Odds of being dealt pocket aces
What are the odds of being dealt pocket aces? The short answer is below, and under it the working: the formula with the numbers put in, and the count from dealing every possible card.
The working
A deck has C(52, 2) = 1,326 two-card hands. Four aces make C(4, 2) = 6 pairs of aces, so:
P(AA) = C(4, 2) / C(52, 2) = 6 / 1,326 = 1 / 221 = 0.452% P(AA twice running) = (1 / 221)² = 1 in 48,841
“Once every 221 hands” is an average, not a schedule. Hands are independent, so the chance of seeing aces at least once in your next N hands is 1 − (220/221)N. It passes 50% after 153 hands and 90% after 508. Long droughts are normal: a 500-hand stretch without aces happens about 10% of the time.
The same 1 in 221 holds for any named pair, kings or deuces. What makes aces feel rarer is that you only notice the hand you are waiting for.
Every starting-hand group
Counted by dealing all 1,326 hands and checked against the formula for each row.
| Starting hand | Probability | 1 in | Odds against | Count |
|---|---|---|---|---|
| Pocket aces (or any one named pair) | 0.45% | 221 | 220 to 1 | 6 / 1,326 |
| Ace-king, suited or not | 1.21% | 82.9 | 81.9 to 1 | 16 / 1,326 |
| Ace-king suited | 0.30% | 332 | 331 to 1 | 4 / 1,326 |
| Queens or better (QQ, KK, AA) | 1.36% | 73.7 | 72.7 to 1 | 18 / 1,326 |
| Any pocket pair | 5.88% | 17.0 | 16.0 to 1 | 78 / 1,326 |
| Two cards of the same suit | 23.53% | 4.25 | 3.25 to 1 | 312 / 1,326 |
| Suited connectors (32s to AKs) | 3.62% | 27.6 | 26.6 to 1 | 48 / 1,326 |
| At least one ace | 14.93% | 6.70 | 5.70 to 1 | 198 / 1,326 |
| Two broadway cards (T to A), pairs included | 14.33% | 6.98 | 5.98 to 1 | 190 / 1,326 |
What aces are worth once you have them is on the AA page: 85.2% against one random hand, and 81.9% against kings. If you hold kings instead, see how often somebody has aces.
More before the flop
Other odds
- Flopping a set11.8%
- Flopping a flush or flush draw0.8%
- Flopping a straight or straight draw1.3%
- Flopping a pair or two pair32.4%
- An overcard to your pair41.4%
- Flush draw (9 outs)35.0%
- Open-ended straight draw (8 outs)31.5%
- Gutshot (4 outs)16.5%
- Combo draw (12 to 15 outs)54.1%
- Two overcards (6 outs)24.1%
- Set to full house33.4%
- The rule of 2 and 4, checkedup to 12.5 pts off
- Counted, not quoted.
tools/build-odds.mjsdeals every possible flop, turn, river or starting hand and counts. Where a closed-form formula exists, the build refuses to publish unless the count matches it exactly. - Made hands come from the engine. Whether cards make a straight, a flush or a full house is decided by the same Rust/WebAssembly evaluator the trainer runs, not by hand-written rules.
- Odds are not equity. Hitting your hand is not winning the pot. For that, the matchup pages deal every board against a specific hand and the spot calculator works against a range.
- Raw data: odds.json.