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Flawless Poker

Universal Law 04

STAR CLASSIFICATION

Final hand frequencies

Seven cards make everything stronger. A Hold'em river is the best five of seven, and that is a different universe from five cards dealt in a row.

Standard high-hand order uses the best five cards. Suits do not break a tie. If both best fives are identical, the pot is split. There are 2,598,960 ways to deal five cards, and 133,784,560 ways to deal seven. The seven-card column is the best five of those seven. It is not the chance of making that hand once your hole cards are known.

  1. Royal flushAce-high straight flush.
  2. Straight flushFive in a row, one suit.
  3. Four of a kindThen the kicker.
  4. Full houseHigher three of a kind, then the pair.
  5. FlushHighest card, then the next.
  6. StraightHigher top card. Ace-to-five is lowest.
  7. Three of a kindThen the two kickers.
  8. Two pairHigher pair, second pair, kicker.
  9. One pairThen three kickers.
  10. High cardFive cards, from the top down.
Every five-card hand and every seven-card holding. Straight flush excludes royal flush. Flush excludes straight flush.
HandBest 5 of 7Hold'em chanceAboutFive cardsFive-card chance
Royal flush4,3240.0032%1 in 30,94040.00015%
Straight flush37,2600.0279%1 in 3,591360.0014%
Four of a kind224,8480.168%1 in 5956240.024%
Full house3,473,1842.60%1 in 393,7440.144%
Flush4,047,6443.03%1 in 335,1080.197%
Straight6,180,0204.62%1 in 2210,2000.392%
Three of a kind6,461,6204.83%1 in 2154,9122.11%
Two pair31,433,40023.50%1 in 4.3123,5524.75%
One pair58,627,80043.82%1 in 2.31,098,24042.26%
High card23,294,46017.41%1 in 5.71,302,54050.12%

In seven cards you finish with high card less often than with one pair, and two pair turns up more often than high card. Five cards dealt in a row are still high card about half the time. Royal flush and four of a kind in seven cards can also be counted directly: 4 suits × 1,081 ways to choose the other two cards is 4,324 royals, and 13 × 17,296 ways to fill around quads is 224,848. The other rows complete the enumeration of all 133,784,560 holdings. Short Deck, Omaha, Razz, and eight-or-better games do not all use this order. Omaha must use exactly two hole cards and three board cards.

FLAWLESS POKER / STUDY CHART

Hand rankings and how often they appear

Standard high-hand order from royal flush to high card, with the chance of each hand in five random cards and in the best five of seven cards.
Exact counts. The five-card column is any five cards dealt. The seven-card column is the best five of seven, which is what one Hold'em player can hold by the river. Your actual chance still depends on the cards you can already see. Open full-size chart ↗

These counts are for study and post-session review. Where a row comes from a simulation, the caption names how many deals were run. Where a stack or a pot is made up, the caption says so. None of these figures is an instruction for a live pot.