In this article, we ranked starting hands in Texas Hold'em by the winning chance. Using our poker odds calculator engine, we first calculated the 'fixed-preflop, post-river' winning probability of all 169 types of starting hands. Then, we ranked and ordered the starting hands from the best to worst in the table and chart. 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. The numbers are exact to the rounding I used, which was.

• No Limit Hold'em Starting Hand Chart

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.

Statistics based on real online play[edit]

Statistics based on real play with their associated actual value in real bets.^[3]

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]

1. ^David Sklansky and Mason Malmuth (1999). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1
2. ^Hold'em Excellence: From Beginner to Winner by Lou Krieger, Chapter 5, pages 39 - 43, Second Edition
3. ^http://www.pokerroom.com/poker/poker-school/ev-stats/total-stats-by-card/^{[dead link]}
4. ^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.
5. ^Martain, Tim (2007-07-15). 'A little luck helps out'. Sunday Tasmanian. Retrieved 2010-01-10.

Based on the tabulated data and chart generated, there are a few interesting observations to be made. The are listed below:

1. Pair A is best hand

There should be no surprise that Pair A is the best hand. Having a pair A, helps you to easily get the best possible double pair combo or three-of-kind combo. While it might be harder to strike straight or flush with it, those scenarios are typically less likely to happen. Thus, making pair A better in general.

2. Offsuit 72 is the worst hand

This might be less known to people and it could be counter intuitive. Some might have thought that perhaps Offsuit J2 would be worse than Offsuit 72. But, that is not the case.

To understand why this is the case, we can start thinking about what are combinations that are most likely to lead to a winning combo assuming no one folds. Given any hands, we are more likely to win with double pair, followed by 3-of-a-kind, straight flush and so forth.

With offsuit 72, we are more likely to win double pair of pair 7 and pair 2, followed by three-of-a-kind and so on. However, it is also worthwhile to note that it is highly like other players has a better double pair or three-of-a-kind. This bring us to the next important lesson to learn.

3. Having a suited, closely connected hand with A, K or Q is better than having pairs that is less than 9

If you were to investigate the table or chart, the hand ranked 5th is Suited AK. What is even more interesting is pairs hand only took 6 spots from rank 1 to rank 20. Most of the remaining spots were taken up by suited, closely connected hands with a high card like A, K or Q.

The reason for this is similar to previous point that we made. It is more frequent that players will win using double pairs or 3-of-a-kind. Therefore, having a higher card helps to push you to a better standing to win.

One final note on this topic - Pair 9 is the last pair hand ranked in the top 20 hands. Playing any other pairs hand may not be as good as conventional wisdom might suggest.

4. Winning chance drops fast within the top 7 ranked hands

This is the lesson that really took us by surprised. While developing our poker odds calculator, we did had a sense that odds of winning was somewhat asymmetric. But, the chart above really solidify how much the asymmetry was.

Within the top 7 ranked hands, the probability of winning drops really fast from paired A to paired K and so forth. If you get the top 7 hands, you really should work hard to get through the preflop.

5. You are more likely to win a 6 players match than a 9 players one

A player with hands that are in the top 7 ranks in a 6 players game have a much better chance of winning in a 9 players game. For example, Paired A has roughly 49.5% preflop winning probability in a 6-player game compared to only 35% in a 9-players game. While 14.5% difference is not as big as it sounds, it has a significant impact on the pot odds that you will need to make a value play. In short, it might be easier to make money off a 6 players game rather than a 9 players game.

6. In a no-folding six players match, your hand range to play is very large

This point is not as crucial as other points we have made. But, we find this observation quite interesting although it is unlikely to happen in real life.

Suppose that we are in a no-folding 6 players Texas Hold'Em match. During every betting session, our pot odds is 5-to-1. This means that for every $1 we bet, we stand to win $5.

Based on this pot odds, our break-even pot equity or winning odds is around 16.67%. Using the chart above, we can see that we can play any hands better than rank 106. This means that players can play 105 types of hands out of 169 types (59.2% of all types) and still perform better than break even! Basically, you have a very large hand range to play in this type of situation.

Nonetheless, this is a just-for-fun analysis, which does not happen that often in real life. Based on some of our experience playing, it could happen sometimes during preflop though.

7. Our hand rankings are similar to Sklansky hand groups

Sklansky hand groups was formulated by David Sklansky and Mason Malmuth. Both of these old school poker players understand the math very well. It is no surprise that our hand rankings aligns very well with their proposed hand groups.

No Limit Hold'em Starting Hand Chart

Sklansky hand group proposes that Tier 1 group consists of pair A, pair K, pair Q, pair J and suited AK. These cards are essentially ranked 1 to 5 via our Monte Carlo simulation. The same observation can be made for Sklansky Tier 2 and Tier 3 hand group.