Probability Of Winning Hands In Texas Holdem
Types of Starting Hands
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. Let us learn all the winning card combinations by reading the sections found below. The Royal Flush. The Royal Flush, as the name suggests, is the best possible hand in Texas Holdem. This hand combination is made up of the five highest cards in a deck – the Ace, King, Queen, Jack and the number 10. In Texas Hold’em, the probability any given hand will win is simply: The probability your opponents will fold + the probability your hand will win in a showdown.
by Rich McComas (updated Feb 6, 2004)
For example: To calculate your hand odds in a Texas Hold'em game when you hold two hearts and there are two hearts on the flop, your hand odds for making a flush are about 2 to 1. This means that for approximately every 3 times you play this hand, you can expect to hit your flush one of those times. The odds of flopping a royal flush in Texas Hold'em in any given hand is 1 in 649,740 (before cards are dealt). If you have a suited hand with two high cards (like Q♠ J♠), you have a 1 in 19,600 chance of hitting a royal flush on the flop.
Below, I have categorized thirteen types of starting hands, in order of their value. The statistics are borrowed from www.pokalyzer.com which has ran 700 billion simulated hands to produce their results.
1. High Pairs (80%ers)
A high pair is a pair of Aces, Kings, or Queens. Some people count Jacks as high pairs, but I do not as they are not statistically matched to the value of other high pairs. My advice is Raise Pre-Flop and drive the garbage out. If you are in a late position, then you do not need to raise if someone else has driven out the garbage for you. However, if you are in the blind and someone else has raised, you might want to re-raise in order to increase the size of the pot from one more round of betting, and to drive out someone like a small blind who may have limped in with a mediocre hand. Whatever you do, DO NOT limp in with a high pair. If you fail to raise above the big blind and get beat by someone with a suited non-connector, it will be your own fault. If no one else has raised, it is your job to do so in every case.
These are legitimately the best hands in poker, so rather than jam the pot and re-raise pre-flop you should probably just call the raise, or slow-bet. If someone else has raised ahead of you, the garbage will be cleared and you can wait till the flop to reveal a betting strategy. If you flop a King and Ace, and you are holding two King, you will be in the driver's seat and no one will know what hit them.
ODDS: You are going to land any given pair every 220 hands you play, so a pocket pair of aces is extremely rare. Assuming you play 100 hands a night, it will only happen every other night. The chance of landing one of the high pairs, however, is once in every 73 hands, so it should happen to you once every evening. Don't lose out on that opportunity.
| HAND | Rank | Win% |
| Pair of Aces | 1 | 84.9% |
| Pair of Kings | 2 | 82.1% |
| Pair of Queens | 3 | 79.6% |
2. Medium Pairs (70%ers)
A medium pair includes Jacks, Tens, Nines, Eights and Sevens. These are medium pairs because odds are that an overcard will flop more than half of the time. Even though the odds of winning with a pair of Jacks is 77.2%, the chances of having the high pair after the flop are only 43%. You are hoping for trips so, but if you don't land them, only continue if you have the high pair possible, and then bet high to throw out the single face cards in the hole. Do not be suckered by landing another board pair, giving you two pair. Either someone else has trips or someone with a face card will get the high pair on the turn or river.
ODDS: The chance of landing any pocket pair of sevens or higher is the same as landing two cards ten or higher. These events happen every 5.4 hands you play (or 16% of the time).
| HAND | Rank | Win% |
| Pair of Jacks | 4 | 77.2% |
| Pair of Tens | 5 | 74.7% |
| Pair of Nines | 6 | 71.7% |
| Pair of Eights | 7 | 68.7% |
| Pair of Sevens | 9 | 65.3% |
3. Ace-Face Suited (65%ers)
An ace with another face card of the same suit is Ace-High suited, which is a winning hand most of the time. Two suited hole cards only draw to a flush 3% of the time, but if they are both high, you have a great shot at winning high pair as well. Because you hold the ace, any draw to a straight is a close-end straight, so your odds are lower than an open-end straight.
