• Texas Holdem Probability Equation
• Flush Texas Holdem
• Straight In Texas Holdem

Now with your A4 you additionally have an inside straight draw, giving three extra outs. Communicating through letters, the two continued to exchange their ideas and thoughts.I think the chances of getting a straight flush is pretty rare and the 20 Jul 2016 Because the deck contains only one of these cards for each of the four suits, there are only four possible royal flushes that can be dealt.

Poker probability chart royal flush odds video poker 5 card poker probability calculator poker probability problems poker hand odds preflop poker hand statistics odds of flopping a straight flush poker odds chart pdf poker hand odds calculator open ended straight draw texas holdem odds preflop open ended straight flush draw odds how to calculate poker odds odds of runner runner straight odds of hitting runner runner trips odds of runner runner full house poker odds chart runner runner flush texas holdem runner runner straight flush poker odds calculator odds of runner runner royal flush odds of flopping a royal flush in texas holdem odds of 4 of a kind in texas holdem texas holdem probability odds of hitting a royal flush odds of getting quads in texas holdem odds of getting a royal flush in texas holdem odds of flopping a flush draw texas holdem probability calculator texas holdem odds texas holdem odds chart odds of flopping a straight draw flop straight flush what are the odds of getting a straight flush in texas hold em?Odds and Probabilities - PokerStars School What is the probability of a straight flush?

Nov 27, 2019  Answers to these and similar questions about Texas Holdem poker probabilities and odds can be found here. This collection of Texas Hold'em odds also contains the probabilities for several long-shot scenarios like set over set, flush over flush and other rather unlikely scenarios. If you're missing a probability, just leave a comment below!

This separates a royal straight flush from a straight flush but they can be combined into just straight flush if that is faster. Not interested in parallel processing. Have a pattern for doing that. For this question just optimize the raw code. This code gives the correct answers to poker hand probability. It runs in about 200 seconds. One of the most important aspects of Texas Hold'em is the value of each two-card hand before the flop. The decision of how to play your first two cards is something you face every hand, and the value of your first two cards is highly correlated to your probability of winning.

Odds and Probabilities - PokerStars School What is the probability of a straight flush?. Holdem/Razz I don't play by the numbers as far as a flush is concerned.all I know is if you have no higher than a K of any suite, you must assume that one opponent may be holding the A same suite & is waiting to go all-in against you!Running into Aces with Kings With aces you have nothing to fear before the flop .

And runner runner cards are not good odds for the serious player!

Much like very large numbers, a probability that is this small is hard to wrap your head around. One way to put this number in perspective is to ask how long it would take to go through 649,740 poker hands. If you were dealt 20 hands of poker every night of the year, then this would only amount to 7300 hands per year. in 89 years you should only expect to see one royal flush. A List of Long-Shot Odds in Texas Holdem Texas Hold 'em - Probability - General - Wizard of Odds Poker Probabilities - Wizard of Odds 20 Texas Hold'em Poker Odds & Statistics You Should Know What is the probability of a straight flush?

Therefore, any strategy is useless. Other flush draws Let’s just look quickly at other flush draw combinations that you might not be aware of. Poker Romania Jocuri

You first need to get your stack in and you need your hand to hold up. Appetizer Ideas for Poker Party Public transport ticket in Paris Where The Sun got hydrogen to work if it is 3rd generation of the stars? Roadhouse Casino Tunica Ms

How do you calculate odds of getting runner? Casino Flotante Puerto Madero HorariOS #8 13th March 2007, 7:10 PM XxJackAcexX [294] Poker at:

There are 47x46/2 of those boards that contain the three cards we need, so dividing again we get 1960. I guess that is part of the reason many players prefer blackjack - a game that does not have this kind of variance in the payouts and short run expected return.

• This is generally only used in games with a flop, turn, and river, to describe a player needing to catch a favorable turn and river in.
• Talk about unlikely!Let me count the ways.
• I don't have time to do the calculations, but here's how you figure it out.
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Combo draws, however, are so powerful that some are actually a favorite versus a made hand. Not great odds, but if you have 2 other aggressive players in the hand you can clean up.

- Poker Forums How do you calculate odds of getting runner? Shane from Santa Rosa Thanks for the kind words.Four Card Stud — Two Jokers Hand Sandia Casino Albuquerque Phone Number Probabilities Four of a kind 195 0.023032 Three of a kind 10488 1 The next table is for a seven-card stud game with one fully wild joker.

