Skip to main content
Calkulon

ગণित

પત્તા સંભાવના કૅલ્ક્યુલેટર

🃏Card Probability Calculator (52-card deck)

e.g. 5 for poker

e.g. 4 aces

What is Card Probability Calculator?

▾

કાર્ડ પ્રોબેબિલિટી, રિપ્લેસમેન્ટ વિના પ્રમાણભૂત 52-કાર્ડ ડેકમાંથી ચોક્કસ કાર્ડ દોરવાની સંભાવનાની ગણતરી કરવા માટે હાઇપરજીઓમેટ્રિક વિતરણનો ઉપયોગ કરે છે. ડાઇસથી વિપરીત (રિપ્લેસમેન્ટ સાથે), દોરવામાં આવેલ દરેક કાર્ડ ડેકની રચનામાં ફેરફાર કરે છે, જે સંભાવનાઓને દ્વિપદીને બદલે હાઇપરજીઓમેટ્રિક બનાવે છે.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

સૂત્ર

▾
f(x)N = deck size (52), K = cards of target type, n = hand size, k = desired count

Variable Legend

▾
પ્રતીકનામએકમવર્ણન
Nn! / (k! × (n−k)!) — combinations formula—n! / (k! × (n−k)!) — combinations formula
Ksum of P(X=k) + P(X=k+1) +—sum of P(X=k) + P(X=k+1) +
nn! / (k! × (n−k)!) — combinations formula—n! / (k! × (n−k)!) — combinations formula
ksum of P(X=k) + P(X=k+1) +—sum of P(X=k) + P(X=k+1) +

How to Card Probability Calculator

▾
  1. 1Hypergeometric: P(X=k) = C(K,k) × C(N−K, n−k) / C(N,n)
  2. 2N = deck size (52), K = cards of target type, n = hand size, k = desired count
  3. 3C(n,k) = n! / (k! × (n−k)!) — combinations formula
  4. 4P(at least k) = sum of P(X=k) + P(X=k+1) + ... + P(X=K)

Worked Examples

▾
Example 1
Given:5-card hand, probability of exactly 1 ace (K=4, n=5, k=1)
પરિણામ:≈ 34.12%

C(4,1)×C(48,4)/C(52,5)

Example 2
Given:5-card hand, at least 1 ace
પરિણામ:≈ 34.12% + 21.37% + ... ≈ 34.12% (exactly 1) + others
Example 3
Given:7-card hand (Texas Hold'em + 2 in pocket), 2 aces
પરિણામ:≈ 6.79% of starting hands are pocket aces

Classic Poker Hand Probabilities

▾
HandCombinationsProbability
Royal flush40.000154%
Straight flush360.00139%
Four of a kind6240.0240%
Full house3,7440.144%
Flush5,1080.197%
Straight10,2000.392%
Three of a kind54,9122.11%
Two pair123,5524.75%
One pair1,098,24042.3%
High card1,302,54050.1%

Frequently Asked Questions

▾
Q

What is Card Probability?

A

Card probability uses the Hypergeometric Distribution to calculate the probability of drawing specific cards from a standard 52-card deck without replacement. Unlike dice (with replacement), each card drawn changes the composition of the deck, making the probabilities hypergeometric rather than binomial

Q

How accurate is the Card Probability calculator?

A

The calculator uses the standard published formula for card probability. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

Q

What units does the Card Probability calculator use?

A

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

Q

What formula does the Card Probability calculator use?

A

The core formula is: Hypergeometric: P(X=k) = C(K,k) × C(N−K, n−k) / C(N,n). Each step in the calculation is shown so you can verify the result manually.

Deep Dive

Read the full guide on how to use this calculator effectively

વધુ વાંચો →
Formula-verified for precision
Reviewed October 2026
Our methodology

Ratings & comments

…

સાપ્તાહિક ગણિત ટિપ્સ મેળવો

12,000+ સબ્સ્ક્રાઇબર્સ સાથે જોડાઓ કે જેઓ દર અઠવાડિયે કેલ્ક્યુલેટર ટીપ્સ મેળવે છે.

🔒
100% मफत
क्यारेय नोंधणी नहीं
✓
सचोट
चकासायेल फॉर्म्युला
⚡
तात्कालिक
टाइप करतां ज परिणाम
📱
मोबाइल रेडी
बधा उपकरणो

સेटिंग्स

गोपनीयताशरतोविशे© 2026 Calkulon