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A standard 52-card deck has 4 suits (♠ ♥ ♦ ♣), 13 ranks (2–10, J, Q, K, A), with 13 cards per suit and 4 cards per rank. The total number of possible 5-card hands is C(52, 5) = 2,598,960.
Probability of any event = (number of favorable outcomes) / (total possible outcomes). For card draws, counting favorable outcomes usually involves combination math.
Drawing one card: P(Ace) = 4/52 = 1/13 ≈ 7.69%. P(Heart) = 13/52 = 1/4 = 25%. P(Ace of Spades) = 1/52 ≈ 1.92%.
Worked example — probability of a 5-card flush (all same suit): Choose 1 of 4 suits (4 ways), then choose 5 from 13 cards of that suit = C(13,5) = 1,287 ways. Total flushes = 4 × 1,287 = 5,148. But subtract royal flush (4) and straight flush (36): flushes = 5,108. P(flush) = 5,108 / 2,598,960 ≈ 0.197%.
P(event) = C(favorable) / C(52, hand_size)
P(first draw matches)
7.69%
4/52
P(at least one in 1 draws)
7.69%
without replacement
| Hand | Ways | Probability |
|---|---|---|
| Royal Flush | 4 | 0.0002% |
| Straight Flush | 36 | 0.0014% |
| Four of a Kind | 624 | 0.0240% |
| Full House | 3,744 | 0.1441% |
| Flush | 5,108 | 0.1965% |
| Straight | 10,200 | 0.3925% |
| Three of a Kind | 54,912 | 2.1128% |
| Two Pair | 123,552 | 4.7539% |
| One Pair | 1,098,240 | 42.2569% |
| High Card | 1,302,540 | 50.1177% |
Total 5-card hands: 2,598,960 = C(52,5)
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.