However that is an average - you might get lucky and hit a royal straight flush a lot sooner, or perhaps you will have to play through 100,000 video poker hands before you finally get that sweet royal flush. 20 romania slot machines Hold'em Poker Odds & Statistics to Improve your Poker Game.Effective stacks are $200. straight flush holdem odds

The probability of getting 3 more jack black wife photos of the same suit is combin(11,3)/combin(50,3) = 0.008418.– Lee Daniel Crocker Mar 2 '15 at 17:09 add a comment | up vote 0 down vote More complex then you would straight flush holdem odds think. Pot Odds and Outs Next » Similar Threads for: Free Texas Holdem Poker For Fun

• 95%NL holdem re:
• Poker & Open straight-flush-draw from flop if all your outs are clean then you will win vs 1 person over half the time, if it is a flop that vs agro player c bets 100% and dont think he hit i will check raise all in.The probability of going 175 hands and never get either of two specific suits is (1-2×0.003764605) 175=0.266442448.
• Then your question is equivalent to asking, “What is the probability of 20 Jul 2016 When you sit down to a game of Texas Hold 'Em, what are the odds you'll get a royal flush on the flop?
• ABCD can be arranged 4!30 Oct 2013 - 8 min - Uploaded by Open Face OddsWhat are the odds your runner runner flush draw hits when you set 3 to a flush in Open Face Hi just lost a 280$ pot had AQ vs A10 flop came AQ3 he bets flop and i check raised all in, he calls and hits runner runner J then K for straight.

But what are the odds that one of your opponents is dealt aces as well?

• For instance, if you have a 8% chance of getting the first card, and assuming you get that one, you have another 8% chance of getting the second, you take:
• Frequency of 7-card poker hands[edit] In some popular variations of poker such as Texas Hold 'Em, a player uses the best five-card poker hand out of seven cards.A spectacular scenario, but quite unlikely.
• For the low hand aces always count as low.
• The Wizard of Odds The Wizard of Odds Wizard Recommends Poker Probabilities Five to Nine Card Stud Low Ball Omaha Median Hand in Five Card Stud Probabilities in Two-Player Texas Hold 'Em Median Hand in Texas Hold 'Em High Hand Probabilities in Texas Hold 'Em Chopped Pots in Texas Hold 'Em Multi-Deck Probabilities Infinite Decks Wild Deck Probabilities Four Card Stud Player Must Use Every Card Two-Player Game Internal Links Wizard Recommends Poker Probabilities $600 $20 Poker Probabilities Last Updated:
• 100 / 25 = 4.
• Error saving comment!For all 5 pocket pairs the probability is 35/4,682,937,402 or about 1 in 133 million.

1. Now here’s my question:
2. Probability of drawing first card is 1/52.
3. $$Pr(H4H5| ext{straight flush}) = 4/36 = 1/9$$ Now, how do we find $Pr(H4H5)$?
4. There is about 2% chance that a player would flop two pairs.
5. There are 46x45/2 boards that make each straight flush (with no ace--else they'd make the royal as well), so that makes 1 out of 1023 5/9 for the straight flushes.
6. Odds and Probabilities - PokerStars School Odds of Straight Flush Versus Straight Flush?

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How do you calculate odds for runner-runner? That is about 1 Poker Documentary Bet Raise Fold in 8.

The probability that these five ranks will represent three suits, two of two, and one of one, is combin(4,2)*2*combin(5,2)*combin(3,2)=360. Hello everybody.

How many ways are there to shuffle a deck of 52 cards? Not folding pockets eights or better and not folding possible straight flushes), you’ll have a qualifying hand once every 7 million attempts .

25%: Casino Near Idaho Falls Idaho (2*combin(12,3)*39/combin(50,4))*(9/46) = 1.458%.

Jonathan Little Makes Basic Poker Math Easy 26 January 2015 Quads over quads? While the player with trips may feel that the other player played badly, in fact they didn't; they just accidentally caught runner-runner. Deltin Casino Goa Packages

1. The number of combinations for this is combin(13,2)*44 = 3432.
2. For example, suited K/2.I was dealt pocket aces.
3. 4 for the 'small' straight', 4 for the 'high' straight, and 2 to complete your pair?
4. Then your question is equivalent to asking, “What is the probability of being dealt 5 cards that are a straight flush?” To get this probability, we count the number of possible straight flushes, and then divide by the number of all possible 5-card hands.
5. A straight flush (five consecutive cards all of the same suit) beats four The worst case for a possible straight flush is holding something like A2s, AKs, A5s, where there's only one possible way to flop the The worst case for a possible straight flush is holding something like A2s, AKs, A5s, where there's only one possible way to flop the straight flush.
6. Have faith in the tables, they are accurate and the math is correct.
7. His friend, Chevalier de Méré, was an avid gambler with the goal to become wealthy from it.

