Poker hand rankings

Every game at Patch-Patch, Patch-Patch itself, NL Hold'em and PL Omaha, uses the same ranking of poker hands. A hand is always exactly five cards, and the hand higher on the chart wins. This page has the chart, how two hands of the same kind are compared, the rule that decides which five cards you may use in Omaha and Patch-Patch, and how often each hand comes.

The chart

Strongest first. In each example, the cards that make the hand are ringed and the others, the kickers, are dimmed.

The ten hands

Royal flush

Ace, king, queen, jack and 10, all of one suit: simply the highest straight flush.

Straight flush

Five cards in a row, all of one suit, such as 9-8-7-6-5 of hearts. A higher top card wins. The lowest is 5-4-3-2-A, where the ace counts low.

Four of a kind

Four cards of the same rank. A higher rank wins; if two players share the same four (on the board), the fifth card decides.

Full house

Three of a kind plus a pair, named by both: queens full of 8s. The three of a kind decides first, then the pair: queens full of 2s beats jacks full of aces.

Flush

Five cards of one suit, not in a row. The highest card decides, then the next, down to the fifth: A-J-8-6-2 beats A-J-8-5-4. Suits never rank against each other.

Straight

Five cards in a row, of mixed suits. The top card decides. The ace plays high (A-K-Q-J-10) or low (5-4-3-2-A), never in the middle: Q-K-A-2-3 is not a straight.

Three of a kind

Three cards of the same rank, plus two kickers. The rank decides, then the kickers. With a pair in your hand and one on the board players call it a set; with one card in your hand and a pair on the board it is trips.

Two pair

Two different pairs and a kicker. The higher pair decides, then the lower pair, then the kicker: kings and 3s beat queens and jacks.

One pair

Two cards of the same rank and three kickers. The pair decides, then the kickers one by one.

High card

None of the above. The highest card decides, then the next, all the way to the fifth.

How ties are broken

1. The kind of hand first. Anything higher on the chart wins, however high or low its cards.
2. Then the cards that make it, from the most important down: the three of a kind before the pair in a full house, the higher pair first in two pair.
3. Then the kickers, the cards that complete the five, highest first.
4. Only five cards count. A sixth card never breaks a tie, however high.
5. Suits never break a tie. Two hands with the same five ranks split the pot.

Omaha and Patch-Patch: exactly two plus three

In Hold'em your five cards are the best five of seven, using two, one or none of yours. In Omaha, and on each of Patch-Patch's three boards, the rule is stricter: exactly two of the hand's four cards and exactly three from the board. Most misread hands come from forgetting it.

A flush needs two cards of the suit in your hand. Four hearts on the board and one heart in your hand is not a flush.

A straight needs two of its cards from your hand, and three from the board.

Four of a kind on the board plays only three of its cards. With 7-7-7-7 showing, nobody has four 7s: each player has three 7s plus his two best cards.

A pocket pair matching the board makes a set; three of a kind in your hand is still only two cards. And a pair on the board with one matching card of yours is trips, not a full house, unless your other card pairs the board too.

The odds of each hand

How often each hand comes depends on how many cards you get to choose from. The first table is the classic one: five cards dealt, no draw. The figures are exact, counted over all 2,598,960 possible five-card hands.

The chart's order comes from this table: the rarer the hand, the higher it ranks.

With more cards to choose from, every strong hand comes more often. The second table is the best hand a player holds by the river if he stays to see all five board cards. The Hold'em column is exact, counted over all 133,784,560 seven-card combinations. The Omaha column, four cards in hand and exactly two of them with three of the board, is from a simulation of 10 million deals, so its figures are rounded.

Two things stand out. In Hold'em, three of a kind is a little more common by the river than a straight, yet ranks below it: the ranking follows the five-card table, not the seven-card one. And in Omaha, full houses, flushes and straights are more than twice as common as in Hold'em, which is why a hand that wins a Hold'em pot often loses an Omaha one.

And in Patch-Patch

Each Patch-Patch board is an Omaha hand, but you choose its four cards from twelve after seeing the flop, so strong hands come more often still. As an upper bound, if one board could take any two of your twelve cards with nothing left for the other two, a simulation of 400,000 deals puts it at a full house or better about one time in three by the river, and never worse than a pair. Your real split shares the twelve cards between three boards, so each board gets less than that. The article on splitting your cards is about that trade-off.

Where to go next

• Patch-Patch rules, NL Hold'em rules and PL Omaha rules.
• Reading three boards at once: what beats you on each board.
• At a Patch-Patch table, the chart is a tap away: the Hand rankings button for your first hands, and the menu (☰) always.