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Card Deck Probability Calculator - Online Poker & Draw

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Card Deck Probability Calculator

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Poker Odds · Draw Probability · Outs Calculator · Hypergeometric Distribution

Input Parameters
Total cards in the deck (standard = 52)
Number of "winning" cards (e.g., 4 Aces, 13 Spades)
How many cards you draw from the deck
Minimum number of success cards you want
Quick Presets:

Enter parameters and click Calculate to see results

A♥ K♠ Q♦ J♣ 10♥
5-Card Poker Hand Rankings & Probabilities

Standard 52-card deck, 5-card draw. Total possible hands: 2,598,960

Rank Hand Frequency Probability Odds (1 in) Cumulative
1 Royal Flush A♥K♥Q♥J♥10♥ 4 0.000154% 649,740 0.000154%
2 Straight Flush 36 0.00139% 72,193 0.00154%
3 Four of a Kind 624 0.0240% 4,165 0.0256%
4 Full House 3,744 0.1441% 694 0.170%
5 Flush 5,108 0.1965% 509 0.366%
6 Straight 10,200 0.3925% 255 0.759%
7 Three of a Kind 54,912 2.1128% 47 2.87%
8 Two Pair 123,552 4.7539% 21 7.63%
9 One Pair 1,098,240 42.2569% 2.37 49.88%
10 High Card 1,302,540 50.1177% 2.00 100%
Key Insights
  • ~50% of all 5-card hands are High Card (no pair)
  • ~42% contain exactly One Pair
  • Only about 7.6% of hands beat Two Pair
  • Royal Flush appears once in 649,740 hands on average
Quick Hand Prob Calculator
Select a hand type
Outs Calculator
Cards that improve your hand (e.g., 9 for a flush draw)
Common Draw Scenarios:

Select stage and outs count, then click Calculate

Try the preset scenarios above for quick results

Frequently Asked Questions

What is hypergeometric distribution in card probability?
Hypergeometric distribution models the probability of k successes in n draws from a finite population of size N containing K success items, without replacement. This perfectly describes drawing cards from a deck — once a card is drawn, it's not put back. The formula is: P(X=k) = C(K,k) × C(N-K, n-k) / C(N,n). Our Draw Probability calculator uses this exact formula.
What are "outs" in Texas Hold'em poker?
Outs are the unseen cards that will improve your hand to a likely winner. For example, if you have 4 hearts after the flop and need one more for a flush, there are 9 remaining hearts in the deck — you have 9 outs. Counting outs correctly is fundamental to making profitable poker decisions. Use our Outs Calculator to quickly convert outs to percentage odds.
What is the "Rule of 2 and 4" in poker?
It's a quick estimation method:
• After the Flop (2 cards to come): Multiply outs by 4 to get approximate % of hitting by the river.
• After the Turn (1 card to come): Multiply outs by 2 to get approximate % of hitting on the river.
Example: 9 outs for a flush draw → ~36% after flop, ~18% after turn. The exact calculation is slightly different but this rule gives a fast, table-ready estimate.
How many possible 5-card poker hands exist?
From a standard 52-card deck, the number of possible 5-card hands is C(52,5) = 2,598,960. This is the denominator for all 5-card poker probability calculations. Our Poker Hand Odds table breaks down all 2,598,960 hands by their ranking categories.
What is the rarest hand in poker?
The Royal Flush is the rarest standard poker hand — A, K, Q, J, 10 all of the same suit. There are only 4 possible royal flushes (one per suit) out of 2,598,960 possible hands. The odds are 1 in 649,740, making it extremely rare. A Straight Flush (including royal) occurs 36 times, with non-royal straight flushes accounting for 32 of those.
What's the difference between probability and odds?
Probability is the fraction of favorable outcomes over total outcomes (e.g., 25% or 0.25).
Odds express the ratio of unfavorable to favorable outcomes. If probability is 25% (1 in 4), the odds are 3 to 1 against (3:1). In our calculator, we show "1 in X" format — meaning you expect the event once every X trials on average. Both represent the same information in different formats.
How do I calculate the probability of at least one pair?
For a 5-card hand: P(at least one pair) = 1 - P(no pair, all ranks distinct). With 13 ranks and 4 suits each: P(no pair) = [C(13,5) × 4⁵] / C(52,5) = [1,287 × 1,024] / 2,598,960 = 1,317,888 / 2,598,960 ≈ 50.7%. So P(at least one pair) ≈ 49.3%. You can verify this using our Draw Probability calculator by setting N=52, K=52 (any card can form a pair conceptually), though for pair-specific calculations, use the Poker Hand Odds tab.
Why do flush draws have 9 outs?
Each suit has 13 cards. If you hold 2 suited cards and the flop shows 2 more of that suit, you've seen 4 of the 13. That leaves 13 - 4 = 9 unseen cards of that suit remaining in the deck — these are your outs. With 9 outs after the flop, you have approximately a 35% chance (using exact hypergeometric calculation) to complete your flush by the river.
What is an open-ended straight draw vs. a gutshot?
• Open-ended straight draw (OESD): You have 4 consecutive cards and can complete the straight on either end. 8 outs. Example: 5-6-7-8 can be completed by any 4 or any 9.
• Gutshot (inside straight draw): You're missing one card in the middle of the sequence. 4 outs. Example: 5-6-8-9 needs a 7. OESDs are twice as likely to hit as gutshots.
Can this calculator help with blackjack or other card games?
Absolutely! The Draw Probability tab uses the general hypergeometric distribution and works for any card game scenario. For blackjack, you can calculate the probability of drawing a 10-value card (K=16 tens in a 52-card deck), or the chance of busting given your current hand. For bridge, calculate suit distribution probabilities. The math is universal — just adjust N, K, n, and k to match your scenario.
Poker Probability Quick Reference
Flop
Flush Draw → River: ~35% (9 outs × 4 ≈ 36%)
OESD → River: ~31.5% (8 outs × 4 ≈ 32%)
Gutshot → River: ~16.5% (4 outs × 4 ≈ 16%)
Turn
Flush Draw → River: ~19.6% (9 outs × 2 ≈ 18%)
OESD → River: ~17.4% (8 outs × 2 ≈ 16%)
Gutshot → River: ~8.7% (4 outs × 2 ≈ 8%)
Pre-Flop
Pocket Pair → Set on Flop: ~11.8%
Suited Cards → Flush on Flop: ~0.84%
Any Pair or Better on Flop: ~32.4%
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