So, for a runner-runner flush (not that this was asked but I'm gonna put it in anyway) - where you have 3 to a flush on the flop - the odds of completing the flush are: You're dealt T♠ 9♠ on the button.

For a detailed view of the chart, mobile and tablet users should check out Holdem Runner-Runner Odds in detailed .pdf format. 'The chances of a royal flush and quads happening in the same hand:

SQL to find Upper case words from a column Using exponentiations instead of ECC multiplication in computing Stealth address Is it legal to “mine” dividends? As you can see in the above table, if you're holding a flush draw after the flop (9 outs) you have a chance of hitting it on the turn or expressed in odds, you're against.

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Any stats you may have at the ready would be wonderful and forever appreciated! You played the hand in a deceptive manner. Pokerstars.fr Skrill

• Odds of straight flush in hold 'em Thread Tools Search Thread Display Odds of straight flush in hold 'em Posting Permissions Thread:
• There is a promotion being advertised by a Las Vegas card room:
• To that end, you can have much of these odds calculations canned and ready to go as you see the situation unfold.
• With two gaps the probability is 4 2/combin(47,2)=0.0148.There are a number of different kinds of flushes. Unlike most flushes, in a royal flush, the value of all five cards are completely specified. The cards in one's hand must be a ten, jack, queen, king and ace all of the same suit.

Your Texas Hold'em poker odds are given below for hitting a draw by the Backdoor:

1. In Omaha I'd count it less because the chance of being beaten when you have the A high flush is greater.
2. Poker Drawing Odds & Outs Basic Math – Odds and Percentages Counting Your Outs Calculating Your Poker Odds Poker Drawing Odds & Outs By Tom 'TIME' Leonard In our poker math and probability lesson it was stated that when it comes to poker; “ the math is essential“.Please try the best alternative which is available for your location:
3. Answer Rival Casino No Deposit Bonus 2019 2012-06-18 15:53:57 You forgot the three remaining two-pair outs.
4. The new code only look about a day to write.

The second table is for a fully wild card. Learn Your Poker Hand Rankings The 10 Best 5-Card Poker Hands What Does the Nickname 'Computer Hand' Mean in Poker?

The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. Pocket Aces Back-to-Back Probabilities of Back-to-Back Hands and Streaks in Hold'em How Many Ways to Shuffle the Deck?

To have fold equity, your bet should be big enough straight flush holdem odds to make them fold. golden monkey slot machine The development of probability theory in the late 1400s was attributed to gambling; when playing a game with high stakes, players wanted to know what the chance of winning would be. – Drunix Sep 11 '15 at 9:17 add a comment | up vote 0 down vote Using combination Will use NcK Lets assume quad aces The board is the easy part Need exactly 4 cards - two remaining aces and the 2 left for the royal flush One random from the remaining 44 4c4 * 44c1 / 48c5 = 0.00002570 = 0.00002570 = 38915 :

1. The number of hands would then be (4-choose-1)*(13-choose-5)-4*10, with probability approximately 0.0019654.
2. If your opponents make zero mistakes against you, you're playing a game you cannot beat.For the first card you have 52 options, for the second 51, for the third 50 and so on.
3. How do I remove a destroyed lug nut?
4. Here is what it looked like in May 1999.Obviously your odds will be better with 6/7s than they would be with A/Ks.

You want to check. 17 9th July 2018 8:01 PM Learning Poker Do you calculate your decisions?No-Limit, Limit, Pot-Limit Chinese Poker Rules | How to Play Chinese Poker Show more » Most Views Most Comments Today Week Month Ever No Articles Found About PokerListings PokerListings.com is the world's largest and most trusted online poker guide, offering the best online poker bonus deals guaranteed, exclusive site reviews and the most free poker content available on the Web.

Table #1 – Outs to Improve Your Hand The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. We use Everett Ma Casino Location the formula for combinations and see that there are a total number of C ( 52, 5 ) = 2,598,960 possible distinct hands.In the next 175 hands the probability of missing a heart flush would be (1-0.003764605) 175=0.51682599.

I threw Poker probability - Wikipedia Poker probability - Wikipedia What Are the Odds? When the board is vip pokerstars 2019 paired every player straight flush holdem odds has a pair.

But how often do The 20 Hold'em Poker odds & statistics you should know if you want to suited connectors being better than aces, because of straight flush holdem odds the straight and flush possibilities. poker online win prizes 73 to 1.

