While the magic of a royal flush might capture the imagination, the cold math of poker reveals that you'll be dealt the mighty pocket Aces only once every 221 hands, a stark probability that shapes every strategic decision from preflop to the river.
Key Takeaways
- The probability of being dealt pocket Aces (AA) preflop in Texas Hold'em is exactly 0.4524% or 1 in 221 hands
- Pocket Kings (KK) preflop occurs 0.4524% of the time, identical to AA due to symmetry
- Pocket Queens (QQ) preflop probability is 0.4524%
- Flop rainbow (three different suits) occurs 49.12% given random flop
- Monotone flop (all one suit) probability: 0.33%
- Paired flop (one pair on board) frequency: 16.90%
- Turn pairs the flop exactly 11.76% of the time
- Turn brings flush draw completion if flop monotone: 19.57%
- River bricks (no improvement) for flush draw: 54.1%
- Pot odds required for flush draw on turn: 4:1 or 20%
- AA equity vs 22+ range preflop: 85.2%
- Top pair top kicker equity vs set: 28.5%
- Implied odds needed for set mining: 10:1 to 20:1
- Pot odds for calling flush draw on flop: 3:1 (25%)
- Reverse implied odds penalty for top pair weak kicker: 15-20%
Poker hand odds involve many precise probabilities for cards and flops.
Equity Ranges
- Pot odds required for flush draw on turn: 4:1 or 20%
- AA equity vs 22+ range preflop: 85.2%
- Top pair top kicker equity vs set: 28.5%
- Open-ended straight draw equity vs overpair: 32.4%
- Flush draw equity on flop: 35%
- Set mining equity preflop vs top range: 11.8%
- Bluff catcher equity in polarized range: 22.1%
- Overpair equity vs flush draw: 42.3%
- AKo equity vs QQ preflop: 44.6%
- Gutshot equity on flop: 16.5%
- AA vs random hand equity: 85.2%
- Pocket pair equity vs two overcards: 55%
- Equity realization in 3-bet pots: 55%
- BB defend range equity vs open: 38%
- Top set equity vs flush: 65%
- Bluff equity needed for 2:1 pot: 25%
- Pocket pair <50% equity vs two overcards dominated: no, 55%
- AA preflop vs tight range equity: 75%
- River value bet thin equity: 45%
- Set equity vs top pair: 82%
- Flush draw + pair equity: 45%
- Overpair equity vs board pair: 35%
- Nut flush equity vs sets: 70%
- TPTK equity vs two pair: 25%
- Bluff equity in iso pot: 30%
- Pocket kings equity vs ace high range: 60%
Equity Ranges Interpretation
While the cold math of poker reminds us that aces can feel like a sure thing at 85%, the brutal beauty of the game is how often that "unbeatable" flush draw will drain your stack, that mighty overpair will crack to a sneaky set, and even a 55% favorite can feel like a coin flip when your rent money is in the middle.
Flop Textures
- Flop rainbow (three different suits) occurs 49.12% given random flop
- Monotone flop (all one suit) probability: 0.33%
- Paired flop (one pair on board) frequency: 16.90%
- High card flop (no paint cards) : 24.5%
- Flop with two broadway cards: 32.1%
- Dry flop (no flush draw, no straight draw) : 28.4%
- Wet flop with multiple draws: 15.2%
- Flop hitting top pair exactly with overpair range: 11.8%
- Connected flop (straight draws possible) : 41.3%
- Low flop (under 9 high) frequency: 19.7%
- Broadway flop probability: 13.6%
- Flop with exactly one ace: 4.92%
- Flop set from pocket pair: 11.8%
- Top pair flop hit rate for Ax hands: 32%
- Flush draw on flop from suited hand: 11%
- Open-ender on flop from connectors: 9.3%
- Two pair flop frequency for suited connectors: 2.1%
- Trips on flop from suited broadway: 1.3%
- Gutshot on flop: 10.2%
- Double gutter frequency: 1.2%
- Flop c-bet frequency on dry boards: 65%
- Monotone flop nut flush equity: 82%
- Flop with three to flush: 1.9%
- Paired flop top set hit: 2.1% per pair
- Flop rainbow high: 22.3%
- Flop two-tone: 48.2%
- Broadway flop with pair: 8.4%
- Low connected flop: 35.1%
- Monotone low flop: 0.1%
- Flop with ace high paired: 5.2%
- Wet coordinated flop: 12.8%
- Flop static board: 25%
- Paired high flop: 17.2%
Flop Textures Interpretation
While the rainbow flop's near-50% ubiquity suggests chaos loves variety, the sobering 0.33% monotone and 11.8% top pair hit rates remind us that poker is a game of patiently waiting for the rare moments when probability and position bless your specific hand with a meaningful advantage.