ODDS: You will receive two suited cards every 3.3 hands, and it is likely that at least two players at the table have suited cards, so don't get over-excited about just any suited combination.
| HAND | Rank | Win% |
| AK Suited | 8 | 66.2% |
| AQ Suited | 10 | 65.3% |
| AJ Suited | 11 | 64.4% |
4. Ace-Face Offsuit (63%ers)
An Ace plus a face card of another suit are the most frequently played hands in Hold 'em. Most people stay in and raise with this hand. If you pair the face card, you will have the high kicker, and if you pair the ace, you will probably have a higher kicker than anyone else. If you draw to a straight, you will beat other straights and at least split the pot.
| HAND | Rank | Win% |
| AK Offsuit | 12 | 64.5% |
| AQ Offsuit | 14 | 63.5% |
| AJ Offsuit | 15 | 62.5% |
5. Ace-Low Suited (60%ers)
An ace with anything 10 or lower in the same suit. This is not a hand to go heads up against someone with. This is best played in late position with a lot of callers already in the pot, giving you higher pot odds for a flush draw. This is also a good hand for stealing the blinds if you are on the button, because at least you have one ace in the hole. Mostly, though, I like to play this hand only in No Limit Hold'em because I may need to stay in to the river to get my cards, and I want to be able to go all-in and make a big score if I have the high flush. Earning a minor pot on such low odds just doesn't make as much sense.
POT ODDS: While the chances of winning against random hands are respectable, the chances of winning in heads-up play are not. Two suited pocket cards will flop a flush less than 1% of the time, and complete a flush by the river 6.52% of the time, and two separated cards (such as A5) will hit a draw will hit a draw only about 0.06% of the time. The probability of making a flush, therefore, is 15 to 1 against, meaning that you should really only enter the pot if there are 15 other players in, which never happens, so playing these cards with any regularity is a losing proposition.
If you are on the button, and the flop is cheap, and you do go with Ace-Low suited, then you should fold unless you immediately receive either two cards that match your hole cards or a four flush. The probability of flopping a four-flush is 8.1/1 or 10.9%, and the possibility of completing the flush by the river is 1.9/1 or 35%. When betting on the turn hoping for flush, you really want at least three people in the pot, or enough money for three in the pot.
| HAND | Rank | Win% |
| AT Suited | 13 | 63.5% |
| A8 Suited | 21 | 60.5% |
| A6 Suited | 30 | 58.2% |
| A4 Suited | 35 | 57.1% |
| A2 Suited | 46 | 55.5% |
6. Face-Face Offsuit (58%)
Two face cards are best used when drawing to a straight, so you want to get into the flop as cheaply as possible. If your high card is a King, you will flop an Ace 23% of the time, and if your highest is a queen, a higher card will flop 41% of the time.
| HAND | Rank | Win% |
| KQ Offsuit | 23 | 60.4% |
| KJ Offsuit | 26 | 59.4% |
| QJ Offsuit | 39 | 56.9% |
7. Low Pairs (55%ers)
Low pairs are sixes or lower. All low pairs are questionable investments at best. If you all you have are have sixes, the chances are that someone will flop a higher pair 95% of the time. If you have a low pair and you flop a open-end straight draw, stay in, because you own TWO of the hole cards needed for the straight, lowering the odds that you will have to split the pot.
ODDS: You are going to land a pocket pair about once every 16 hands so don't get too excited about the lower pairs. Half the time, your pocket pairs will be high or medium pairs. Stick to those.
POT ODDS: Some people play low pairs in late position hoping to see trips, which is also the hope for higher pairs. If you take a pocket pair to the river, you have a 4.2/1 (19%) chance of making a set or better, so NEVER put money in the pot with this hand unless there are at least five other players. However, I don't bet on low pairs EVER, because it is more likely that someone else will take a straight or a flush or higher trips or a full house to the river and beat my low trips. With low pairs, I would never want to stay in unless I saw trips on the flop, and the chances of that are 7.5/1 (or 11.8%) so I would need 9 other people in the pot to make money, which is a very rare occurrence.
| HAND | Rank | Win% |
| Pair of Sixes | 17 | 62.7% |
| Pair of Fives | 27 | 59.6% |
| Pair of Fours | 48 | 56.3% |
| Pair of Threes | 66 | 52.8% |
| Pair of Deuces | 87 | 49.4% |
8. King Flush Draw (55%ers)
A king plus another card in the same suit is a dangerous hand, unless the Ace is on the board, which will happen one-third of the time that you draw to a flush. These cards should be considered the same value as low pairs, except with a low pair, at least you know if you have trips on the flop. With a King Flush draw, you could have the ace on the flop, and still not get the flush on fifth street, so this is a potentially costly hand. See the section on 'Sucker Hands' for more info.
| HAND | Rank | Win% |
| KQ Suited | 16 | 62.4% |
| KT Suited | 22 | 60.6% |
| K8 Suited | 37 | 56.8% |
| K6 Suited | 50 | 54.8% |
| K4 Suited | 60 | 52.9% |
9. Ace-Low Offsuit (55%ers)
An Ace plus a non-suited card lower than a face card is one of the biggest losers in Hold'em. Most players stay in with any ace, especially if you are playing with less than 10 at a table. However, I routinely fold this hand because 75% of the time, with 20 cards dealt into the pocket, someone else is ALSO holding an Ace in the pocket, and more often than not, their kicker will be higher than yours.
