Over on the left-hand side of the grid we have the offsuit combos. Each square represents 12 combinations of hands. There are 72 squares so this results in a total of 864 individual holdings. Notice that there are 3 times as many offsuit combos of certain holdings compared to suited.

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Introduction

Rules

1. A single 52-card deck is used. All cards count as its poker value. Aces may be high or low.
2. One player is designated as the dealer, usually with a laminated marker. This person does not have to physically deal the game. However it is important that a symbolic dealer position rotate around the table.
3. The player to the dealer's left must make a 'small blind' bet. The player to the left of the small blind must make a 'big blind' bet. The amounts of both blinds should be specified in advance. The purpose of the blinds is to get the ball rolling with some money in the pot.
4. Two cards shall be dealt down to each player, starting with the person to the dealer's left.
5. The player to the left of the big blind must either call or raise the big blind bet. The play in turn will go around the table according to normal poker rules, which I assume the reader already knows. Table rules will specify any limits on the size or number of allowed raises.
6. The small blind may also raise the big blind. If nobody raises the big blind the player making the big blind has the option to raise his own bet. The term for this is the 'big blind option.'
7. Three community cards will be dealt face up in the center of the table. This is called the 'flop.'
8. Another round of betting will ensue, starting with the player to the dealer's left.
9. A fourth community card will be dealt face up in the center of the table. This card is called the 'turn.'
10. Another round of betting will ensue, starting with the player to the dealer's left. Generally the minimum bet is double the first two rounds of betting.
11. A fifth and final community card will be dealt face up in the center of the table. This card is called the 'river.'
12. Another round of betting will ensue, starting with the player to the dealer's left. The minimum bet is generally the same as the previous round.

13. Each player still in the game at the end will determine the highest poker value among his own two cards and the five community cards. It is NOT a requirement that the player use both of his own cards. The player with the hand of highest poker value shall win. Following are the hand rankings.

    1. Straight flush: Five consecutive and suited cards. For example 5, 6, 7, 8, 9.
    2. Four of a kind: Four cards of the same rank, plus any fifth card. For example Q, Q, Q, Q ,4.
    3. Full house: Three of a kind and a pair. For example 6, 6, 6, J , J.
    4. Flush: Any five cards of the same suit, except for a higher ranking straight flush. For example A, Q, 8, 4 , 3.
    5. Straight: Five consecutive cards, except for a higher ranking straight flush. For example 8, 9, 10, J, Q.
    6. Three of a kind: Three cards of the same rank, plus any other two cards. For example 5, 5, 5, Q ,2 .
    7. Two pair: Two pairs, plus any fifth card. For example 8, 8, 2, 2 ,Q .
    8. Pair: A pair and any other three cards. For example 7, 7, 2, 5 ,A .
    9. ? High: Any five cards that do not form any higher poker hand. A king high hand for example might be K, Q, 7, 5 ,4 .
14. If two or more players have poker values of the same rank then the individual cards will be used to break the tie. If necessary all five cards will be considered.
15. I get asked a lot whether the two unused cards in a player's hand are used to break a tie. The answer is a firm NO. The two unused cards do not matter.
16. If a new player arrives at the table he should either wait for the big blind position or put up an amount equal to the big blind, amounting to a call of the big blind.
17. If a bet is made after another player runs out of money, then a separate pot is created. The player that ran out of money is not eligible to win the second pot. If more than one player runs out of money then multiple separate pots can be created.
18. In formal games players may not bet with cash or buy chips with cash in the middle of a hand.
19. There are numerous rules of etiquette, which I won't get into.
20. There house may set the betting rules. There are three main types. A 'structured' game features raises of specified amounts. For example a '3/6 game' would mean that raises after the deal and flop are $3, and after the turn and river are $6. There is usually a limit to the number of raises a player may make, typically three. A 'pot limit' game has structured minimum raises but the maximum raise may be anything up to the amount in the pot at the time the raise is made. A 'no limit' game also has structured minimum raises but there is no maximum raise.

Examples

Example 1

Board: A, 2, 4, 5, 6
Player 1: J, 6
Player 2: 7, Q

Player 1 wins. Both have an ace high flush, so the second highest card is considered. Player 1's jack beats player 2's 7. The only way to have a flush tie is if the flush is entirely on the board and no hole cards are higher than the lowest card on the board in the same suit.

Example 2

Texas Holdem Poker Hand Rankings

Board: J, A, 7, 5, 6
Player 1: 2, J
Player 2: 10, J

Player 2 wins. Both have a pair of jacks so the singletons are considered. High highet singleton in both hands is an ace so the second highest singleton is considered. Player 1's second highest singleton is a 7, compared to player 2's 10. A 10 beats a 7 so player 2 wins.

