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Why Can’t I Get A Royal Flush?

Thousands of hands played. Thousands more to go.

By Jerry “Stickman” Stich

 

I received an email recently from someone bemoaning the fact that he never had a royal flush even though he had played video poker for many years. His story went something like this:

 

I play video poker a lot and I always look for the machines with the best return when I play. I have friends that play all day and almost every day. I have never had a non-wild royal flush in 40 years of play. Some of my friends have one now and then.

 

A royal flush is usually the most prized hand in video poker although there are some games where other hands pay as much and sometimes even more. For most of the common video poker varieties the royal flush will appear once in about 40,000 to 48,000 hands. In some games the royal flush appears only once in about 352,000 hands (pick‘em poker). What does the 40,000 to 48,000 number actually mean?

It means that in the “long term” you can expect a royal once in every 40,000 to 48,000 hands. But what is the long term? It is millions and millions of hands.

I was unable to get additional information from this individual as to how much he plays. Information such as the number of sessions played in a year, the average length of a session and the speed of play all are important in determining how many hands have been played.

I track several items when I play video poker in a casino including number of hands played. I do this by writing down the starting slot club point balance. I also determine the amount of play required per point and calculate the number of points per hand. Sometimes it is a fraction of a point. Then at the end of a session I again note the slot club point balance. By subtracting the starting points from the ending points and dividing by the points per hand, the result is the number of hands played. With this information I can track the number hands I have played since my last royal flush.

Let’s look at the length of play required. For the following discussion I will use 40,000 hands as the average number of hands between royal flushes.

Most people to whom I have talked are totally unaware of how long it takes to play 40,000 hands of video poker. Playing at a relatively fast 500 hands per hour, it takes 80 hours of play to reach the 40,000 hand mark. At four hours per day it would take 20 days to achieve the mark. That means 20 one-day trips, 10 two-day trips or five four-day trips.

However, most people don’t play 500 hands per hour. Most are closer to 200. At that rate it will take 200 hours to play 40,000 hands. Using the previous examples, it takes 50 days at four hours of play each day to reach 40,000 hands. It takes 100 days at two hours of play per day and 200 days at one hour of play per day to reach 40,000 hands. That is more than half a year of play. Spread that out over 40 years and it averages out to five hours of play per year. It is certainly within the realm of possibility that he only played this much over the 40 years.

Remember, 40,000 hands between royal flushes is an average. The problem with this average, however, is it is just that; an average. It means that on any given hand there is a one in 40,000 chance the player will get a royal flush. That average is spread out over millions and millions of hands played. Though not very likely, it is possible to get two royal flushes in a row. Looking at the opposite end of randomness it is also possible to not receive a royal flush for 100,000, 200,000 or even 500,000 hands. That is how it goes in a random game. Virtually no one ever gets two royal flushes in a row, but they also don’t go 500,000 hands without a royal flush.

The vast majority of video poker players get a royal within three to four normal “royal cycles.” This means for our example of 40,000 hands between royals, a royal will appear within 120,000 to 160,000 hands. Since I have been keeping records my longest period between royal flushes has been 126,000 hands. On the other end, I also got three royals in about 26,000 hands. All things balance out over time if you play enough.

If our player above played 15 hours of video poker per year at 200 hands per hour, he has played 120,000 hands. He is still well within the “normal” distribution.

All we do know is if he keeps playing, that elusive royal flush will occur sometime, so keep the faith.

 

Video Poker Strategy: How Would You Play These Hands?

Let’s look at a couple of hands with a potential for a royal flush. Playing a full-pay Jacks or Better game with max credits of 5, you are dealt:

 

A♣ Q♣ J♣ J♦ 6♠

 

Would you go for the royal flush by saving the A♣ Q♣ J♣? Or would you take the sure thing and save the two Jacks?

Going for the royal flush you have one chance to hit the jackpot. There are also 675 chances out of 1,081 possible draws that you will get nothing.

Keeping the pair of jacks, you are guaranteed even money. This will happen in 11,559 out of a possible 16,215 draws. But there are also 2,592 chances to get two pairs paying 2-for-1, 1,854 chances for a three-of-a-kind paying 3-for-1, 165 chances for a full house paying 9-for-1, and 45 chances for four-of-a-kind paying 25-for-1.

The average return for saving three of a royal flush in this case is 6.96 per five credits played versus 7.68 when saving the pair of jacks. Saving the jacks is easily way to go.

Let’s look at one more hand. Playing the same game with max credits you are dealt a very similar hand: A♣ Q♣ T♣ J♦ 6♣

What would you do? There are three cards of a royal, four of a flush and four of a straight. Would you save the three of a royal or is there a better option?

Saving the four of a straight is a very weak play returning only 2.66 per five credits played. The problem here is there are only 47 possible draws and only two possible results—jacks or better at even money and a straight at 4-for-1.

Saving three of the royal gives 1,081 possible draws with opportunities for jacks or better, two pairs, three-of-a-kinds, straights, flushes and the ultimate draw—the royal flush. The average return for this save is 6.35 per five credits played.

By saving four of a flush you are also limited to only 47 possible draws with jacks or better or a flush as the only two possible ways to not lose this bet. Due to the higher pay for a flush over a straight (6-for-1 instead of 4-for-1), the return for saving four of a flush is 6.38 per five credits played. It is a very close call, but saving for of a flush is the best save for this hand.

Is that how you would have played them?

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