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In the last couple of years, as theoretical understanding of poker has galloped forward, an entire new vocabulary has emerged. I mean, when I was playing limit hold'em in San Jose 25 years ago, had you said, 'minimum defense frequency,' they'd have thought you were talking about the 49ers.

This means there are 3 times as many offsuit (non-pair) hands compared to suited. In total there are 154 hand types which are not pocket-pairs. 78 of these are suited, 78 of these are offsuit. Since there are 4 combos of every suited hand this results in (78. 4) 312 combos. A Texas Hold’em tournament is the same as any other game of Hold’em with a few added rules and twists. Learn more about the unique rules of Texas Holdem poker tournaments. Meanwhile, a Texas Holdem cash game is played on a single table with 2 to 10 players. In Texas Hold’em poker there are 2,652 possible starting hands. The way that you first get all the possible starting hands is to take the number of cards (52) and multiply that by 51 times. Remember that the first 2 cards that can be dealt can be anything from the deck. We'd agreed that she would three-bet all of her ace-king combos plus queens, kings, or aces, so we conclude she has one of 34 possible hands: 18 pocket pairs and 16 ace-kings. All Texas Hold’em starting hands can be separated into two categories: “suited” and “offsuit”. Suited hands contain two cards of the same suit, like J♣9♣, A ♥ K ♥, K♠Q♠ and 9 ♦ 3 ♦. All other starting hands are in the offsuit category, like A♠8 ♦, 7♣5 ♥ and K ♥ 9 ♦.

One of the words that you hear most frequently now is 'combinations' or 'combos.' Once you accept the concept of an opponent (or yourself) having a range of hands, the next interesting question is, 'Well, how many hands are in that range?' The way you answer that is to figure out how many 'combinations' there are of the hands that make up the presumed range.

Counting Combos: Pocket Pairs

Let's try one. Suppose you are playing $1/$3 no-limit hold'em and before the flop, you raise to $12 in early position with a pair of jacks. A straightforward and uncreative player in late position reraises you to $40. It folds back around to you. Based on your knowledge of this player, you expect her to three-bet with only a pair of queens or better, and all of her ace-kings. So her three-betting range is Q-Q, K-K, A-A, and A-K. How do your jacks fare against her presumed range?

Well, there are six combos of every pocket pair. To determine that, we see that we can randomly pick any of the four queens in the deck, and now have three remaining queens with which to make a pair. So that's 4 x 3 = 12. However, if we pick the first, and then the , that's no different than picking the first and then the . So we must divide by two to get a total of six.

Another way of skinning the same cat: pick the and see that you can then pick the , , or to make a pair. That's three. Now pick the first, leaving just the and to pair. Two more. Finally, the has only the to pair it. One more. 3 + 2 + 1 = 6. Math is beautiful.

So, six combos for each pocket pair. For Q-Q / K-K / A-A, that's a total of 18 combos. So far so good.

Counting Combos: Non-Paired Hands

What about A-K combos? If we give the villain all of the ace-king combos, then she can make one by taking any of the four aces and crossing them with any of the four kings. 4 x 4 = 16 and that's the number of combos.

Of course, if she restricts herself to suited ace-kings, then pretty clearly there are just four of those — , , , .

Calculating Our Equity

How Many Possible Hands In Texas Holdem Poker

We'd agreed that she would three-bet all of her ace-king combos plus queens, kings, or aces, so we conclude she has one of 34 possible hands: 18 pocket pairs and 16 ace-kings.

The 18 pocket pairs are 81-to-19 favorites against us, while we are a 57-to-43 favorite against the 16 ace-kings. To determine our equity against her, we weight each combo by its share of the range pie, compute our equity against that slice, and then sum them up.

For this example, we can compute our equity as follows:

1. Against the higher pairs, we have 0.18 (18%) equity. The higher pairs make up 18 / 34 of the villain's presumed range. So our equity for that piece = 0.18 x 18 / 34 = 0.10 or 10% (0.095 to be closer).
2. Against the ace-king combos, we have 0.57 (57%) equity. The ace-kings make up 16 / 34 of the villain's range. Our equity against that piece is 0.57 x 16 / 34 = 0.27 or 27%.
3. Summing the two, we get 0.10 + 0.27 = 0.37 or 37% equity against her presumed range.

The good news is that there are programs such as Pro Poker Tools and the like that let you ask questions such as 'How much equity does a pair of jacks have against a range of Q-Q / K-K / A-A / A-K?' But it's useful to know how those things are calculated.

Using Combos to Improve Decision-Making

What to do with that information is beyond the scope of this article, but as an example, if the villain were all in for her $40, we'd know exactly how to proceed.

Setting aside rake for the moment, there's $12 + $40 + $1 + $3 = $56 in the pot. It costs us another $28 to call. Conveniently enough, we're getting exactly 2-to-1 odds to call, so we must have at least 33.3% equity to call her shove. We have a hair above that (37%), so we shrug, slide in the extra $28, and ask the dealer to run out the board.

By the way, I had suggested that we ignore the rake for simplicity. Note that in this case once we take the rake into effect, this could turn into a fold. If you don't see that, subtract the rake ($5 or whatever) from the pot and redo the pot odds calculations, remembering that you still need to call the full $28.

Conclusion

I grant that counting pairs and ace-king combos is relatively simple. But suppose in the heat of battle, a flop comes down and you believe that your opponent could have (among other possible hands) any of the heart flush draws that are two suited Broadway cards, plus all of the ace-high flush draws. How many flush draw combos does she have? (See the answer below.)

Not surprisingly, the best way to get better at this is to practice in the lab (a.k.a. 'your kitchen table'). Go over common situations and learn the arithmetic. Eventually, you'll be as comfortable with the important ones as you're sure that jacks have 37% equity against a range of {QQ+, AK}.

This stuff is not trivial and if you're not used to working with numbers, it can be a bit daunting. But at least some of your opponents are already doing it, and once you get the hang of it, you might even enjoy the mental gymnastics.

P.S. Your villain can have the suited-in-heart combos of A-Q, A-J, A-T, A-9, A-7, A-6, A-5, A-4, A-3, A-2, Q-J, Q-T, J-T, for a total of 13.

Lee Jones can help you count combos and then count your winnings. Go to leejones.com/coaching and schedule a free coaching consultation. Lee specializes in coaching live cash game players.

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  cash game strategytournament strategyno-limit hold'emcombinationscombospot oddsprobabilitiesequityrangesrange readinglive pokeronline 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.

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%

Texas Holdem Starting Hands

• 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)

Top Hands In Texas Holdem

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]

Good Hands In Texas Holdem

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.

Texas Holdem Hands

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.

How Many Possible Hands In Texas Holdem

Different Hands In Texas Holdem