Poker

What poker is

Poker is a family of card games in which the participants bet on the value of their hands. Unlike most casino games, in its classic form the players do not play against the house but against one another: the stakes go into a pot, and the pot goes either to the player with the best hand at the end or to the last player left after everyone else has folded. The game uses a standard 52-card deck without jokers, and the ranking of five-card hands is the same in almost every variant.

The most widespread variant today is Texas hold'em, described in detail below.

Texas hold'em: how a hand is played

The button and the blinds

A table usually seats between two and ten players. A disc called the "button" marks the dealer position and moves one seat to the left after every hand. Before the cards are dealt, the two players to the left of the button post forced bets: the small blind (usually half of the big one) and the big blind. Forced bets exist so that every hand has something to be won. Some games also add a small stake from every player, called an ante.

Hole cards and betting rounds

Each player receives two cards face down, which only that player sees. Four betting rounds follow:

• Preflop: after the hole cards are dealt. The action starts with the player to the left of the big blind.
• Flop: three community cards are turned face up on the table, followed by the second round.
• Turn: a fourth community card is turned, followed by the third round.
• River: a fifth community card is turned, followed by the last round.

From the flop onwards, the action starts with the first player still in the hand to the left of the button. On their turn, players may fold, call (match the largest bet so far) or raise it. If nobody has bet yet in that round, a player may check (pass without putting money in) or make the first bet. A round ends when all remaining players have put in the same amount. If everyone but one player folds, that player takes the pot without showing any cards.

How much a player may bet depends on the structure of the table: in "limit" games the bets are fixed, in "pot-limit" games a bet may not exceed the size of the pot, and in "no-limit" games a player may bet all the chips in front of them at any moment (all-in). When someone is all-in for less than the others, the remaining bets form a side pot, which that player cannot win.

The showdown

If at least two players remain after the last round, they show their cards. Each makes the best five-card hand from the seven available: the two hole cards and the five community cards, in any combination. A player may use both hole cards, only one, or none. The best hand wins; equal hands split the pot. Suits have no order among themselves, and between hands of the same type the higher cards decide, including cards outside the combination (the kicker).

Other variants, briefly

• Omaha: each player receives four hole cards and must use exactly two of them together with exactly three community cards. The betting rounds are the same as in hold'em; it is often played pot-limit.
• Five-card draw: each player receives five hole cards, a betting round follows, then each player may exchange some of their cards for new ones from the deck, once. A second betting round and the showdown follow. Some rules limit how many cards may be exchanged.
• Seven-card stud: there are no community cards and no blinds, usually an ante instead. Each player receives seven cards in total, some face down and most face up, with a betting round after each stage. At the end, the best five-card hand out of the seven counts.

Hand ranking

From strongest to weakest:

1. Royal flush: A, K, Q, J, 10 of the same suit.
2. Straight flush: five consecutive cards of the same suit.
3. Four of a kind: four cards of the same rank.
4. Full house: three cards of one rank and two of another.
5. Flush: five cards of the same suit, not consecutive.
6. Straight: five consecutive cards of mixed suits. The ace can be high (10-J-Q-K-A) or low (A-2-3-4-5), but not in the middle (K-A-2-3-4 is not a straight).
7. Three of a kind: three cards of the same rank.
8. Two pair.
9. One pair.
10. High card: no combination; the highest card counts.

The order follows rarity: the less often a hand occurs, the more it is worth. The table below counts all 2,598,960 possible five-card hands from a full deck. Each row includes only the hands that do not belong to a higher category (straight flushes, for example, exclude royal flushes).

These figures describe five cards dealt at random. In hold'em, where a player picks the best five out of seven cards, strong hands occur more often than the table shows, but the ranking of hands does not change.

Starting-hand probabilities

Two cards from a 52-card deck can be dealt in 1,326 combinations. A few simple probabilities follow:

• a pair (two cards of the same rank): 5.88%;
• one particular pair, for example two aces: 0.45%, that is 1 in 221;
• two cards of the same suit: 23.53%.

A strong starting hand has only a statistical edge, not an assured result: the five community cards can reverse the balance entirely, and even the best two cards lose fairly often.

Outs

"Outs" are the unseen cards that would improve a player's hand to one the player assumes would win. After the flop a player sees five cards (two hole cards and three community cards), so 47 remain unseen; after the turn, 46 remain. Some typical situations:

• four cards of the same suit, needing a fifth: of the 13 cards of that suit, four are already visible, leaving 9 outs;
• four consecutive cards open at both ends (for example 8-9-10-J): any 7 or Q completes the straight, which makes 8 outs;
• a straight with a gap in the middle: only one rank completes it, which makes 4 outs;
• a flush and a straight possible at the same time: 9 plus 8, minus the two cards counted twice, which makes 15 outs.

The probability that the turn is an out is the number of outs divided by 47. For both remaining cards, the calculation starts from the opposite: the probability that neither the turn nor the river is an out is (47 minus the outs) over 47, multiplied by (46 minus the outs) over 46; the probability sought is 1 minus that product.

The calculation treats all unseen cards as equally likely, because the opponents' cards are unknown. An out does not guarantee the pot: the completed hand can still lose to an even better one.

Pot odds

Pot odds compare the price of a decision with what it can win. When an opponent bets, a player considering a call has a certain amount to pay. Dividing the amount to be paid by the size of the pot after the call (the existing pot, plus the opponent's bet, plus the call itself) gives the share of the final pot that the player is funding.

If the probability of winning the hand is greater than that share, the call has a positive average result in that situation; if it is smaller, the average result is negative. The comparison has limits: the probability of winning is not the same as the probability of completing a hand, bets in later rounds change the calculation, and the house fee makes the pot smaller. Above all, it is an average over many similar situations: any single hand is decided only by the cards that follow.

Poker between players and poker against the house

When poker is played between participants, the house takes no part in the hands and has no stake in their outcome. Its income comes from a fee: a small part kept from each pot, an entry fee for tournaments or, in some card rooms, a charge for the time spent at the table. Before this fee, what one player loses another wins; after it, the players taken together lose exactly what the house keeps.

There are also casino variants in which the player faces not other players but the dealer's hand, with fixed payouts set out in a table, as well as video poker machines. In these games, as in any game against the house, the rules and payouts are set so that the house keeps a mathematical edge.

Chance in the short term

Decisions affect the average result only over a very large number of hands. In the short term, results are dominated by chance: the deal decides who receives the strong hands and whose outs arrive, and a player can lose many hands or sessions in a row whatever the decisions. Because these swings are large, even the player concerned cannot easily tell luck apart from anything else in their own results. This variation, and how slowly averages settle, is explained in the article Variance and the law of large numbers.

Terms

• House edge
• RTP
• Variance
• Probability basics