There are exactly 78 unique pocket pair combinations in a standard 52-card deck. These highly sought-after starting hands are a key element of poker strategy.
Understanding Pocket Pairs
A pocket pair refers to the two private cards dealt to a player in games like Texas Hold'em, where both cards are of the same rank (e.g., two Aces, two Kings, two Sevens). These hands are considered strong because they are already paired, offering immediate equity and potential to form powerful hands on later streets.
The Calculation Behind the Number
The total number of pocket pair combinations is derived from the structure of a standard 52-card deck:
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Number of Ranks: A deck contains 13 distinct card ranks: Ace (A), King (K), Queen (Q), Jack (J), Ten (T), Nine (9), Eight (8), Seven (7), Six (6), Five (5), Four (4), Three (3), and Deuce (2).
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Combinations Per Rank: For each of these 13 ranks, there are 6 possible ways to form a pair. This is because there are four suits (clubs ♣, diamonds ♦, hearts ♥, spades ♠) for each rank. To choose two cards of the same rank from four suits, the calculation is "4 choose 2" (⁴C₂), which equals:
(4 * 3) / (2 * 1) = 6 combinations.For example, if you consider a pair of Aces (AA), the 6 possible combinations are:
- A♠ A♥
- A♠ A♦
- A♠ A♣
- A♥ A♦
- A♥ A♣
- A♦ A♣
Total Pocket Pair Combinations
To find the total number of pocket pairs, you multiply the number of ranks by the number of combinations per rank:
Total Pocket Pairs = Number of Ranks × Combinations Per Rank
Total Pocket Pairs = 13 × 6 = 78
This breakdown can be visualized in the table below:
| Rank of Pair | Number of Combinations | Example Pairs |
|---|---|---|
| Aces (AA) | 6 | A♠A♥, A♠A♦, etc. |
| Kings (KK) | 6 | K♠K♥, K♠K♦, etc. |
| Queens (QQ) | 6 | Q♠Q♥, Q♠Q♦, etc. |
| Jacks (JJ) | 6 | J♠J♥, J♠J♦, etc. |
| Tens (TT) | 6 | T♠T♥, T♠T♦, etc. |
| Nines (99) | 6 | 9♠9♥, 9♠9♦, etc. |
| Eights (88) | 6 | 8♠8♥, 8♠8♦, etc. |
| Sevens (77) | 6 | 7♠7♥, 7♠7♦, etc. |
| Sixes (66) | 6 | 6♠6♥, 6♠6♦, etc. |
| Fives (55) | 6 | 5♠5♥, 5♠5♦, etc. |
| Fours (44) | 6 | 4♠4♥, 4♠4♦, etc. |
| Threes (33) | 6 | 3♠3♥, 3♠3♦, etc. |
| Deuces (22) | 6 | 2♠2♥, 2♠2♦, etc. |
| Total | 78 |
Probability of Being Dealt a Pocket Pair
Understanding the total number of pocket pairs also helps in calculating the probability of being dealt one. Since there are 78 possible pocket pair combinations out of a total of 1,326 possible two-card starting hands (combinations of 52 cards taken 2 at a time), the probability is:
Probability = 78 / 1326 ≈ 0.0588
This means you have approximately a 5.9% chance of being dealt a pocket pair, or roughly once every 17 hands.
