Texas Hold 'Em
Texas Hold 'Em is a popular version of the cardgame poker, played in casinos, home games and online. At the Main Event of the World Series of Poker in recent years, the winner has received millions of dollars after besting a field of thousands of entrants.
Choosing the dealer
The dealer position is determined in one of two ways. In tournaments, players pick numbers to determine both table and position. In single table games, the deck of cards is spread out on the table and each player flips up one card.
The ranking of cards is the usual one in poker, such that Ace > King > Queen, and so on. If two players should pick the same high card, then the suits of the cards determine the dealer. The priority of suits is in reverse alphabetical order, that is spades > hearts > diamonds > clubs.
The initial deal
Before the deal, the player immediately to the left of the dealer is mandated to place a bet, called the small blind, and the next player to the left of the dealer if mandated to place a bet twice as large, called the big blind. The name "blind" derives from the fact that these bets are laid before any cards have been seen. The amount of the blinds increase as the games progresses, generally based on time.
Cards are dealt face down, one at a time, in a clockwise direction starting with the player to the left of the dealer, until each player holds two cards. After the initial two cards are dealt, the player to the left of the big blind is the first to act, as the prior two players have already made their bets. That player can fold his hand, match the big blind, or raise. Each subsequent player to the left can then match the current bet, raise, or fold. If no player has raised the bet, the player in the big blind position may raise, fold, or check (keep playing but make no raise).
In a typical "limit" game, the size of any raise on the initial deal must be equal to the size of the big blind. In a "no limit game", the raise may be of any amount at least equal to the size of the big blind.
Community cards: the flop, turn and river
After the first round of betting indicated above, three community cards, called the flop, are dealt face up, which all players can use, and a second round of betting ensues. Unlike the first betting round, in which the person third to the left of the dealer is first to act, in this and all subsequent rounds of betting the player to the immediate left of the dealer is first to act. After the second round of betting, a fourth community card, called the turn, is dealt face up and another round of betting occurs. Finally, a fifth community card, called the river, is dealt face up and the final round of betting follows. In years past, the fifth community card, now referred to as the river, was called the turn.
In a typical "limit" game, a bet or raise on the flop must be equal to the size of the big blind, and a bet or raise on the turn or river must be equal to twice the size of the big blind.
Making a hand
Each player still remaining in the pot makes his hand using the best five cards possible out of the two cards in his hand and the five community cards that are displayed face up. The cards "speak for themselves", meaning that if a player inadvertently calls out a hand weaker than his best possible hand, he still gets to play his best hand. It sometimes occurs that the best hand possible uses all five of the community cards, in which case the players remaining in the hand split the pot.
Poker hand rankings
Texas Hold 'Em poker hand strengths follow the same ordering as in other poker games, as outlined below:
|Royal Flush||Ace-King-Queen-Jack-Ten in one suit|
|Straight Flush||A straight and a flush, starting below an ace|
|Four of a kind (Quads)||Four cards of the same number|
|Full House ("A boat")||three of a kind (a "set") and two of a kind (a "pair")|
|Flush||Five cards in the same suit|
|Straight||Five sequential cards. An ace can be played as a one.|
|Three of a Kind (a "set")||Three cards of the same number|
|Two Pair||Such as Ten-Ten & 4-4|
|A Pair||Two cards of the same number, such as jack-jack|
|High Card||The highest card in the players hand|
Preflop Hand Rankings
Since in Hold'em you are dealt only two cards on the initial (preflop) deal, much of the mathematics of the game is based on the strength of those two cards.
In broad strokes, a preflop hand is classified as being in one or more groups:
- A Pair: A pair of cards, such as two queens (QQ) or two fours (44)
- Connected: Two cards that differ by 1, such as a seven and a six (76)
- Suited: Two cards that are of the same suit. Suited cards are typically denoted with an 's', and "off-suit" cards (unsuited cards) are denoted with an 'o', eg, 76o (seven six offsuit) or KQs (king queen suited)
Having more of these properties, and consisting of higher cards, make the preflop hand stronger. For example two aces, the strongest preflop hand, is the highest possible pair. Additionally, seven two offsuit, the weakest preflop hand, is low, not a pair, not connected and not suited.
In Texas Hold'em, there are 169 preflop hands when hands of equivalent strength are removed. Hands of equivalent strength have the same properties and differ only by suit. An example of two equivalent hands would be 7 of diamonds, 5 of clubs and 7 of clubs, five of hearts.
Odds on the Flop
The flop - the dealing of the first three community cards - is widely considered to be the defining point in a Hold'em hand because
- They are the three cheapest cards you can buy in a hand. One round of betting gets you three cards, vs the turn and the river where one round of betting gets you only one card.
- This is the first time you have enough cards to complete a full poker hand (5 cards)
If the flop gives you a complete hand, then you don't need to worry about making your hand with the additional cards that come on the turn or the river.
However, short of that happening, after the flop is laid out you will have to figure out whether you want to continue with the hand or fold.
After the flop there are many different ways to calculate the odds of you winning that hand, but the most basic way is to count what are called outs. A out is a single card that can come, on the river or the turn, that will give you (what you believe to be) the winning hand. Once you calculate how many outs you have, you can do some simple arithmetic to figure out your probability of winning that hand.
- If you have AQ (ace queen) of diamonds as hole cards, and a 27 of diamonds comes out with a 6 of clubs, any diamond card will give you the nut flush, a winning hand. Since there are already 4 diamonds on the board, you know there are (13-4) = 9 diamond cards left that could come out. Therefore, you have 9 outs.
- If you have JT of hearts as hole cards, and a AQ of clubs comes out with a 2 of spades, any King (K) will give you a ten to ace straight (also known as Broadway) and the winning hand. Since there are 4 Kings in the deck, you have 4 outs.
To convert your outs to a probability, recall that there are 52 cards in a full deck. Since you hold 2 cards and there are an additional 3 already showing as the flop, the other 47 are unknown to you (note that since you do not know the hands of the other players, the number of other players in the hand is irrelevant). Since one out is 1 card out of the remaining 47, the probability of one card coming up is approximately 2%.
Therefore, multiplying the number of outs you have by 2, will result in the approximate percentage of you getting one of your outs. Following from our examples above, 9 outs = ~18% of getting a winning hand, 4 outs = ~8% chance of getting a winning hand.