- Maths reviewed by Josh Miller
- Tested by Diana Westfield
One card off the top of a shuffled deck is a king 1 time in 13, or 7.69%. Deal five and the chance of at least one king climbs to 34.1%. The CasinoCalcs card probability calculator above works that out for any card, rank, suit or colour, any deck size, and any number of cards drawn. It’s free, it handles shoes as well as single decks, and it shows the exact and “at least” chances side by side.
Card probability calculator: a quick chart
| What you want | Cards drawn | Chance | Odds |
|---|---|---|---|
| A king | 1 | 7.69% | 1 in 13 |
| At least one king | 5 | 34.1% | 1 in 2.9 |
| At least one ace | 2 | 14.9% | 1 in 6.7 |
| Two aces | 2 | 0.45% | 1 in 221 |
| At least one face card | 3 | 55.3% | 1 in 1.8 |
| Five red cards | 5 | 2.53% | 1 in 40 |
| Five hearts | 5 | 0.050% | 1 in 2,019 |
Pocket aces at 1 in 221 is the number every Hold’em player knows. It’s the same sum: 4/52 × 3/51.
Why “at least one” is the useful question
Most real questions are “will I see at least one?”, not “will I see exactly one?”. The trick is to flip it. The chance of no kings in five cards is 48/52 × 47/51 × 46/50 × 45/49 × 44/48, about 65.9%. Everything else is at least one king: 34.1%. The calculator does the same thing for “at least 2”, “at least 3” and so on by adding up the cases below and taking them away.
Cards don’t go back in the deck once dealt, so every draw changes the odds of the next. That’s why the maths here is hypergeometric rather than a simple multiply. If you want to treat it like a dice roll, put a big number in for the deck size and the two answers get close.
Cards at the casino table
This is the same arithmetic behind blackjack bust charts and poker outs. A blackjack shoe of six decks has 96 ten-value cards in 312; set the deck to 312 and pick “Ten-value cards” to check. For a whole hand of poker, the poker hand odds chart has every hand worked out, and the blackjack bust calculator applies it to hitting. For the general tool with any population, use the hypergeometric calculator.
Guessing whether the next card is higher or lower? The Hi-Lo calculator tracks the cards gone and gives the odds each time.
How the deck breaks down, suits, face cards and jokers, is in how many cards in a deck. For repeated independent tries, the binomial calculator takes over.