If you’ve ever played poker and tried to figure out the probability of getting a royal flush, you know that it’s one of the hardest hands to get. The likelihood is much higher for a royal if you have five cards. The probability is 1% when you hold two cards and it’s one of the few situations when holding three cards increases the chance of a royal. However, if you hold just one card, you have a 6% chance of getting a royal flush.
If you play a game of Jacks or Better on a video poker machine, the probability of hitting at least one royal is 0.00010268. That’s four times higher than the probability of hitting a royal flush in a single session. But it’s never more than five times higher. If you’re lucky enough to get a royal flush, you have a one in every 47,000 hands played.
The probability of a royal flush is one in 1,081 in a single draw. A three-card royal flush has a slightly lower chance of hitting a royal flush than a pair of queens, which is one in eight hundred seven. In video poker, there are several chances for you to hit a royal flush in any given game. You can calculate the probability of a royal flush for a particular hand by examining a few simple math tables.