Texas Holdem Probability Of Hands
Follow these hand charts and learn how to play your starting hands at Texas Holdem.
In the case of Texas Hold'em, there's the 2 pocket cards and 5 on the board. This way of working out the probabilities would be the more accurate way - however, just to note, the probabilities worked out on 5 of 52 are practically the same, and far easier to calculate. Number of possibilities. 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. Holdem Hand Strength from SharkfacePoker LLC is a free Poker tool which helps you gain a greater insight into the game of Texas Holdem. This tool gives you the ability to understand how strong your starting hand is against all other hands and any random number of opponents along with useful stats that help you identify the overall probabilities.
The charts below will give you a great starting point on how to play your starting hands. For all of you beginners, we recommend consulting these charts will playing online.
We provide 4 separate charts depending on where you are seated relative to the dealer. You can find out how to play the Blinds, Early Position, Middle Position, and Late Position.
These 169 hands are not equally likely. Hold 'em hands are sometimes classified as having one of three 'shapes': Pairs, (or 'pocket pairs'), which consist of two cards of the same rank (e.g. One hand in 17 will be a pair, each occurring with individual probability 1/221 (P(pair) = 3/51 = 1/17). Alternative means of making this.
After the flop, you can consult the Drawing Odds Chart at the bottom, but you will also have to develop your reads, pot odds and other skills to develop your post-flop strategies.
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How to Read the Starting Hand Charts
Let’s look at some examples of how to use these poker odds charts…
| Early Position 88 77 | Unraised Pot Call 1 | Raised Pot Fold |
| * In early position, only call with A8s or 77 if there is already at least one caller in the pot. Fold if you are first in or if the pot has been raised. | ||
| Middle Position 98s | Unraised Pot Call 3 | Raised Pot Fold |
| * In middle position, only call only play 98s if there are already three or more callers. Do not call raises. | ||
| Late Position JJ TT 99 | Unraised Pot Raise 1, Call 2 Raise First In, Call 1 | Raised Pot RR 1 Option, Call All RR or Fold against 1 Player, Call 3 |
| * In late position, you should raise with JJ against one caller or first in, and call against two callers or more. You have the option of rerasing a lone raiser; otherwise, always call a raise. * Raise 99 when you are first in from late position; otherwise, call if the pot has not been raised. If the pot has been raised, you should either re-raise or fold when against a single player, or call if there are three players in the hand. | ||
| Blinds AQs AQ A9s KJ | SB Unraised Pot Raise 1 or 2, Call 3 Call Call | SB Raised Pot RR 1 or 2, Call 3 RR Lone Late, Fold Fold | BB Raised Pot Call (raise 1 or 2 limpers) Call Call 2, or 1 Late |
* In the small blind, you can raise or reraise one or two opponents with AQ, otherwise, call against three or more opponents. * In the small blind, always call A9s against limpers. If the pot has been raised, you should reraise a late position player. You should fold if the raiser is in early or middle position or against two or more opponents. * In the big blind, you can call with KJ against two opponents or a lone late player. Fold against a lone player from early or middle position. | |||
With a little practice, you should be able to find the appropriate poker strategy very quickly. I recommend keeping these charts open to provide guidance as you play. May the odds be with you! – Matthew Hilger
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In the poker game of Texas hold 'em, a starting hand consists of two hole cards, which belong solely to the player and remain hidden from the other players. Five community cards are also dealt into play. Betting begins before any of the community cards are exposed, and continues throughout the hand. The player's 'playing hand', which will be compared against that of each competing player, is the best 5-card poker hand available from his two hole cards and the five community cards. Unless otherwise specified, here the term hand applies to the player's two hole cards, or starting hand.
Essentials[edit]
There are 1326 distinct possible combinations of two hole cards from a standard 52-card deck in hold 'em, but since suits have no relative value in this poker variant, many of these hands are identical in value before the flop. For example, A♥J♥ and A♠J♠ are identical in value, because each is a hand consisting of an ace and a jack of the same suit.
Therefore, there are 169 non-equivalent starting hands in hold 'em, which is the sum total of : 13 pocket pairs, 13 × 12 / 2 = 78 suited hands and 78 unsuited hands (13 + 78 + 78 = 169).
These 169 hands are not equally likely. Hold 'em hands are sometimes classified as having one of three 'shapes':
- Pairs, (or 'pocket pairs'), which consist of two cards of the same rank (e.g. 9♠9♣). One hand in 17 will be a pair, each occurring with individual probability 1/221 (P(pair) = 3/51 = 1/17).
- Alternative means of making this calculation
- First Step
- As confirmed above.
- There are 1326 possible combination of opening hand.
- Second Step
- There are 6 different combos of each pair. 9h9c, 9h9s, 9h9d, 9c9s, 9c9d, 9d9s. Therefore, there are 78 possible combinations of pocket pairs (6 multiplied by 13 i.e. 22-AA)
- To calculate the odds of being dealt a pair
- 78 (the number of any particular pair being dealt. As above) divided by 1326 (possible opening hands)
- 78/1326 = 0.058 or 5.8%
- Suited hands, which contain two cards of the same suit (e.g. A♣6♣). 23.5% of all starting hands are suited.