Example 3

Board: A, A, K, Q, J
Player 1: Q, J
Player 2: Q, 2

Tie. Both have a two pair of aces and queens, with a king singleton. Some people incorrectly believe that in such cases the unused cards are considered, in this case player 1's pair of jacks beating player 2's jack/2. Only the top five cards matter. The jacks and deuce are irrelevant.

Texas Holdem Poker Hand Order

One of the most important aspects of Texas Hold'em is the value of each two-card hand before the flop. The decision of how to play your first two cards is something you face every hand, and the value of your first two cards is highly correlated to your probability of winning.

The following table shows my power rating for each initial 2-card hand in a 10-player game. The numbers are on a 0 to 40 scale. Basically, you should only play hands that are dark green, blue, or purple. Of course you should be more be more liberal in late position and picky in early position. If forced I would say you should need 10 points in late position and 19 points in early position to call the big blind. If your table is loose, as if often the case online, you can play a bit looser yourself.

Use the top table if you have a pair, the middle table if your cards are suited, and the bottom table if your cards are unsuited. Except for a pair,look up your high card along the left and your low card along the top.

Following are the links to my tables of the value of each intial hand according to the number of players. The 10-player section explains the methodology for creating the table table.

Poker Hands Texas Holdem

Pot Odds

The following table shows the probability of making various hands after the flop and the correct 'pot odds.' The pot odds are the breakeven ratio of money in the pot to the amount you have to bet for the player to be indifferent about calling, assuming the player would definitely win if he makes the hand (a big if) and there are no additional bets (another big if). This table is a good starting point the player should make mental adjustments for the probability of winning without making the hand, losing with making the hand, and expected future bets. The odds of a two pair improving to a full house are the same as those for four to an inside straight.

Pot Odds — After Flop

The next table shows the pot odds after the turn.

Pot Odds — After Turn

Hand Strength Calculator

I'm proud to present my new and improved Poker Odds Calculator. Enter any situation in Texas Hold 'Em, and it will tell you the probability of each possible outcome.

Poker Tournament Calculator

My Poker Tournament Calculator will determine each player's probability, for up to nine players, of finishing in each place, and his expected share of any prize pool, assuming equal skill among all players. It produces the same results as what is known as the Independent Chip Model.

Internal Links

• Pinapple — Strategy and analysis of which card to discard before the flop.
• Bad Beat Jackpots: What is the Probability of Hitting one?
• Texas Hold 'Em Dominated Hand Probabilities: What is the probability one of your opponents has similar, and better, hole cards than yours?

Effective Hand Strength (EHS) is a poker algorithm conceived by computer scientistsDarse Billings, Denis Papp, Jonathan Schaeffer and Duane Szafron that has been published for the first time in a research paper (1998). 'Opponent Modeling in Poker'(PDF). AAAI-98 Proceedings.

It has since then been considered as a reference in the realm of poker artificial intelligence and has been the basis of further research such as:

• 'Computer poker: a review'(PDF). Artificial Intelligence, Department of Computer Science, University of Auckland, New Zealand: 962–963. 2010.
• 'Application of AI in poker'(PDF). VU University Amsterdam Faculty of Sciences: 12–13. 2011.
• 'Advances in artificial intelligence – SBIA 2008 : 19th Brazilian Symposium on Artificial Intelligence, Salvador, Brazil, October 26–30, 2008 ; proceedings'. 2008: 85–86.Cite journal requires |journal= (help)

Algorithm[edit]

The algorithm is a numerical approach to quantify the strength of a poker hand where its result expresses the strength of a particular hand in percentile (i.e. ranging from 0 to 1), compared to all other possible hands.The underlying assumption is that an Effective Hand Strength (EHS) is composed of the current Hand Strength (HS) and its potential to improve or deteriorate (PPOT and NPOT):

${\displaystyle EHS=HS\times (1-NPOT)+(1-HS)\times PPOT}$

where:

• ${\displaystyle EHS}$ is the Effective Hand Strength
• ${\displaystyle HS}$ is the current Hand Strength (i.e. not taking into account potential to improve or deteriorate, depending on upcoming table cards
• ${\displaystyle NPOT}$ is the Negative POTential (i.e. the probability that our current hand, if the strongest, deteriorates and becomes a losing hand)
• ${\displaystyle PPOT}$ is the Positive POTential (i.e. the probability that our current hand, if losing, improves and becomes the winning hand)

Texas Holdem Strength Of Hands

Pseudocode[edit]

Poker Hands Texas Holdem

Hand Strength (HS) will enumerate all possible opponent hand cards and count the occurrences where our hand is strongest (+50% of the cases where we are tied):

In addition, EHS will consider the hand potential (i.e. its probabilities to improve or deteriorate):

Applicability[edit]

Holdem Poker Hand Strength

EHS is applicable to a wide variety of poker games such as Texas hold 'em poker, Omaha hold 'em poker, ...

Given the complexity of the algorithm, it can not be computed manually and has to be used in an Artificial Intelligence context.

Texas Holdem Poker Hands Chart