What are your Odds of getting a Video Poker Royal Flush?

Video Poker Odds Royal Flush

Once in every 92 hands, on average, you’ll be dealt a three-card royal flush (about 7-8 per hour). This is what makes video poker exciting; namely, that you’ll have several opportunities to draw for a royal flush even if the odds are somewhat long (see next question). A Royal Flush is a poker hand made out of 10, Jack, Queen, King, Ace, all of the same suit. It is the best out of all the poker hands that can be created in a standard game of poker. And don’t try to hit that royal flush every time you get dealt a face card, as the odds of hitting it are 1 in 40,000. Stick to the video poker strategies, as they will give you the best chance at a big payday. Also, just because the odds say you should get a royal flush every 40,390 hands doesn't mean it's guaranteed. You could go five times that many hands and never hit one, or get five in the first hundred hands. Both scenarios are improbable, yet quite possible. Such is the allure of chance. For the 1 in 2,777 times that you'll be dealt four royal flush cards, you have 1 in 47 odds of grabbing video poker's largest payout. The reason why it's a 1-in-47 chance is because five cards have already been dealt, and one of the remaining 47 cards (standard 52-card deck) will net you the jackpot.

While there are lots of nice payouts available in video poker games, most players have their minds fixated one one specific hand: the royal flush. The amount of money you win for a typical royal flush differs depending upon the specific game; but a standard, non-progressive 9/6 Jacks or Better game will pay 4,000 coins - or $5,000 on a 5-coin ($1.25) wager.

Obviously anybody would be thrilled to win this kind of cash with a single video poker hand. But as you may have guessed, royal flushes don't come around very often when compared to other hands. In fact, let's take a look at your exact chances of hitting a royal on any single hand.

Long Shot

Using the aforementioned Jacks or Better game as an example, your odds of being dealt a royal flush right away are 1 in 649,740, or a 0.00015% chance. Sure this isn't very good, but remember that these odds are before you start discarding/drawing cards. So it's also worth looking at your chances of being dealt each component of a royal, which you can see below:

Getting a royal flush = 1 in 649,740 odds
Starting with 4 royal flush cards = 1 in 2,777
3 RFCs = 1 in 92
2 RFCs = 1 in 13
1 RFC = 1 in 6

Drawing to a Royal

We just discussed how players can receive certain parts of a royal flush and improve their opportunities of getting video poker's best hand. And by now you may be wondering exactly what the odds are of hitting a royal flush payout based on the number of royal cards you have. Well here are the odds of this happening based on each situation:

Drawing from 4 RFCs = 1 in 47 odds
Drawing from 3 RFCs = 1 in 1,081
Drawing from 2 RFCs = 1 in 16,215
Drawing from 1 RFC = 1 in 178,365
Drawing from 0 RFCs = 1 in 383,484

For the 1 in 2,777 times that you'll be dealt four royal flush cards, you have 1 in 47 odds of grabbing video poker's largest payout. The reason why it's a 1-in-47 chance is because five cards have already been dealt, and one of the remaining 47 cards (standard 52-card deck) will net you the jackpot.

Beating the Odds

No matter how you slice it, getting a royal flush isn't exactly easy. Even with four cards to a royal, you're still praying for good luck. However, it's important to understand that these odds only represent the long-term cycle (based on hundreds of thousands of hands) that video poker games go through.

Many players have beaten these odds and earned a royal flush in much less time. So the point is that while some people will never get the game's highest hand, there's always a chance that it will happen.

Other Casino Guide

American Roulette Bad Casino Bets Blackjack Myths Blackjack side Bets Blackjack Table Pick Blackjack or Video Poker Casino Bonuses Tips Casino Freerolls Casino Games Tips Casino Tricks Casino Trip Craps Strategy Free Spins Fruit Machines Online Slots Features Roulette Bets Type Roulette Games Roulette Systems Slots Payout Slots Tournaments Strategy Superstitons Video Poker Royal Flush

The ins and outs of that most elusive of hands

By Henry Tamburin

I get many questions about a royal flush in video poker. That’s not too surprising since the royal flush is the premier hand that all video poker players dream (and hope) of getting. Here’s a sample of questions and my responses.

Q: I’ve been playing video poker several times a week for over a year. You keep saying that a royal flush occurs once in every 40,000 hands yet I still haven’t gotten a royal. What gives?

Firstly, I never wrote that you could expect one royal flush after playing 40,000 hands (or one cycle). What I wrote was, “On average, you will hit a royal flush once in every 40,000 hands.” The word “average” means a whole bunch of sets of 40,000 hands. In other words, in any given set of 40,000 hands, you could hit more than one royal flush or, heaven forbid, possibly no royals. In fact, you have a 36.8% chance that you won’t get a royal in one cycle (40,000 hands), and a 13.5% chance after two cycles (80,000 hands). Ouch! Therefore, the fact that you went over a year without a royal is statistically possible.

