For a royal flush, that is the question
By Jerry “Stickman” Stich
As a gambling writer, everything you commit to print is subject to review, interpretation and opinions of the readers. In a previous Casino Player article I noted that it had been a very long time since my last royal flush while playing video poker. Also, as regular readers know, each of the monthly Casino Player articles I write contains a section where readers can test their skill at video poker play with few sample hands. A recent article contained the following hand in the “How Would You Play These Hands” section. The specified game was full pay (9/6) Jacks or Better and is shown below.
This hand contains three cards of a royal flush, four cards of a flush with two high cards, and four cards of an inside straight. A few years earlier I showed a very similar hand. In that article I used a more basic strategy which stated the proper hold would be the three cards of the royal flush.
I was immediately called to task by several observant readers who stated I was wrong.
I was wrong. They were right.
That is why the recent article using the above hand stated that the proper hold was the four cards of a flush.
Here are the specifics assuming a five credit bet on a full pay (9/6) Jacks or Better game.
Saving the three cards of a royal flush returns 6.346 credits on average.
Saving the four cards of a flush with two high cards returns 6.383 credits on average. Notice that the difference is only .037 credits. The small difference is why in the “basic” strategy all three card royal flushes were lumped together above four cards of a flush. The difference in return was so small that is was not worth adding another line to the strategy chart.
To put the strategy into a narrative, the proper play is to hold three cards of a royal flush before holding four of a flush—UNLESS— the three cards of a royal flush are an ace, 10 and a high card (jack, queen, or king)—AND— there are two penalties (straight or flush)— AND—the flush has two high cards. This hand has an ace, 10 and king. There is a flush penalty (the 3 of hearts) and a straight penalty (the jack of clubs). The flush also has two high cards (the ace and king of hearts). So while it is only by a very small margin that the flush hold is correct, and this situation does not happen very often at all, it is still the proper hold. This hold will return more to the player over time than saving for the royal flush.
The reader commented that he and his wife always save for the royal flush and surmised most video poker players would do the same (he could very well be correct). He went on to state that even though the proper hold might return a bit more in the long run, it comes at the cost of shots at a royal flush. He stated the he and his wife were quite successful using the “basic” strategy play of always holding three cards of a royal flush over four cards of a flush. In fact, he stated, they got seven royals in the last year with their strategy. He went on to imply that this minor difference in strategy could be the reason for my dearth of royals that I had mentioned in a different article.
It is true that saving the four cards of a flush eliminates any possibility of getting a royal flush. However, by saving three cards of a royal flush, there is only a one in 1,081 chance of actually hitting that royal flush. Over those same 1,081 hands, saving the four cards of a flush would return an additional 40 credits or eight addition hands in which to try for a royal flush or other paying hand. The particular combination of cards that call for saving four cards of a flush over three cards of a royal flush are not dealt all that often. This means that even though there is a very small increase in the occurrence of a royal flush when always holding three cards of a royal flush, this strategy does not give the player enough to make it a profitable play. In full-pay Jacks or Better the player will lose a bit more by always saving three cards of a royal flush over four cards of a flush. And, it certainly does not explain a very long drought in royals versus getting seven royal flushes in a year. That is the result of randomness.
Please note that this playing strategy is valid for 9/6 and 8/6 Jacks or Better. The 9/5 or 8/5 versions of the game have the player hold ANY three cards of a royal flush over four cards of a flush. If the reader who wrote in was playing either of the games paying 5-for-1 for a flush, always holding three cards of a royal flush over four cards of a flush is the proper play.
The bottom line is maximizing profit (or limiting loss). The number of royal flushes will ultimately balance out. For example, consider my situation with royal flushes (actually the lack of them). Here is an update. The floodgates have opened. In the last couple of months (over the course of about 13,250 hands), I have snagged four royals. That gives me a total of five (counting the last royal before the drought) royal flushes in the last approximately 223,000 hands. This works out to one royal flush for every 44,000 hands. That is very close to the mathematical average of one per approximately every 40,390 hands. With more play, I am confident the average will ultimately become even closer to the mathematical average. The math always wins out. It may just take a while for it to happen.