That 3-card-to-a-straight possibility counts as one out

• Otherwise the only cards that are known to u is ur hand #6 31st August 2009, 1:31 PM Maid Marian [11,669] Poker at:
• If everything you do is hidden and deceptive then your opponents will assume you're doing just that and will adjust their play accordingly.The probability of getting exactly one of the needed suit is 9*38/combin(47,2) = 342/1081 = 31.64%.
• Here are the commulative probabilities.
• I was hoping you could answer a few questions that would help me with my project:Did experimenting change as your site became more well-known?
• Why or why not?

• - Poker Stack Exchange What is the probability of seeing a royal flush and a four of a kind in the same round with ten players?
• What do u think of :Poker & Open straight-flush-draw from flop if all your outs are clean then you will win vs 1 person over half the time, if it is a flop that vs agro player c bets 100% and dont think he hit i will check raise all in.
• Let's start with the first possibility, as it is both the easiest, and will never result in a chopped pot.
• Statistically, you should on average get a royal straight flush once every 40,000 hands played.I think the chances of getting a straight flush is pretty rare and the chances of 20 Jul 2016 When you sit down to a game of Texas Hold 'Em, what are the odds you'll get a royal flush on the flop?
• -Ben #12 2nd September 2009, 12:26 AM chris_the_terrible [7] I got it.

The next club flush would be 2C, 3C, 4C, 5C, 6C

May https://defidaitari.web.id/casino-campione-orari-natale 9, 2017 Poker odds #3:There are 1,712,304 possible ways to deal the board.AZDuffman The answer and solution appear in the following spoiler tag. Poker Legislation & PPA Discussion hosted by Rich Muny Twitch - texas city casino trips Watch and Discuss Live Online Poker straight flush holdem odds Televised Poker General Poker Strategy Beginners Questions Books and Publications Poker Tells/Behavior, hosted by:Let’s talk numbers:Even the worst combo draw is even money vs. I am wanting to know simply how often I can expect this to happen (because it DID happen to me).Many players without a few thousand hours of experience in the game will miss this possibility completely.Zachary Elwood Poker Theory Psychology No Limit Hold'em Strategy Medium-High Stakes PL/NL Micro-Small Stakes PL/NL Medium-High Stakes Full Ring Micro-Small Stakes Full Ring Heads Up NL Live Low-stakes NL Limit Texas Hold'em Strategy Mid-High Stakes Limit Micro-Small Stakes Limit Tournament Poker Strategy STT Strategy Heads Up SNG and Spin and Gos Mid-High Stakes MTT Small Stakes MTT MTT Community Tournament Events Other Poker Strategy High Stakes PL Omaha Small Stakes PL Omaha Omaha/8 Stud Draw and Other Poker Live Poker Casino & Cardroom Poker Venues & Communities Regional Communities Venues & Communities Tournament Events WPT.com Home Poker Cash Strategy Tournament Strategy Internet Poker Internet Poker nj.partypoker.com Global Poker MPN https://en.wikipedia.org/wiki/Poker_probability Poker probability - Wikipedia Poker probability Contents History[edit] Frequency of 5-card poker hands[edit] Frequency of 7-card poker hands[edit] Frequency of 5-card lowball poker hands[edit] Frequency of 7-card lowball poker hands[edit] See also[edit] Notes[edit] External links[edit] Navigation menu Poker probability From Wikipedia, the free encyclopedia This article has multiple issues.

1. With suited hole cards:
2. 3 is the number of ways to choose one rank out of the three left for the first suit of one.May 29, 2008 I was not sure what the odds are, blindly, on getting a straight flush, and straight ROYAL flush in hold 'em.
3. Although I strongly feel poker based games https://www.goldenmagic.net/bro-hof-slott-golf-club-banguide should be played with only one deck, I will submit to the will of my readers and present the following tables.
4. Royaled.Below we've compiled a comprehensive list of unusual long-shot odds for Texas Hold'em – numbers and percentages to impress (or possibly annoy) your fellow players at the table.

Probability of a chopped pot. However, statistically straight flush holdem odds you will only hit im roulette gewonnen a royal straight flush once every 40,000 hands. Free Slots Android Phone

When the board is paired every player has a pair. But what we really want is the % of winning the hand.The math shows this scenario is extremely unlikely. Combin(4,2) is the number of ways to choose two suits out of four for the suits represented twice.There are 6 ways that two of the four can show.Not casino in lindsay ontario many players sit down at a poker machine and play through that many hands, and without those nice royal straight flush straight flush holdem odds hands your expected return becomes a lot lower then the 99.50%. Cherry Red Casino Review

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• Conclusion In this lesson we’ve covered a lot of ground.
• - Beginning Poker Questions - Beginner Poker Forum Hello everybody.Each hand in Hold 'Em is is one of the most common scenarios in Hold'em.
• With kings it's possible, but unlikely, to run into a better hand pre-flop .
• If you'd like to see how the get altered try punching some scenarios into the poker odds calculator above.
• The general who loses a battle makes but few calculations beforehand.
• I.My answer keeps on coming out to be 5.8% but this seems ulimately incorrect, your help would be much appreciated thanks Nathan S.

