Texas Holdem Poker Hand Combinations

How can I improve my hand-reading? I often get asked this question. It's an interesting question because in a way it's the same as asking How can I get better at poker? Hand reading is such an integral part of the game, that there is unlikely be a simple answer to this simple question. Hand reading is something that improves slowly and is the product of a large amount of experience and practice. Nevertheless, we will attempt to accelerate that progress with a few tips and tricks.

1. Understanding Ranges

We often refer to a range in percentage format. For example, “our opponent has a 3-bet range of 10%”. On it's own this statement has extremely limited meaning. Logic tells us that these 10% of hands are probably reasonably strong. But that idea is not conferred in a frequency or percentage. Our opponent could be 3betting the worst 10% of hands.
  1. Of the 1,326 combinations, there are 169 distinct starting hands grouped into three shapes: 13 pocket pairs (paired hole cards), 13 × 12 ÷ 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 169.
  2. The world's most trusted Texas hold'em poker odds calculator. Improve your poker or find out just how bad that bad beat was. Poker odds calculate the chances of you holding a winning hand.
  3. Of the 1,326 combinations, there are 169 distinct starting hands grouped into three shapes: 13 pocket pairs (paired hole cards), 13 × 12 ÷ 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 169.
In other words there has to be more to a range than just a frequency. Sure, the frequency is extremely useful, but we also need to assign a type to that range.
Merged/Depolarized/Linear

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– Ideally this is the easiest type of range to understand. The three terms here can be used interchangeably. The notion of “linear” suggests that we are referring to only the top hands. The irony is that there is no way of knowing which the top hands are, it really depends on how we rank them. Hands have no equity in the absolute sense, they only have equity when compared to another hand or range. So some hands might have good Texas Holdem Poker Hand Combinationsequity vs certain ranges but not so good equity vs other ranges. We may not even choose to rank hands in terms of equity. In fact, the deeper the stacks get in general the less we care about equity as opposed to playbility.
Even if we identify our opponent's range as linear 10% (which is a great start), we still want to observe if he shows a preference or leaning to any specific types of holdings over others.
So there is no “correct” or “absolute” version of a linear range, it will be partly subjective. Most people would agree that AA is the best hand in NLHE, but would they choose A9o or 9Ts as part of their linear range if they had to make a choice? A9o has noticeably better equity vs any 2 cards but 9Ts has a playbility advantage in most situations. Even if we identify our opponent's range as linear 10% (which is a great start), we still want to observe if he shows a preference or leaning to any specific types of holdings over others.
Polarized – Generally considered the opposite type of range to that described above. Players generally have a value-range and a bluff-range but not so much of the stuff in between. For example a player decides to fire 3 big barrels on flop, turn, and river. He is unlikely to have a mid-strength hand here, it doesn't make any sense. He either has something really strong, or he is bluffing.
True polarization only occurs on the river (or at least it should if we are playing optimally). On the river we fire our best hands for value and our worst hands as a bluff. On any other street while there are still further cards to come, we do not bluff with our worst possible holdings, simply hands weaker than those we opt to play passively with. For example preflop we'd have something like AA in our value-range and maybe something like Q9s in our bluff range. Q9s is a reasonable hand and has some equity/playability. We wouldn't generally use something like 23o which would be true polarization. The same applies on the flop and turn. We don't generally bluff with zero-equity holdings, we pick those with some equity/potential.
Generally we recognize a polarized range when someone is playing aggressively across multiple streets, especially facing a three-barrel. Any time our opponent is essentially representing a super strong hand which is not made frequently he can be considered polarized.
Condensed – Players often overlook this type of range, but it is nonetheless very important. It's common to mistakenly assume that there are only 2 main types of range, polarized and depolarized. Condensed is similar to a merged range except it doesn't contain super strong holdings. So imagine something like a J78ss texture and our opponent decides to check/call. He is unlikely to check/call garbage here. He is also unlikely to check/call any super strong hand like straights or sets. These need protection on such a drawy texture and would likely get check/raised. So our opponent has a range that consists of mid-strength hands and draws, but no air, and no nuts.
As a rough guide someone who is passively calling down is more likely to have a condensed range while someone who is being aggressive is more likely to have a polarized range.
Capped – Very similar to a condensed range. The main difference is that a capped range could consist entirely of air hands while a condensed range has some showdown hands. In the example above on the J78ss we could say that our opponent is capped if the turn card is blank. If the turn card completes possible draws then our opponent is no longer capped. Identifying capped ranges is a crucial part of increasing our non-showdown winnings (red-line).
Weighted – Ranges can have different weightings. Even if we know our opponent has a 10% polarized range it's good to be able to specify which percentage of that range is for value and which percentage of that range is a bluff. It makes a big difference whether our opponent is “weighted towards value”, or “weighted towards bluffs”.

