In the fixed preflop pairing of As Ah against Qs Qh with five board cards to come, pocket aces win 81.97% of the time, pocket queens win 17.51% of the time, and the remaining 0.52% of boards result in a tied pot. Equity represents a hand’s expected share of the pot over the long run based on its winning and tying probabilities. For this fixed matchup, equity totals 82.23% for pocket aces and 17.77% for pocket queens.
The Model and Exact Enumeration
Calculating exact probabilities in Texas Hold’em requires defining a strict mathematical model. In this setup, two hole cards are assigned to each player before any community cards are dealt. The deck contains 52 cards, and four hole cards are fully known: the ace of spades, ace of hearts, queen of spades, and queen of hearts.
This leaves 48 unseen cards remaining in the deck. The total number of unique five-card community board combinations is calculated using the mathematical formula C(48,5), which equals exactly 1,712,304 possible five-card boards.
Every single one of these 1,712,304 boards was evaluated in a full enumeration calculation verified on 2026-11-09. This process checks every board to determine whether the aces win, the queens win, or the hand ends in a tie, using the evaluation method listed in the Data Used section:
- Pocket aces (As Ah) win: 81.97%
- Pocket queens (Qs Qh) win: 17.51%
- Split pot (tie): 0.52%
These calculations apply strictly to the specific fixed pairing of As Ah versus Qs Qh. Do not extend these exact numbers to any other ace-queen suit combination, as different suit overlaps yield slightly different totals.
Why the Gap Is So Significant
The gap in winning potential between pocket aces and pocket queens is a classic overpair-versus-underpair gap, sometimes described as card domination: a weaker starting hand is blocked by a stronger hand of the same category, leaving the weaker hand with fewer paths to improve to the best river hand.
Because aces outrank queens naturally, the player holding pocket queens starts behind without community cards. To overtake pocket aces by the river, pocket queens usually need to hit a set, which means catching one of the two remaining queens in the deck on the board.
If the board does not improve the queens to three of a kind, a straight, or a flush, and the five community cards do not themselves complete a straight, flush, or higher hand that both players end up sharing, the player holding aces wins simply by holding a higher pair than the board offers. The aces also retain the ability to improve into sets, full houses, or higher pairs if the board pairs other cards, maintaining their large structural advantage across the vast majority of board distributions. You can compare this dynamic to lower pair interactions like pocket jacks vs pocket tens to see how dominated pocket pairs perform across different matchups.
Understanding the Tie Case
In poker, a split pot occurs when both players’ best five-card hands have identical ranks, one card position at a time; suits never break the tie. In this fixed matchup, tied boards are exactly the boards where the five community cards play for both players, as the example below shows.
Consider a verified board example containing 2c 3c 4c 5c 6c. This board displays an all-club five-card hand that evaluates to a six-high straight flush. Because As Ah holds no clubs and Qs Qh holds no clubs, neither player can form a higher five-card flush or straight flush using their hole cards. Both players must play the five board cards directly. As a result, both hands evaluate to the exact same six-high straight flush, and the pot splits.
In equity calculations, ties are shared equally between the two players. Adding half of the 0.52% tie percentage (0.26%) to each player’s win rate gives As Ah an overall equity of 82.23% and Qs Qh an overall equity of 17.77%.
Honest Boundaries of Equity
Even though pocket aces are a massive favorite in this preflop matchup, equity is a long-run measure across many identical matchups, not a promise about a single hand.
Holding an 82/18 advantage means the underdog still wins roughly 17.51% of all runouts outright (about 17.5%, with rounding). Expecting an 82% favorite to win every single time misinterprets how probability works in card games. Short-term outcomes vary widely, and only as the number of identical boards grows do the observed frequencies approach the exact probabilities; any finite sample can deviate from them.
To review broader preflop equity trends and see how various hand matchups compare across the deck, consult our comprehensive poker odds chart.
Three Common Mistakes to Avoid
- Quoting the numbers without the fixed-hands model. Using 81.97% as a global figure for all ace-versus-queen matchups is inaccurate. The specific suits involved dictate exact board interactions, so the model premises must always be stated.
- Treating the tie case as a win for queens or ignoring it entirely. A split pot returns half the pot to each participant. Omitting the 0.52% tie frequency leads to flawed equity totals.
- Calling aces vs queens unbeatable before the board arrives. Pocket queens still win 17.51% of boards outright. Calling any preflop matchup completely guaranteed ignores the mechanics of board distribution.
FAQ
What is the exact win percentage for pocket aces against pocket queens?
In the fixed matchup of As Ah against Qs Qh preflop, pocket aces win 81.97% of the time, pocket queens win 17.51% of the time, and 0.52% of boards result in a split pot.
How are these probabilities calculated?
The numbers come from a full enumeration of all 1,712,304 possible five-card boards generated from the 48 unseen cards, with integer counts and the evaluation method listed in Data Used, verified on 2026-11-09.
Can suit holdings change this exact math?
Yes. This exact math applies strictly to the fixed pairing of As Ah versus Qs Qh. Different suit combinations alter the exact board combinations, so do not extend these specific numbers to other ace-queen suit pairings.
Why do pocket aces and pocket queens tie on some boards?
A tie occurs when the five board cards form the best overall five-card hand for both players, such as a six-high straight flush with no clubs held by either player. Suits never break ties in poker.
This comparison is one of many in our vs series; each page states its model and premises so the numbers mean the same thing every time you read them.
Data Used
- Fixed matchup: As Ah versus Qs Qh; 52-card deck; 48 unseen cards; C(48,5) = 1,712,304 possible five-card boards.
- Method: each board evaluated as the best five cards out of seven (two hole cards plus board) with an independent seven-card hand evaluator; counts verified on 2026-11-09.
- Results: pocket aces win 1,403,604 boards (81.97%); pocket queens win 299,878 boards (17.51%); ties 8,822 boards (0.52%). Equity = wins plus half of ties: 82.23% for the aces, 17.77% for the queens.
- The exact results apply only to As Ah versus Qs Qh; the counts and evaluation method are listed above so the results can be reproduced.
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