Pot Implied Odds
- Implied odds needed for set mining: 10:1 to 20:1
- Pot odds for calling flush draw on flop: 3:1 (25%)
- Reverse implied odds penalty for top pair weak kicker: 15-20%
- Break-even point for semi-bluffing: 33% equity needed
- Implied odds multiplier for flush draw: x4 pot
- Pot odds on turn for open-ender: 4:1 (20%)
- Effective implied odds in short stack: reduced by 50%
- Minimum implied odds for gutshot: 11:1
- Pot odds adjustment for multiway pots: +10-15%
- Backdoor draw implied value: 5-10% equity boost
- Pot odds for combo draw: 2:1 (33%)
- Implied odds for overpair thin value: 3:1
- River overbet bluff frequency: 20%
- Implied odds cap for deep stack: 15x bet
- Pot odds multiway adjustment: divide by players
- Implied for combo draw: 1.5:1 sufficient
- Pot odds river jam: pot / (pot + bet)
- Implied odds short stack penalty: -70%
- Pot odds for slowplay: 2x implied needed
- Implied for set mining deep: 12:1+
- Pot odds check-raise: pot + bet / pot
Pot Implied Odds Interpretation
To profitably navigate poker's complex landscape, you must balance the precise mathematics of pot odds with the subtle art of implied odds, remembering that chasing a flush draw requires different math than set mining, and a short stack drastically reduces your room for creativity.
Preflop Probabilities
- The probability of being dealt pocket Aces (AA) preflop in Texas Hold'em is exactly 0.4524% or 1 in 221 hands
- Pocket Kings (KK) preflop occurs 0.4524% of the time, identical to AA due to symmetry
- Pocket Queens (QQ) preflop probability is 0.4524%
- Any pocket pair preflop is 5.8808% or 1 in 17.01
- Suited connectors like 76s preflop: 0.3046%
- Offsuit broadway hands like AKo: 0.9412%
- Any Ace preflop: 23.24%
- Suited Aces (Axs): 1.125%
- Probability of AA vs KK preflop equity: AA 82.35%
- Top 10% preflop hands include 88+, ATs+, KJs+, QJs, AJo+
- Preflop all-in AA survival rate in tournaments: 75% vs calling range
- Pocket Aces win rate heads-up: 81%
- Suited hand premium preflop: +3-5% equity
- Any pair preflop equity vs overcards: 52%
- Broadway suited equity boost: +2.1%
- Trash hand preflop fold equity: 100% in EP
- Preflop 3-bet range top 8%: JJ+, AKs, AKo
- Preflop limp-fold rate in cash: 70%
- Preflop suited connector playability: top 20% hands
- KK preflop win% vs calling station: 65%
- Preflop top 5% hands: 22+, A2s+, K9s+, QTs+, JTs, AJo+, KQo
- QQ preflop vs AA/KK risk: 18% dominated
- Preflop 4-bet shove equity premium: +10%
- AKs preflop nut potential: 65%
- Preflop wheel aces suited: 0.47%
- Preflop button open range: 40%
- Preflop cold call equity avg: 35%
Preflop Probabilities Interpretation
The poker gods grant you a pair of aces less than once every two hundred hands, but those same odds apply to kings and queens, proving that even in a game of chance, royalty is frustratingly democratic.
Turn River Odds
- Turn pairs the flop exactly 11.76% of the time
- Turn brings flush draw completion if flop monotone: 19.57%
- River bricks (no improvement) for flush draw: 54.1%
- Turn blank (low non-pairing card) frequency: 31.2%
- Probability of runner-runner flush on turn and river: 0.33%
- Turn completes open-ended straight draw 17.39%
- River pairs board if unpaired turn: 12.45%
- Full runout to quadz from set on flop: 0.21%
- Turn scare card (ace or king) frequency: 8.5%
- Turn runner-runner straight outs: 8
- Flush outs on turn: 9
- River improve overpair: 18% vs draw
- Turn fold equity realization: 40-60%
- Board pairing on river: 12%
- Turn ace blocker value: reduces villain flush outs by 1
- Straight flush runner probability: 0.0013%
- Turn check-raise bluff equity req: 40%
- Turn brings straight completion: 31.5% for OESD
- Gutshot + overcard outs: 12
- Turn fold to c-bet: 55%
- Runner-runner full house: 0.15%
- Turn out for set: 1 out 33.3%
- River bluff catcher block: +5% equity
- OESD turn hit rate: 17%
- Turn blank low card: 28%
- River improve gutshot: 16.5%
- Turn flush complete rate: 19%
Turn River Odds Interpretation
While the turn might flirt with your draws just enough to keep hope alive—like a 19% chance of completing a flush or a 17% shot at a straight—the river is a notorious heartbreaker, often slamming the door with a 54% brick rate that forces you to realize fold equity is as crucial as hitting your outs.
Sources & References
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