2. Thinking Backwards

Hopefully if you are reading this article you already get the basic idea of hand-reading. Our opponent starts out with all possible combinations of hands. Based on his actions we remove combinations of hands that don't make sense and his range gets progressively narrower. By the river we have hopefully narrowed his range down to one of a few possible holdings and can make the best decision vs that range.
Sometimes this is not the best way to do things however. The human brain is not really wired to keep track of hundreds of different hand combinations at the same time. Sometimes it is significantly easier to focus on what our opponent does not have rather than what he has. So if he's representing something strong on the river and we know he would have raised it on an earlier street then it's not necessary to visualise his entire range in order to understand that we have a call.
By the river we have hopefully narrowed our opponent's range down to one of a few possible holdings and can make the best decision vs that range.
So depending on the exact situation it might be easier to think about what our opponent has or it might be easier to think about what he does not have. Experiment with both depending on the situation.

3. Combinatorics

We at least need a vague idea of how to employ combinatorics. This is not easy to calculate mid-hand, but even having a rough idea of how many combinations of certain hands are possible can increase our decision-making efficiency. See the article on combinatorics here at pokervip.com for more information.

4. Reverse Hand Reading

This is a very effective technique when playing against regulars. Reading the hand of a good regular can be difficult – their hand strength might often be disguised. However we do know what our own possible range might look like. Reverse hand reading is a technique where we read our own range from villain's perspective and base our play off this.
In other words if we take a super strong line and we still get raised, it's generally safe to say that we can be folding some big hands. However if we take a line where we look weak, we should be more inclined to continue with our bluff-catchers when we face aggression.

5. Recognizing Capped Ranges

This is an important technique that allows us to make zero-equity plays and generate automatic profit. It essentially revolves around understanding when opponent would have done something different on earlier streets with his monsters.
So on the J78ss, when our opponent check/calls and the turn card is a blank we can typically assume that he is very unlikely to have anything strong. This is a good situation to keep the pressure on. In the same situation if the board comes J55 rainbow, our opponent would often slowplay his premiums so we can't automatically assume that he is capped if he takes a passive line.
Other situations where many opponents are capped involve any situation where our opponent misses a continuation bet on flop turn or river. Naturally we should skip cbets with strong hands for range protection purposes, but the fact is, most players don't do this enough. Check out the article “Common Bluff Spots” for more information on this topic.

6. Understanding Tendencies

This is absolutely crucial and essentially comes with experience. We could be very strong at putting our opponents on specific ranges and keeping track of individual combinations, but if our assumptions about our opponents' tendencies are incorrect, then it is all for nothing.
This kind of thing can often vary from network to network and from stake to stake. It's often the case that we will not maximise our full potential winrate until we have played at least 10k hands at a certain limit and started to gauge the general tendencies of the games.
Even if our assumptions about our opponents range are perfect, we can still end up losing if our expectations regarding his tendencies are not accurate. Imagine we've narrowed our opponents range down to one specific hand, a mid-pair hand. (Probably impossible in practice). We assume this player would fold his mid pair facing a large bet on the river. He doesn't. We've correctly identified his holdings but still lost money.
One reason why players have difficulty moving up limits is that don't allow for that 10k hands or so worth of adjustment and they try to adjust to quickly, after only a few hundred hands.
One reason why players have difficulty moving up limits is that don't allow for that 10k hands or so worth of adjustment. For example they might play a few hundred hands or so and then say something like “Wow, players 3bet a lot more aggressively at this limit”. Could be true, might not be. The point is, we are not qualified to make such a judgement after only a few hundred hands at the current limit. There is a reasonable chance our opponents have similar 3betting frequencies to the other limit but are running good over a small sample. If we start responding with aggression and keep running into AA/KK, we shouldn't always be surprised. Perhaps we tried to adjust too quickly.