Probability of first card is 1.0 (any of the 52 cards)Probability of second hand suit matching the first:There are 13 cards per suit, and one is in your hand leaving 12 remaining of the 51 cards remaining in the deck. 12/51=.2353 or 23.5%
- Offsuit hands, which contain two cards of a different suit and rank (e.g. K♠J♥). 70.6% of all hands are offsuit hands
Offsuit pairs = 78Other offsuit hands = 936
It is typical to abbreviate suited hands in hold 'em by affixing an 's' to the hand, as well as to abbreviate non-suited hands with an 'o' (for offsuit). That is,
- QQ represents any pair of queens,
- KQ represents any king and queen,
- AKo represents any ace and king of different suits, and
- JTs represents any jack and ten of the same suit.
Limit hand rankings[edit]
Some notable theorists and players have created systems to rank the value of starting hands in limit Texas hold'em. These rankings do not apply to no limit play.
Sklansky hand groups[edit]
David Sklansky and Mason Malmuth[1] assigned in 1999 each hand to a group, and proposed all hands in the group could normally be played similarly. Stronger starting hands are identified by a lower number. Hands without a number are the weakest starting hands. As a general rule, books on Texas hold'em present hand strengths starting with the assumption of a nine or ten person table. The table below illustrates the concept:
Chen formula[edit]
The 'Chen Formula' is a way to compute the 'power ratings' of starting hands that was originally developed by Bill Chen.[2]
- Highest Card
- Based on the highest card, assign points as follows:
- Ace = 10 points, K = 8 points, Q = 7 points, J = 6 points.
- 10 through 2, half of face value (10 = 5 points, 9 = 4.5 points, etc.)
- Pairs
- For pairs, multiply the points by 2 (AA=20, KK=16, etc.), with a minimum of 5 points for any pair. 55 is given an extra point (i.e., 6).
- Suited
- Add 2 points for suited cards.
- Closeness
- Subtract 1 point for 1 gappers (AQ, J9)
- 2 points for 2 gappers (J8, AJ).
- 4 points for 3 gappers (J7, 73).
- 5 points for larger gappers, including A2 A3 A4
- Add an extra point if connected or 1-gap and your highest card is lower than Q (since you then can make all higher straights)
Phil Hellmuth's: 'Play Poker Like the Pros'[edit]
Phil Hellmuth's 'Play Poker Like the Pros' book published in 2003.
| Tier | Hands | Category |
|---|---|---|
| 1 | AA, KK, AKs, QQ, AK | Top 12 Hands |
| 2 | JJ, TT, 99 | |
| 3 | 88, 77, AQs, AQ | |
| 4 | 66, 55, 44, 33, 22, AJs, ATs, A9s, A8s | Majority Play Hands |
| 5 | A7s, A6s, A5s, A4s, A3s, A2s, KQs, KQ | |
| 6 | QJs, JTs, T9s, 98s, 87s, 76s, 65s | Suited Connectors |
Statistics based on real online play[edit]
Statistics based on real play with their associated actual value in real bets.[3]
| Tier | Hands | Expected Value |
|---|---|---|
| 1 | AA, KK, QQ, JJ, AKs | 2.32 - 0.78 |
| 2 | AQs, TT, AK, AJs, KQs, 99 | 0.59 - 0.38 |
| 3 | ATs, AQ, KJs, 88, KTs, QJs | 0.32 - 0.20 |
| 4 | A9s, AJ, QTs, KQ, 77, JTs | 0.19 - 0.15 |
| 5 | A8s, K9s, AT, A5s, A7s | 0.10 - 0.08 |
| 6 | KJ, 66, T9s, A4s, Q9s | 0.08 - 0.05 |
| 7 | J9s, QJ, A6s, 55, A3s, K8s, KT | 0.04 - 0.01 |
| 8 | 98s, T8s, K7s, A2s | 0.00 |
| 9 | 87s, QT, Q8s, 44, A9, J8s, 76s, JT | (-) 0.02 - 0.03 |
Nicknames for starting hands[edit]
In poker communities, it is common for hole cards to be given nicknames. While most combinations have a nickname, stronger handed nicknames are generally more recognized, the most notable probably being the 'Big Slick' - Ace and King of the same suit, although an Ace-King of any suit combination is less occasionally referred to as an Anna Kournikova, derived from the initials AK and because it 'looks really good but rarely wins.'[4][5] Hands can be named according to their shapes (e.g., paired aces look like 'rockets', paired jacks look like 'fish hooks'); a historic event (e.g., A's and 8's - dead man's hand, representing the hand held by Wild Bill Hickok when he was fatally shot in the back by Jack McCall in 1876); many other reasons like animal names, alliteration and rhyming are also used in nicknames.
Notes[edit]
- ^David Sklansky and Mason Malmuth (1999). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1
- ^Hold'em Excellence: From Beginner to Winner by Lou Krieger, Chapter 5, pages 39 - 43, Second Edition
- ^http://www.pokerroom.com/poker/poker-school/ev-stats/total-stats-by-card/[dead link]
- ^Aspden, Peter (2007-05-19). 'FT Weekend Magazine - Non-fiction: Stakes and chips Las Vegas and the internet have helped poker become the biggest game in town'. Financial Times. Retrieved 2010-01-10.
- ^Martain, Tim (2007-07-15). 'A little luck helps out'. Sunday Tasmanian. Retrieved 2010-01-10.