| HAND | Rank | Win% |
| AT Suited | 19 | 61.6% |
| A8 Suited | 32 | 58.4% |
| A6 Suited | 42 | 55.9% |
| A4 Suited | 49 | 54.7% |
| A2 Suited | 59 | 53.0% |
10. Suited Connectors (45%ers)
Two suited cards next to each other are only slightly better than non-suited connectors because they help with the straight flush. If you draw to a flush or a straight ONLY, however, you are in serious risk of losing to larger straights or flushes. Don't get too excited about these cards because they share the same suit. The flush draw potential only increases your chances of winning by 3%. I generally fold all suited connectors, occasionally keeping a QJ or JT if I am in late position and several players are in and none have raised. If, after the flop, your hole card is at the low end of the straight, this is a classic 'Sucker Hand.' I know of some good players who love suited connectors, however, because they know on the flop if they have a killer hand, and a further investment will not be required. My attitude is that if you love suited connectors pre-flop, you might as well get equally excited about any low straight draw.
ODDS: You will receive a suited connector once every 46 hands (or 2.1% of the time), and this is so rare, that people tend to jump for joy whenever it happens, not thinking that the changes of getting a 2-4 are even worse.
| HAND | Rank | Win% |
| JT Suited | 45 | 56.2% |
| 98 Suited | 83 | 48.9% |
| 76 Suited | 115 | 42.8% |
| 54 Suited | 136 | 38.5% |
| 32 Suited | 163 | 33.1% |
11. Low Straight Draw (42%ers)
Two cards of different suits next to each other in value are going for a straight draw, and they are 3% less likely to win than the comparable suited connectors. Like suited connectors, only stay in if the pot is big because there are lots of other players calling pre-flop. Two low cards not in order is a Trash hand, and is not a Low Straight draw even if they are separated by only one card. Also, 3-2 in the pocket is the worst possible hand in poker even it if is a straight draw. An excellent analysis of unsuited connectors can be found at: http://www.pokerstove.com/unsuited.txt.
| HAND | Rank | Win% |
| JT Offsuit | 57 | 53.8% |
| 98 Offsuit | 99 | 46.1% |
| 76 Offsuit | 133 | 39.7% |
| 54 Offsuit | 153 | 35.0% |
| 32 Offsuit | 169 | 29.2% |
12. Two Suited Cards (40%ers)
Two other suited cards, with at least one NOT being a face card, results in a four-flush flop only 10% of the time, and only a third of those finish as a flush. This is a loser hand.
| HAND | Rank | Win% |
| T7 Suited | 84 | 48.7% |
| T2 Suited | 118 | 42.5% |
| 83 Suited | 139 | 38.3% |
| 73 Suited | 143 | 37.3% |
| 62 Suited | 156 | 32.8% |
13. Trash Hands
Everything not mentioned above is a trash hand (as are some of the hands above, in my opinion), and there is no coincidence that these are in unlucky category 13. The only reason anyone stays in with these hands is that the flop was so cheap that the couldn't say no, such as being in the big blind with no raises. If you get a trash hand, and you are in the small blind, only consider calling if everyone else has and if you are sure that the person in the big blind won't raise you.
Based on 4,000,000,000 simulated gamesUse at your own risk
(I'm terrible at Poker, and there could be a bug in my code)
Pre-Flop Hole Card Winning Odds/Probabilities:
Given hole cards XY in an n-player Texas Holdem game, with no cards on the table, what is the probability that XY will beat all other n-1 hole cards after the river?
Actually winning your hands depends on many more factors (as my poker buddies will be quick to point out!)—knowing when to fold on flop/turn/river (even if you started out well), your betting strategy (maybe you're good at bluffing people out), what you think your opponents have (this is probably the most important), the blinds, etc. Poker is complicated. These tables just tell you how good your hole cards are (statistically) just after the deal, which may help you decide whether it's worth paying for the flop or not. That is all.
Historical note:
These statistics were the result of a fun, personal coding project on the side during grad school at the University of Illinois. Enough people are finding this page useful, and so I've decided to keep the page up. May the odds be with you.
Ranked by Winning Percentage
10 Player9 Player
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3 Player
Probability Of Winning Hands In Texas Holdemhold Em
2 Player
Ranked by Wins+Ties Percentage
10 Player9 Player
8 Player
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Probability Of Winning Hands In Texas Holdemem Poker
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Check out a heat-map based visualization of these probabilities by Jeff Lowery
These statistics are © Apu Kapadia, 2005