7. Thinking Deeply

With the invention of fast-fold poker formats, it's easy to get into the habit of making decisions quickly. It's easy to forget that poker is a game of strategy and requires a deep level of thought, similar to chess.
We need to give ourself a fighting chance by slowing down our decisions and thinking as deeply as time permits about our opponents' holdings. Don't be afraid to use your time bank. It doesn't cost us any additional chips and gives us a big advantage, especially if our opponents are making decisions in 2-3 seconds without really thinking.
Often quick decisions can be a result of poor mindset. So while we might ordinarily be reasonably strong hand readers, tilt has the ability to shut-down our rational thinking processes and make our hand-reading non-existent. It's amazing how this can happen subtly without us realising.
As mentioned at the outset, hand-reading ability is something that we develop through playing large volume and deliberate study off the table. Don't be discourage if you feel it's taking longer than you imagined to develop strong hand-reading fundamentals. The 7 suggestions in this article should help to accelerate you along the way.
A pair of aces is the best pre-flop hand in Texas Hold'em Poker

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.

  • 2Limit hand rankings

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, AJ and AJ 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':

Combinations


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  • Pairs, (or 'pocket pairs'), which consist of two cards of the same rank (e.g. 99). One hand in 17 will be a pair, each occurring with individual probability 1/221 (P(pair) = 3/51 = 1/17).

An alternative means of making this calculation

First Step As confirmed above.

There are 2652 possible combination of opening hand.

Second Step

There are 6 different combos of each pair. 9h9c, 9h9s, 9h9d, 9c9s, 9c9d, 9d9s

To calculate the odds of being dealt a pair

2652 (possible opening hands) divided by 12 (the number of any particular pair being dealt. As above)

2652/12 = 221


  • Suited hands, which contain two cards of the same suit (e.g. A6). Four hands out of 17 will be suited, and each suited configuration occurs with probability 2/663 (P(suited) = 12/51 = 4/17).
  • Offsuit hands, which contain two cards of a different suit and rank (e.g. KJ). Twelve out of 17 hands will be nonpair, offsuit hands, each of which occurs with probability 2/221 (P(offsuit non-pair) = 3*(13-1)/51 = 12/17).

Texas Holdem Poker Hand Combinations List

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.

There are 25 starting hands with a probability of winning at a 10-handed table of greater than 1/7.[1]

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[2] 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.[3]

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]

Texas Holdem Poker Hand Ranking

Phil Hellmuth's 'Play Poker Like the Pros' book published in 2003.

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TierHandsCategory
1AA, KK, AKs, QQ, AKTop 12 Hands
2JJ, TT, 99
388, 77, AQs, AQ
466, 55, 44, 33, 22, AJs, ATs, A9s, A8sMajority Play Hands
5A7s, A6s, A5s, A4s, A3s, A2s, KQs, KQ
6QJs, JTs, T9s, 98s, 87s, 76s, 65sSuited Connectors

Statistics based on real online play[edit]

Statistics based on real play with their associated actual value in real bets.[4]

TierHandsExpected Value
1AA, KK, QQ, JJ, AKs2.32 - 0.78
2AQs, TT, AK, AJs, KQs, 990.59 - 0.38
3ATs, AQ, KJs, 88, KTs, QJs0.32 - 0.20
4A9s, AJ, QTs, KQ, 77, JTs0.19 - 0.15
5A8s, K9s, AT, A5s, A7s0.10 - 0.08
6KJ, 66, T9s, A4s, Q9s0.08 - 0.05
7J9s, QJ, A6s, 55, A3s, K8s, KT0.04 - 0.01
898s, T8s, K7s, A2s0.00
987s, 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.'[5][6] 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.

Texas Holdem Card Combinations

Notes[edit]

  1. ^No-Limit Texas Hold'em by Angel Largay
  2. ^David Sklansky and Mason Malmuth (1999). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1
  3. ^Hold'em Excellence: From Beginner to Winner by Lou Krieger, Chapter 5, pages 39 - 43, Second Edition
  4. ^http://www.pokerroom.com/poker/poker-school/ev-stats/total-stats-by-card/
  5. ^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.
  6. ^Martain, Tim (2007-07-15). 'A little luck helps out'. Sunday Tasmanian. Retrieved 2010-01-10.

Texas Holdem Poker Practice

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