Poker Hand Odds Calculator
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Poker Hand Odds Calculator
Calculate the exact probability and odds of being dealt any specific poker hand from a standard 52-card deck (5-card draw).
Select Poker Hand
Royal Flush Straight Flush (excl. Royal) Four of a Kind Full House Flush (excl. Straight/Royal) Straight (excl. Straight Flush) Three of a Kind Two Pair One Pair High Card (No Pair)
Deck Size
Standard 52-card deck 48-card deck (no Jacks) 36-card deck (6–Ace only) 32-card deck (7–Ace only)
Hand Size (cards dealt)
5 cards 7 cards (Texas Hold'em best hand)
Calculate Select a hand and click Calculate.
function pokC(n, k) { // Binomial coefficient C(n, k) if (k n) return 0; if (k === 0 || k === n) return 1; k = Math.min(k, n - k); let result = 1; for (let i = 0; i Error: Hand size cannot exceed deck size.'; return; } if (handSize === 7 && deckSize !== 52) { resultDiv.innerHTML = '⚠️ 7-card probabilities are only accurate for a standard 52-card deck. Showing 52-card approximation.'; }
const [favorable, total] = pokHandCombos(hand, deckSize, handSize);
if (favorable This hand is not possible with the selected deck/hand configuration.'; return; }
const probability = favorable / total; const percentage = (probability * 100).toFixed(6); const oddsAgainst = ((total - favorable) / favorable).toFixed(1); const oddsFor = (favorable / (total - favorable)).toFixed(6); const expectedIn = Math.round(1 / probability);
const handName = pokHandName(hand); const note7 = (handSize === 7) ? '* 7-card probabilities use best 5-of-7 hand statistics.
' : '';
resultDiv.innerHTML = ` ### Results for: ${handName}
Deck Size${deckSize} cards (${handSize}-card hand) Favorable Combinations${favorable.toLocaleString()} Total CombinationsC(${deckSize},${handSize}) = ${total.toLocaleString()} Probability${probability.toExponential(4)} (${percentage}%) Odds Against${parseFloat(oddsAgainst).toLocaleString()} : 1 Odds For1 : ${parseFloat((1/probability - 1).toFixed(1)).toLocaleString()} Expected Once Every${expectedIn.toLocaleString()} hands
${note7} `; }
// Auto-calculate on load pokCalc();
#### Formulas Used
Total 5-card combinations: C(n, 5) = n! / (5! × (n−5)!)
Probability: P = Favorable Combinations / C(n, 5)
Odds Against: (Total − Favorable) / Favorable
Key hand combination counts (52-card deck, 5-card hand):
- Royal Flush: 4 × 1 = 4
- Straight Flush: 4 × (ranks−4) = 4 × 9 = 36
- Four of a Kind: C(13,1) × C(4,4) × 48 = 624
- Full House: C(13,1)×C(4,3) × C(12,1)×C(4,2) = 3,744
- Flush: C(13,5)×4 − straight/royal flushes = 5,108
- Straight: 10×4⁵ − 40 straight flushes = 10,200
- Three of a Kind: C(13,1)×C(4,3) × C(12,2)×4² = 54,912
- Two Pair: C(13,2)×C(4,2)² × 44 = 123,552
- One Pair: C(13,1)×C(4,2) × C(12,3)×4³ = 1,098,240
- High Card: Total − all above = 1,302,540
- Total: C(52,5) = 2,598,960
#### Assumptions & References
- References: Sklansky, D. The Theory of Poker; Perez, R. Poker Probability Tables; Wikipedia — Poker probability.
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