Ever wonder what the odds are of getting a royal flush in Poker? What about four Aces?
These questions are easy to answer mathematically, but we must first be clear about which variant of Poker is played. Let’s consider Five-Card Draw Poker, the version most popular amongst casual players until Hold ‘Em took the world by storm in 2003. Receiving a royal flush in the first five cards in Draw Poker happens only once in 649,740 hands on average.
Those are the chances of getting ANY royal flush. The chances of getting a specific royal flush are 1 in 2,598,960 hands. You’re five times more likely to get struck by lightning than get the same hand twice!
In Hold ‘Em, each player potentially has seven cards (the two cards in your hand and the five community cards) with which to hit the elusive royal. The chances of getting a royal flush in Hold ‘Em are 1 in 30,940 hands. Incidentally, the chances of getting a royal flush in 7-Card Stud are the same as in Hold ‘Em. Here are a few more fun poker probabilities:
Chances of getting four Aces in 5-Card Draw: 1 in 54,145 hands on average.
Chances of getting any four of a kind in Hold ‘Em: 1 in 4,165 hands on average.
Chances of getting pocket Aces in Hold ‘Em: once every 221 hands on average.
Chances of a royal flush beating four Aces in Hold ‘Em: about once every 165 million hands!