• Zynga Texas Holdem Poker
• Poker Probability Texas Holdem Wikipedia Codes
• Poker Probability Texas Holdem Wikipedia Game
• Texas Holdem Probability Equation
• Texas Holdem Odds And Probabilities

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]

For example, if after the flop in Texas hold 'em, a player has a backdoor flush draw (e.g., three spades), the probability of catching two outs on the turn and river is (10 ÷ 47) × (9 ÷ 46) = 4.16 percent. Backdoor draws are generally unlikely; with 43 unseen cards, it is equally likely to catch two out of seven outs as to catch one out of one. Six-plus hold 'em (also known as short-deck hold 'em) is a community card poker game variant of Texas hold 'em, where the 2 through 5 cards are removed from the deck.Each player is dealt two cards face down and seeks to make the best five card poker hand from any combination of the seven cards (five community cards and their own two hole cards). Texas hold 'em and Omaha are two well-known variants of the community card family. There are several methods for defining the structure of betting during a hand of poker. The three most common structures are known as 'fixed-limit', 'pot-limit', and 'no-limit'. In fixed-limit poker, betting and raising must be done by standardised amounts. Limit Texas hold'em example With one card to come, Alice holds a made hand with little chance of improving and faces a $10 call to win a $30 pot. If her opponent has a weak hand or is bluffing, Alice expects no further bets or calls from her opponent. In poker, the probability of many events can be determined by direct calculation. This article discusses computing probabilities for many commonly occurring events in the game of Texas hold 'em and provides some probabilities and odds for specific situations. In most cases, the probabilities and odds are approximations due to rounding. When calculating probabilities for a card game such as.

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

Zynga Texas Holdem Poker

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]

Poker Probability Texas Holdem Wikipedia Codes

Poker Probability Texas Holdem Wikipedia Game

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 Probability Equation

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.

Texas Holdem Odds And Probabilities

Playing poker is about playing the odds. The following list gives the odds for outcomes in Texas Hold’em hands. When you realize how heavily the odds are stacked against you, you may want to rethink going all-in before the flop with two suited cards. Use the odds to your advantage:

• 1 percent (1-in-100): Percentage of time that no player holds an Ace or a King at a table in a 10-handed game

• 1 percent (1-in-100): Percentage of time that if you hold two suited cards, you’ll flop a flush

• 6 percent (about 1-in-20): Percentage of time that five community cards will give pocket suited cards a flush

• 6 percent (about 1-in-20): Percentage of time that you’ll be dealt a pocket pair

• 8 percent (about 1-in-12): Percentage of time that you’ll hit at least trips after having a pair on the flop

• 12 percent (about 1-in-8): Percentage of time that you’ll flop trips if holding a pocket pair

• 12 percent (about 1-in-8): Percentage of time that two more cards will flop in the same suit as a suited pocket pair

• 19 percent (about 1-in-5): Percentage of time that the five community cards will at least trip your pocket pair

• 32 percent (about 1-in-3): Percentage of time that you’ll pair one of your cards on the flop (with no pocket pair)

• 33 percent (about 1-in-3): Percentage of time that you’ll make a full house or better after having trips on the flop

• 35 percent (about 1-in-3): Percentage of time that you’ll make a flush on the turn or river if you have four cards to a flush after the flop