poker hand calculator is an indispensable tool to have in your arsenal.
Why a Poker Calculator is Important?
Aside from psychology and timing, poker is essentially a game of odds and outs which means you have to know how the numbers stack up in each situation. By using a poker probability calculator, you’ll be able to build up an awareness of when you’re in a position or strength and when you should head for the hills.
By knowing the numerical breakdown of poker’s common situations, you’ll stand a much better chance of pulling off a successful bluff, profitably chasing a gin card and making money against less informed opponents.
To break the rules and manipulate players you need to master the rules and that’s why it’s important to review your poker hands using an odds calculator.
How to use our Online Poker Calculator
So, you’ve decided you’re ready to start bluffing like a champ and only chase that pretty flush draw with the right odds, now all you need to use our poker calculator. In an effort to make the software as efficient and intuitive as possible, our probability calculator looks like a standard online table.
Allowing you to animate poker hands as they happened, the Poker Sites calculator will crunch numbers and spit out the correct answer in the following ways:
- Choose your poker variant: Texas Hold’em, Omaha, Omaha Hi/Lo, Seven Card Stud, Seven Card Stud Hi/Lo, Seven Card Stud Hi/Lo No Qualifier or Razz.
- Select at least two starting hands by “Dealing In” a player (players can also be “Dealt Out) and clicking (or dragging) the appropriate cards.
- Click “Calculate Odds” to find out the pre-flop statistics for each hand: Win, Tie and Lose.
- To compare post-flop numbers, click three cards to complete the flop and hit “Calculate Odds”. This process can be repeated for the turn card.
- If you’re playing a poker variant where it’s important to know the folded cards, such as Seven Card Stud, then you can also choose to “Fold” an active player. This will dim their hand but still take the visible cards into consideration when performing a calculation.
- To clear a scenario and start again, simply click “Reset”.
Using Poker Sites Calculator to Improve Your Game
Now you know how to use our poker calculator online, you’re probably keen to know how you can use it to improve your game.
Although you don’t have to be Albert Einstein when it comes to solving mathematical equations, it does pay to have some appreciation of the numbers involved in various poker showdowns. Fortunately, for those with arithmophobia (someone scared of numbers), a lot of the math you’re required to do at the table is too complex to work out on the spot.
Because of this, an online poker calculator is a necessary tool. By running through enough situations, you’ll build up an unconscious awareness of when a situation is mathematically profitable and when it isn’t.
To make sure you play all your poker hands correctly and get maximum value from our probability calculator, make sure you keep the following points in mind:
- Different Games = Different Odds: Our exclusive poker calculator has been designed to cover seven poker variants. Although this may seem excessive, it’s actually important because each game has different dynamics and, therefore, odds. In fact, when you play with our poker hand calculator enough, you’ll see that statistical match-ups you find in Hold’em will be vastly different from those in Omaha, Stud and Razz.
- Hold’em to Memory: One of the best ways to improve your overall understanding of poker probability is to start with Texas Hold’em. Because each player only has two cards, it’s a lot easier to memorize the numbers in each major scenario. For example, in Texas Hold’em a pair of overcards, such as A-K, against a pair of deuces will basically be a 50/50 match-up (Deuces are actually a 52.35% favorite).
As you can see, it’s not vitally important that you memorize the exact percentages. Instead, you should remember that a pair versus two overcards is roughly an even money race. Using this logic you can run through dozens of match-ups and once you’ve built up a bank of knowledge you can use it to understand other games.
While you’ll still need to use the Poker Sites calculator to run through scenarios for each variant, the data you’ve gleaned from mastering Hold’em will give you a solid foundation to work from. For example, in Omaha, you may not know that statistical breakdown of A-K-7-6 vs. 8-8-5-4. However, because you know from your knowledge of Hold’em that A-K vs. 8-8 is roughly 50/50, you’ll be able to work out that the odds will be similar this figure. In fact, when use our online poker calculator, you’ll see that the odds are actually 53.18% in favor of 8-8-5-4 which is pretty close.
- Do Your Homework: On top of running through pre and post-flop situations without any context, you should use our poker probability calculator to assess how you played a session. By saving the poker hands you play at our recommended poker sites, you’ll be able to reconstruct them using our hand replayer.
In fact, every successful player will use a probability calculator to run through tricky hands they’ve played. Pouring over poker hands and working out the mathematics in each spot will help you understand why a move lost you money. Conversely, you can also use our poker calculator to assess winning hands so you can see why the pot went your way.
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Texas Hold Em Probability Calculator
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Texas Holdem Hand Odds Calculator
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Texas Holdem Poker Odds Calculator
Texas Holdem Probability Equation
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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.
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.
| Number of Outs | Turn & River Combined | River Only |
|---|---|---|
| 1 | 22.26 to 1 | 45 to 1 |
| 2 | 10.9 to 1 | 22 to 1 |
| 3 | 7 to 1 | 14.33 to 1 |
| 4 | 5.06 to 1 | 10.5 to 1 |
| 5 | 3.93 to 1 | 8.2 to 1 |
| 6 | 3.15 to 1 | 6.67 to 1 |
| 7 | 2.6 to 1 | 5.57 to 1 |
| 8 | 2.17 to 1 | 4.75 to 1 |
| 9 | 1.86 to 1 | 4.11 to 1 |
| 10 | 1.6 to 1 | 3.6 to 1 |
| 11 | 1.4 to 1 | 3.18 to 1 |
| 12 | 1.22 to 1 | 2.83 to 1 |
| 13 | 1.08 to 1 | 2.54 to 1 |
| 14 | 0.95 to 1 | 2.29 to 1 |
| 15 | 0.85 to 1 | 2.07 to 1 |
| 16 | 0.75 to 1 | 1.88 to 1 |
| 17 | 0.67 to 1 | 1.71 to 1 |
| 18 | 0.6 to 1 | 1.56 to 1 |
| 19 | 0.54 to 1 | 1.42 to 1 |
| 20 | 0.48 to 1 | 1.3 to 1 |
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
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.
Texas Holdem Probability Chart
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.
Poker Probability Calculator
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.
Texas Hold'em Full House Probability
Summary
Texas Hold'em Probability Chart
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.