Reference

Ten hand types decide which five-card poker hand wins, ranked from Royal Flush at the top to High Card at the bottom. The order below is the complete list, with no numbers attached. Rank Hand 1 Royal Flush 2 Straight Flush 3 Four of a Kind 4 Full House 5 Flush 6 Straight 7 Three of a Kind 8 Two Pair 9 One Pair 10 High Card How to use the order at the table Read the list from rank 1 downward. When two players reach showdown, compare hand types first: a Flush at rank 5 beats a Straight at rank 6 no matter how high the cards inside each hand are. Only after both players hold the same type do you compare the cards themselves. That single step removes most of the guesswork from a showdown, because you do not have to weigh a high Straight against a low Flush. The type settles it before the cards do. ...

A standard 52-card deck contains 2,598,960 possible five-card hands. Every one of those hands belongs to exactly one of the ten types below, so the counts add up to that total without overlap. Rank Hand Five-Card Combinations Probability Frequency (1 in N) 1 Royal Flush 4 0.000154% 1 in 649,740 2 Straight Flush 36 0.001385% 1 in 72,193 3 Four of a Kind 624 0.024010% 1 in 4,165 4 Full House 3,744 0.144058% 1 in 694.2 5 Flush 5,108 0.196540% 1 in 508.8 6 Straight 10,200 0.392465% 1 in 254.8 7 Three of a Kind 54,912 2.112845% 1 in 47.33 8 Two Pair 123,552 4.753902% 1 in 21.04 9 One Pair 1,098,240 42.256903% 1 in 2.37 10 High Card 1,302,540 50.117739% 1 in 2.00 How to read the three number columns Five-Card Combinations counts how many of the 2,598,960 hands fall into that type. Probability is that same count expressed as a share of the full set. Frequency (1 in N) restates the figure as an average: a Full House appears about once per 694.2 randomly dealt five-card hands. That column is not “odds against” in the betting sense. Reading it as a price will give you the wrong number when you compare it with the chips in front of you. If you need a betting figure, work from the Probability column, or use the pot odds formula with the actual chip count. ...

On the flop, 47 cards are still unknown, so one out is one chance in 47 on the next card. The first table fixes that denominator for each street; the second converts any out count from one to fifteen into a share. Street Known Cards Unseen Cards One-Card Outs Convert As Preflop 2 50 outs / 50 Flop 5 47 outs / 47 Turn 6 46 outs / 46 River 7 45 no cards remain Why the unseen count is not 52 minus five An opponent’s two hole cards are unknown to you, and an unknown card is still unseen even though it is no longer in the deck from their point of view. On the flop you know your two cards and the three board cards, which leaves 47 cards you cannot see. On the turn one more board card is known, leaving 46. The river row says “no cards remain” because no further card will be dealt, not because the unseen count has reached zero. ...

Two hole cards from a 52-card deck form 1,326 distinct combinations, which collapse into 169 strategically different starting hand types. The difference between those two numbers is the whole reason a preflop chart fits on one page. Group Count Examples Pocket pairs 13 AA, KK, QQ, … 22 Suited non-pairs 78 AKs, T9s, 76s Offsuit non-pairs 78 AKo, T9o, 76o Total 169 All starting hand types Why combinations collapse Suits are interchangeable before the flop. A pair of aces in spades and hearts plays the same as a pair of aces in clubs and diamonds, so all of those combinations share one line in a range chart. What remains is the rank shape and whether the two cards share a suit. Pocket pairs form one group, non-pairs split into suited and offsuit, and that is the entire grid. ...

Nine players at a full-ring table act in one order before the flop and a different order after it. The table below gives both, keyed to the same nine seats. Preflop Order Position Full Name Postflop Order 1 UTG Under the Gun 3rd 2 UTG+1 Under the Gun plus one 4th 3 UTG+2 Under the Gun plus two 5th 4 MP Middle Position 6th 5 HJ Hijack 7th 6 CO Cutoff 8th 7 BTN Button 9th 8 SB Small Blind 1st 9 BB Big Blind 2nd Reading the preflop column Preflop action starts at UTG and moves clockwise through the seats toward the blinds. The Button is seventh, with the Small Blind and Big Blind behind it. Those last two seats have already posted chips, which is why they still get to act after the Button even though they sit at the end of the seating order. ...