Four Players, One Ace Each

A standard 52-card deck is dealt evenly to four players. What is the probability that each player gets exactly one Ace?

Focus only on the 4 Aces

Which 4 of the 52 dealt positions contain an Ace?

Each player owns 13 positions. Success means exactly one Ace lands inside each 13-card hand.

Answer 10.55%

Counting argument

All possible Ace-position sets

C(52, 4)

Choose any 4 of the 52 card positions to hold the Aces.

Successful sets

13 × 13 × 13 × 13 = 13⁴

Choose one Ace position from Player 1's 13 slots, one from Player 2's, and so on.

P = 13⁴ / C(52,4)

≈ 0.105498 = 10.55%

Same idea, Ace by Ace

1st Ace

Anywhere is fine.

2nd Ace

Must be in another player's hand → 39/51

3rd Ace

Must be in one of the two unused hands → 26/50

4th Ace

Must be in the last unused hand → 13/49

1 × 39/51 × 26/50 × 13/49

≈ 10.55%

Key insight: don't count complete 13-card hands. Since the only thing that matters is where the four Aces land, reduce the problem to choosing four positions among 52.