Q: How come every time I need one card for a royal flush, it never shows up, but that exact card that I needed always seems to show up on the very next hand?

That’s because you have “selective memory.” The computer program in the video poker machine that randomly selects the cards for each hand doesn’t use the information from previous hands to determine which cards it will deal. Every hand is a random deal regardless of what cards appeared (or didn’t appear) on the previous hand.

Q: Over three years, I hit seven royal flushes in the same casino and none in two other casinos that I play regularly. I’m beginning to believe those casinos somehow tighten their video poker machines so players can’t get a royal.

You will average one royal flush per roughly every 40,000 hands at any casino. Casinos can’t change the odds of hitting a royal flush. (What they can do is change the payout … some casinos will pay less than 4,000 coins for a royal flush; therefore, always check to be sure that the payout for a five-coin royal flush is 4000 coins.) The bottom line is as long as the pay schedule is the same for a particular video poker game, the odds of getting a royal flush will be the same no matter where the machine is located (assuming a random deal).

Q: I’ve been dealt many three- and four-card royal flushes lately. What are the odds of this happening?

Playing Jacks or Better, you’ll experience the thrill of being dealt a four-card royal flush once in every 2,777 hands (roughly once every four hours on average). Once in every 92 hands, on average, you’ll be dealt a three-card royal flush (about 7-8 per hour). This is what makes video poker exciting; namely, that you’ll have several opportunities to draw for a royal flush even if the odds are somewhat long (see next question).

Q: When you hold three cards to the royal flush, what is the chance of getting the two cards that you need on the draw for a royal flush?

You have a one in 1,081 chance of getting the two cards you need for the royal flush. The following table shows the chance of hitting the royal flush on the draw when you hold x cards to the royal flush.

Q: If I’m dealt a three-card royal flush and a high pair in the same hand, why does the strategy say to hold the high pair when the royal flush pays so much more?

You need to analyze all the possible winning hands that you could get when you hold a three-card royal flush vs. when you hold a high pair in the same hand. These calculations have already been done for you. For example, suppose your initial hand contains 10-J-Q of diamonds along with a queen of clubs. The expected return (ER) for holding the pair of queens is 7.6827 vs. 7.4098 for holding the three-card royal flush (this is for 9/6 Jacks or Better). In dollars and cents, you’d earn 27 cents more on average for a max coin wager on a dollar denomination machine by holding the high pair vs. the three-card royal flush in this example.

Q: My wife plays Jacks or Better. The other day she was a dealt a hand that contained a four-card straight flush with a gap and a three-card royal flush. She held the three-card royal flush. Was that the correct play?

I’m sorry to say it wasn’t. The correct play was to hold the four-card straight flush—even with a gap—over the three-card royal flush. (Tip: If your wife had a strategy card with her, she would have made the right play.)

Q: What are the odds of being dealt a royal flush in the initial hand?

The odds are one in 649,740 hands. You might think that’s close to impossible but it could happen. (This happened to me once while I was showing my father-in-law how to play a Triple Line video poker game in a Las Vegas casino, resulting in a royal flush on each line. How’s that for luck?)

Q: How much does the royal flush contribute to the 99.54% return for 9/6 Jacks or Better?

The royal flush contributes 1.9807% toward the overall 99.64% return. The following table summarizes the contribution of each winning hand toward the overall 99.54% return (for 9/6 Jacks or Better). When you don’t hit the royal or straight flush, the best return you can expect, even playing perfectly, is about 97%.

Got a video poker question? Send it to HTamburin@aol.com.

Tamburin’s Tip of the Month

You are playing NSU Deuces Wild. How would you play these hands that don’t contain a deuce?

Video Poker Royal Flush Odds

In the top hand, your best play is to hold the consecutive three-card straight flush 6-7-8 (2.77 ER) over the four card straight 5-6-7-8 (2.55 ER). In the bottom hand, because the three-card straight flush has a gap (2.47 ER) your best play is to hold the consecutive four-card straight 4-5-6-7. When you play NSU Deuces Wild and your initial hand doesn’t contain a deuce, you should hold a consecutive three-card straight flush (5-6-7 through 9-10-J) over a consecutive four-card straight (from 4-5-6-7 to 10-J-Q-K), but the latter over a three-card straight flush with one or two gaps.

————————————————————————————————————-

Henry Tamburin is a blackjack and video poker expert. He is the host of the smartgaming.com website and the editor of the Blackjack Insider newsletter (for a free three-month subscription, visit www.bjinsider.com/freetrial). For a free copy of his Casino Gambling Catalog, which contains books, strategy cards, and software for video poker players, call toll free 1-888-353-3234, or visit the web store at smartgaming.com.