The more mistakes you can encourage your opponents to make, the more opportunities you'll have to make some serious money at the tables.holdem Depends on your stack too, if short stacked I would shove. A couple years ago I took the Mensa entrance exam, and didn't make the requisite top 2%.

While the player with trips may feel that the other player played badly, in fact they didn't; they just accidentally caught runner-runner. John from Trinity, Texas For those readers who don’t know, the river is the fifth and last Closest Casino To Door County community card in Texas hold-em.Quads over Quads:

Michael from Perth You could complete foxwoods poker tournament schedule 2019 the full house with an ace and straight flush holdem odds a K, Q, or 9. POST REPLY How do you calculate odds for runner-runner? Gambling Taxation Canada With kings it's possible, but unlikely, to run into a better hand pre-flop .Pot Odds for Fourth Street - Poker Odds - Calculating Odds in Texas Hold'em Poker Forget math, use these 11 Texas Hold'em odds instead [2018] Texas Hold'Em Poker Odds and Statistics to Make You a - Unibet 20 Hold'em Poker Odds & Statistics to Improve your Poker Game.

• 3 more ways to make j q 8 9 T k 9 T k a 7 8 9 T 3 x 39 adds 117 for 0.0011 = 905.453 And there are 3 5 heart boards = 0.0011 = 1 / 904.29 share | improve this answer edited Mar 27 at 16:23 answered Mar 27 at 15:56 paparazzo 5,7111933 add a comment | Your Answer draft saved draft discarded Sign up or log in Sign up using Google Sign up using Facebook Sign up using Email and Password Post as a guest Name Email Post as a guest Name Email discard By clicking 'Post Your Answer', you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies.
• How to play a flush draw | Poker School | Paul Phua Poker Probabilities - Wizard of Odds Poker probability - Wikipedia Poker Drawing Odds & Outs | odds - Percentage chance of flopping straight or flush draw for This instant poker odds calculator tells your immediate odds of winning or losing in Open ended straight flush draw, Straight/Flush/Pair, 21, 5 Jul 2018 If you're going to win the pot 50% of the time, your break-even odds only have to be 1-1 to Say you flop an open-ended straight-flush draw.The way I calculated these probabilities assumed independence between hands, which is not a correct assumption, but the results should be a close estimate.
• – Radu Murzea♦ Sep 10 '15 at 15:28 1 I'm pretty sure most professional players never thought of this, except for fun – user1165 Sep 10 '15 at 17:47 2 Well, whatever it is, it's certainly less than the odds of a Royal and Quads AND Ray Romano at your table.
• Wake up with the smartest email in your inbox.But what are the odds that one of your opponents is dealt aces as well?
• How to handle technical tests that are absurd?
• 100 / 20 = 5.Texas Hold 'Em -- High Hand Probabilities -- 1 to 5 Straight Flush, If your hole cards are a pair, or in fact anything other than two of AKQJ10 of the same suit, your chance is zero.

There is no easy formula for this one. At a full-ring https://editorialmongtse.com/het-slot-vredenburg-tot-utrecht table the odds for that to happen are 1 in 13.

Learn how to play poker and improve your game on poker night! Poker Hands - What Beats What The Basics of How to Play Pai Gow Poker Hold'em Nicknames Learn to Win at High Card Flush The Features of a Standard Deck of Cards How Does a Joker Work in Poker?

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Flush by turn: Walker Poker Review 1 (The frequencies given are exact; the probabilities and odds are approximate.) Since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits.

2-to-1 against = 1 out of every 3 times = 33.3% 3-to-1 against = 1 out of every 4 times = 25% 4-to-1 against = 1 out of every 5 times= 20% 5-to-1 against = 1 out of every 6 times = 16.6% Converting odds into a percentage: 100 / 20 = 5.

Another example would Downs Casino Albuquerque New Mexico be if you hold a hand like and hit two pair on the flop of . The probability these five ranks will represent four suits, one of two, and three of one, is 4*combin(5,2)*3*2=240.

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.

Texas Holdem Probability Equation

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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.

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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.

Flush Texas Holdem

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.

Straight In Texas Holdem

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.