Card Probability Calculator
Drawing Specific Cards
Probability of drawing at least one target card from a deck
Poker Hand Odds
Reference odds for standard 5-card poker hands
Formula
P(X = k) = C(K,k) x C(N-K, n-k) / C(N,n) | P(at least k) = 1 - P(X < k) | Expected value = n x K / N
Frequently Asked Questions
How is card draw probability calculated?
Card draw probability uses the hypergeometric distribution. P(X = k) = C(K,k) x C(N-K, n-k) / C(N, n), where N is deck size, K is target cards, n is cards drawn, and k is successes wanted. It accounts for drawing without replacement.
What are the odds of drawing an ace from a standard deck?
Drawing at least one ace when drawing 1 card from a 52-card deck: 4/52 = 7.69%. Drawing at least one ace in a 5-card hand: about 34.1%. Drawing at least one ace in a 7-card hand: about 45.3%.
How does this apply to trading card games?
This calculator works for any card game. For MTG (60-card deck, 7-card opening hand) or Yu-Gi-Oh (40-card deck, 5-card hand), just set the deck size, target card count, and draw count accordingly.
You may also need
~
D&D Dice Calculator
Free D&D dice probability calculator. Calculate statistics for any dice roll notation (d4, d6, d8, d10, d12, d20, d100) with modifiers.
Everyday+
Probability Calculator
Free probability calculator. Calculate probability of events, combinations, permutations, and coin flip odds.
Math~
Poker Odds Calculator
Free poker odds calculator. View the probability of common poker hands from a standard 5-card deal, including royal flush, straight flush, and more.
Everyday