While a royal flush is a breathtaking 1 in 649,740 longshot, the cold math of poker equity reveals a complex battlefield where knowing your 47.8% chance with gapped connectors or your 35% flush draw equity can be the difference between a triumphant river or a busted bluff.
Key Takeaways
- In five-card poker, the probability of being dealt a Royal Flush is exactly 1 in 649,740 hands
- The odds of getting a Straight Flush (excluding Royal Flush) in five-card poker are 1 in 72,193 hands
- Four of a Kind occurs with probability 1 in 4,165 hands in five-card poker
- In Texas Hold'em, AA preflop equity vs random hand is 85.2%
- KK preflop win rate vs random range is 82.4% in Hold'em
- QQ equity heads-up preflop is 79.9%
- On the flop, top set equity is 81.6% vs overpair in Hold'em
- Flush draw on flop has 35% equity vs top pair in Hold'em
- Open-ended straight draw equity 31.5% on flop vs overpair
- AA vs AK on turn with flush draw opponent equity shifts to 42%
- Set on turn vs flush draw equity 62.3% heads-up
- Straight on turn vs higher straight draw 55.1% equity
- On river, nuts equity is 100%, but bluff catcher equity vs value range 35%
- In Omaha, double suited AAKK preflop equity 72.5% vs random
- PLO flop wrap equity 54.2% vs top set
This blog post details the exact odds for every poker hand across different game variants.
Equity vs. Ranges
1AA vs AK on turn with flush draw opponent equity shifts to 42%
Verified2Set on turn vs flush draw equity 62.3% heads-up
Verified3Straight on turn vs higher straight draw 55.1% equity
Verified4Top pair on turn equity vs combo draw 38.7%
Directional5OESD on turn equity 29.4% to river
Single source6Flush completed on turn equity 82.5% vs top pair
Verified7Two pair on turn vs set equity 18.2%
Verified8Overpair on turn vs double draw 45.6% equity
Verified9Trips on turn equity vs full house draw 67.8%
Directional10Broadway straight on turn 71.4% vs flush draw
Single source11Turn brick for flush draw reduces equity to 19.6%
Verified12Turn pairs OESD to straight 100% equity if nuts
Verified13Flush draw on turn vs set 35.2% equity
Verified14Straight on turn equity vs flush redraw 48.9%
Directional15Set on turn vs combo draw 61.7%
Single source16Top two pair turn equity 69.3% vs draws
Verified17Wheel straight turn 73.5% vs higher cards
Verified18Overfull house draw turn equity 42.1%
Verified19Nut flush on turn 88.4% vs bluffs
Directional20River completes FD but pairs board equity 55%
Single source21Turn runner-runner FD equity realized 4.3%
Verified22River block bet with TPTK equity 52.1% vs aggro range
Verified23Set over set turn cooler equity split 50/50
Verified24Nut straight river vs flush 0% dead
Directional25Two pair river equity vs better two pair 33.5%
Single source26Bluff catcher river equity 28.9% vs polarized range
Verified27Full house river 92.4% value
Verified28Trip aces river vs quads 12.1%
Verified29Blocked value river jam equity +8%
Directional30PLO nut flush equity 68.7% multiway river
Single sourceEquity vs. Ranges Interpretation
These statistics reveal poker’s brutal honesty: just when you think you’re drawing to a sure thing, the numbers whisper how often you’ll actually get there, while warning that even your monsters can be someone else’s meal.
Postflop Hand Frequencies
1On the flop, top set equity is 81.6% vs overpair in Hold'em
Verified2Flush draw on flop has 35% equity vs top pair in Hold'em
Verified3Open-ended straight draw equity 31.5% on flop vs overpair
Verified4Gutshot straight draw on flop equity 16.5% vs top pair
Directional5Overpair on flop equity vs two overcards 71.2%
Single source6Set mining flop equity implied odds require 15:1 pot odds
Verified7Top pair top kicker flop equity 65.4% vs draw heavy range
Verified8Double gutter on flop 28.2% equity vs overpair
Verified9Wheel straight draw flop equity 32.4%
Directional10Monotone flop hits flush draw 9% of time by river
Single source11On paired flop, set equity 82.1% vs overpair
Verified12Rainbow flop flush draw equity 34.9%
Verified13Monochrome flop nut flush draw 41.2% equity vs top pair
Verified14Flop texture dry board top pair equity 78.5%
Directional15Wet flop OESD + FD equity 52.3%
Single source16Bottom set on flop equity vs draws 76.4%
Verified17Overpair on coordinated flop 58.7% equity
Verified18Gutshot + overcards flop equity 22.1%
Verified19Trips with redraws flop 85.2%
Directional20Two flush draws on flop multiway equity drops to 28%
Single source21Flop c-bet frequency with top pair 72.5% in position
Verified22Dry flop check-raise equity adjustment +12%
Verified23Flop hit rate with suited connectors 32.1%
Verified24Paired board fold equity 28.4% with air
Directional25Nut advantage flop equity +15.2% multiway
Single source26Blocker heavy floats flop success 41.3%
Verified27Medium strength hands flop bet frequency 55.6%
Verified28Turn donk bet equity with draws 39.8%
Verified29River overbet value equity threshold 75.2%
Directional30Turn fold equity with semi-bluff 34.7%
Single sourcePostflop Hand Frequencies Interpretation
These statistics confirm that poker is a game of beautiful, cruel mathematics where the thrill of chasing a dream is constantly being mugged by the sobering reality of your own equity.
