Card Draw Odds Calculator
Poker style draw odds for any outs and draw count.
What it does
Card odds run on counting without replacement. Each drawn card changes the rest, so simple multiplication misleads.
The tool above counts combinations. Four outs across five cards hit at least one 34.1 % of the time and exactly one 29.9 %, or 1 in 2.9.
Missing them all sets the base. Ways to dodge every out over all possible hands give the complement to subtract from one.
Exactly one refines further. One hit times the ways to fill the rest, over all hands, splits the headline chance.
Odds translate percents. One hundred over the percent reads naturally at tables.
How to use
- Enter outs: 4 suits aces.
- Enter cards drawn: 5 suits a hand.
- Read at least one first.
- Read exactly one next.
- Read odds and play accordingly.
Formula
- outs
- Wanted cards left in the deck.
- drawn
- Cards drawn.
Exact hypergeometric counting without replacement. Odds read 100 divided by the percent.
Worked example
Example: 4 outs in 5 cards
Defaults: 4 outs with 5 cards drawn. These are also the default values, so the page opens on this answer.
- Outs: 4 aces in a 52 deck.
- Drawn: 5 cards.
- No ace ways over all ways: C(48,5)/C(52,5).
- At least one: 1 - 0.6588 = 34.1 %.
- Exactly one: C(4,1)xC(48,4)/C(52,5) = 29.9 %. Odds: 1 in 2.9.
- Tool shows 34.1 % at least one, 29.9 % exactly one, 1 in 2.9.
Reference table
| Draw | At least one ace | Odds |
|---|---|---|
| 2 cards | 7.6 % | 1 in 13.1 |
| 5 cards | 34.1 % | 1 in 2.9 |
| 7 cards | 45 % | 1 in 2.2 |
Limits
- 53 card math only with fair decks.
- Replacement needs other formulas.
- Jokers need 53 card math.
- Dependent events assumed.
Common mistakes
- Multiplying single draw odds.
- Forgetting cards leave the deck.
- Reading 34 % as guaranteed.
- Counting jokers as outs silently.
- Trusting cold decks.
Try it yourself
Quick checks. Answers sit tucked under each question.
At least one of 4 kings in 7 cards?
No king ways over all: C(48,7)/C(52,7) = 0.5503, so at least one is 45 %.
Ace in 2 cards from 4 aces?
C(50,2)/C(52,2) misses both aces: 1225/1326 = 0.9238, so at least one is 7.6 %.
Questions
Ace in 5 cards?
One minus missing them all: 1 - C(48,5)/C(52,5) = 34.1 %.
Exactly one ace?
Hypergeometric counting: C(4,1)xC(48,4)/C(52,5) = 29.9 %.
Odds format?
Divide 100 by the percent. Here 100 / 34.1 = 1 in 2.9.
More outs help?
More outs or more cards both raise the chance. Four outs in 5 beats one out in 2.
With replacement?
Yes. Replacement changes everything; this page draws without it.
Stacked decks?
No. Shuffling fairness needs trusted decks.