If you are interested in video poker and read specialized literature dedicated to it, you may have read about the concept of royal flush cycle. It means the frequency of the highest hand in the game. In other words, the question is "After how many hands played according to the best strategy, we can get a royal flush?"
Many inexperienced users faced with this term think that the result of the game in video poker is predetermined, that it is not random and predictable. But it is not so. If we say that the royal flush comes once-in-forty thousand hands, it does not mean that you will play this number of games and surely get this hand.
It's just mathematically calculated theoretical rate. In fact, you can get a royal flush in half an hour or collect no in the whole month playing all day in the casino.
You may also wonder why every video poker has its rate of royal flush. This is explained by the fact that the optimal strategy developed for individual games require different decisions in similar situations, resulting in the probability of a royal flush.
Now let's see how often the highest hand is in the most popular versions of video poker:
- Jacks or Better - 40,391 hands
- Double Double Bonus - 40,782 hands
- Not So Ugly Deuces Wild - 43,456 hands
- Full Pay Deuces Wild - 45,282 hands
- Joker Wild - 46,214 hands
- Double Bonus - 48,048 hands
Now let's see the probability of having one or more royal flush in one cycle. We took for example Video Poker Jacks or Better. Calculations were made for forty thousand hands.
- No royal flush - 36.8%
- A royal flush - 36.8%
- Two royal flush - 18.4%
- Three royal flush - 6.1%
- Four royal flush - 1.5%
- Five Royal Flush - 0.3%
- Six or more royal flush - 0.1%
As you can see, the chance to become the owner of one or more royal flush in forty thousand hands 63.2%, which, in general, not so little. On the other hand, we know many cases where players saw the maximum of several hands. So be ready for such tests of your nerves and prepare a good bankroll.
The following table will help you understand the "black stripes". It shows the probability of a different number of hands without a royal flush.
- One cycle - 36.8%
- Two hands - 13.5%
- Three hands of - 5%
- Four hands - 1.8%
- Five hands - 0.7%
- Six hands - 0.3%
- Seven hands - 0.09%
- Eight hands - 0.03%
Thus the probability that you will not get a royal flush, for example, in three hands is approximately 1 to 20. Fortunately, in video poker you win only with the highest possible hand. Otherwise you would need a huge bankroll.
Summing up, in reality you may get a royal flush in forty thousand hands, but you can also not get it at all or have several royal flush hands.