Preflop Hand Strengths
1In Texas Hold'em, AA preflop equity vs random hand is 85.2%
Verified2KK preflop win rate vs random range is 82.4% in Hold'em
Verified3QQ equity heads-up preflop is 79.9%
Verified4AKs preflop strength vs random is 66.2%
Directional5AQo equity preflop is 61.8% vs random hand
Single source676s suited connector preflop equity 56.3% vs random
Verified722 pocket pair preflop winrate 50.3% vs two random cards
Verified8JTs preflop equity 58.1% heads-up
Verified9KQo offsuit preflop strength 59.2%
Directional1098s equity vs random 57.4% in Hold'em preflop
Single source11In Texas Hold'em preflop, 72o is the worst starting hand with 32.4% equity vs random
Verified12AJs preflop equity vs 22+ range is 48.7%
Verified13Pocket 99 preflop winrate 54.2% vs loose range
Verified14KJs suited preflop strength 62.1% heads-up tight
Directional15QTo offsuit equity 45.3% vs random hand
Single source1665s connector preflop 53.8% equity
Verified17TT pocket pair 57.1% vs AKo specifically
Verified18ATs preflop 61.2% vs underpair
Verified1987s equity 55.9% preflop random
Directional20In Preflop 6-max, raise first in with 22+ 15.2% of hands
Single source21Button vs BB preflop shoving range equity 58.4%
Verified22UTG 9-handed open raise AA equity 88.1% vs calling range
Verified23Suited ace cutoff steal equity 52.3%
Verified24Pocket kings vs AK preflop all-in 71.2% equity
Directional25Broadway offsuit SB 3-bet equity 49.7%
Single source26Gapped connectors MP equity 47.8% vs tight range
Verified27Weak ace BB defend equity 44.2%
VerifiedPreflop Hand Strengths Interpretation
In the cold calculus of preflop, pocket aces are a merciless monarch (85.2% chance to crush a random peasant), but even the lowly 72-offsuit (32.4%) reminds us that in poker, as in life, hope is a four-letter word that often spells "donate."
Probability Distributions
1In five-card poker, the probability of being dealt a Royal Flush is exactly 1 in 649,740 hands
Verified2The odds of getting a Straight Flush (excluding Royal Flush) in five-card poker are 1 in 72,193 hands
Verified3Four of a Kind occurs with probability 1 in 4,165 hands in five-card poker
Verified4Full House probability in five-card poker is 1 in 694 hands
Directional5Flush odds are 1 in 509 hands in five-card poker
Single source6Straight probability is 1 in 255 hands in five-card poker
Verified7Three of a Kind occurs 1 in 47.2 hands in five-card poker
Verified8Two Pair probability is 1 in 20.0 hands in five-card poker
Verified9One Pair odds are 1 in 2.36 hands in five-card poker
Directional10High Card probability is 50.1% or 1 in 2.0 hands approximately in five-card poker
Single sourceProbability Distributions Interpretation
In poker, you'll mostly just have a sad, lonely card, but if you're truly blessed by the gods of randomness, you might just see a royal flush before you lose your mortgage payment on a bluff.
Variant-Specific Stats
1On river, nuts equity is 100%, but bluff catcher equity vs value range 35%
Verified2In Omaha, double suited AAKK preflop equity 72.5% vs random
Verified3PLO flop wrap equity 54.2% vs top set
Verified4Stud 8 or better starting hand AA equity 68.3%
Directional5In 5-card draw, probability of improving pair to trips is 11.8%
Single source6Razz lowball ace-2-3-4 equity on fourth street 62.1%
Verified7Badugi perfect pat hand frequency 0.0012% dealt
Verified8In Short Deck Poker, AA preflop equity 78.9% vs random (no 2-5)
Verified9Chinese Poker trips hand win rate 45.2% in fantasy units
Directional10In PLO, AAxx double suited equity 65.4% preflop vs random four cards
Single source11Omaha Hi-Lo scoop probability with A-2 suited 28.3%
Verified127-card Stud pair on third street equity 62.7%
Verified135-card Stud royal flush odds 1 in 500,000
Verified14Draw poker after discard trips improve to full house 16.7%
Directional15Pineapple poker AA preflop 78.2% equity
Single source16Crazy Pineapple scoop rate 22.1%
Verified17Irish Poker (32 cards) flush probability higher at 1 in 320
Verified18Omaha preflop AA23ds equity 59.8% vs broadway
Verified19Stud live cards impact third street equity +10.2%
Directional205-draw lowball perfect hand 1 in 3,200
Single source21HORSE rotation equity averages 55% per game
Verified22Courchevel PLO flop all-in equity with trips 64.3%
VerifiedVariant-Specific Stats Interpretation
From the river’s cold certainty to the long-shot dreams of Badugi, these numbers prove poker is a beautiful, brutal math problem where hope and equity share a very tense drink.
Sources & References
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