Poker Equity & OddsOdds of being dealt pocket aces
Short answer
You get pocket aces 0.45% of the time, one hand in 221: 6 of the 1,326 ways to be dealt two cards. Any pocket pair is one hand in 17 and AK one in 82.9. One in 221 is an average, though. Half the time aces show up within 153 hands, and 36.7% of the time you play 221 hands without seeing them once. All 1,326 starting hands are counted below, each one once.
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How often each hand comes
I get aces way less than that.
| You are dealt | Hands | Chance | One in |
|---|---|---|---|
| Pocket aces (AA) | 6 | 0.45% | 221 |
| One given pair, like KK or 77 | 6 | 0.45% | 221 |
| AA or KK | 12 | 0.90% | 110.5 |
| QQ, KK or AA | 18 | 1.4% | 73.7 |
| Any pocket pair | 78 | 5.9% | 17 |
| AK suited | 4 | 0.30% | 331.5 |
| AK offsuit | 12 | 0.90% | 110.5 |
| AK, suited or not | 16 | 1.2% | 82.9 |
| AA, KK, QQ or AK | 34 | 2.6% | 39 |
| Any two suited cards | 312 | 23.5% | 4.3 |
| At least one ace | 198 | 14.9% | 6.7 |
| Two cards ten or higher | 190 | 14.3% | 7 |
A pair has 6 combos because four suits pair up six ways. AK has 16: 4 suited, 12 offsuit. So you hold AK almost three times as often as aces, and AK offsuit three times as often as AK suited. The combos guide has the counting rule.
One in 221 is not every 221 hands
| Hands dealt to you | Aces at least once | No aces at all |
|---|---|---|
| 100 | 36.5% | 63.5% |
| 153 | 50.0% | 50.0% |
| 221 | 63.3% | 36.7% |
| 500 | 89.6% | 10.4% |
| 1,000 | 98.9% | 1.1% |
The waits are lumpy. Most stretches end sooner than 221 hands, and a few run very long, which pulls the average up. So a few hundred hands with no aces at all is normal, and so is a short stretch with aces twice. Neither says anything about the deck.
Kings into aces
one opponent
When you hold kings, a given opponent has aces one time in 204.
eight opponents
At a full table someone has aces about one time in 26. With five opponents, 2.4%.
Your kings take two cards out of the deck, so all four aces are among the 50 you can't see. Each opponent's chance is small, and it adds up across the table. So at a full table kings are still ahead of everyone before the flop about 96 times in 100, and that is why players don't fold them before the flop. Same count with aces and kings swapped: when you hold aces, someone has kings just as often.
How good the hand is when you get it
| Your hand | Against a random hand |
|---|---|
| AA | 85.2% |
| KK | 82.4% |
| 79.9% | |
| AKs | 67.0% |
| AKo | 65.3% |
Aces have 85.2% against a random hand, so about one time in seven they don't hold up. Against a real hand the numbers drop: the preflop equity chart has AA against every pair, and pocket pair vs overcards has AK against all of them. With more players in the pot it drops further, and pocket aces against multiple players shows by how much.
See all 1,326 hands on the grid
The range grid lays out all 169 starting hands with their combos. The Range trainer then has you guess your equity against common ranges, and the engine shows the real number.
Questions
What are the odds of being dealt pocket aces?
6 of the 1,326 possible starting hands are AA, so 0.45%, one hand in 221. The same goes for any one pair you name, kings or sevens.
How often do you get a pocket pair?
78 of 1,326 hands, 5.9%, about one hand in 17.
What are the odds of being dealt AK?
16 combos: 4 suited and 12 offsuit. That is one hand in 82.9, close to three times as often as aces.
If I have KK, how often does someone have AA?
Against one opponent one time in 204. With eight opponents at a full table, 3.9%, about one time in 26.
Where the numbers come from. Every figure on this page comes from the app's own engine, the code that runs on your phone. Outs come from the Outs & Odds tool, hit chances are exact counts, and equities count every runout with no sampling. Engine build 482550e8. More worked numbers: flush draw odds and the pot odds cheat sheet.