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The ins and outs of that most elusive of hands

What are the odds of getting a Royal Flush on a video poker game by holding two cards and drawing three to make the royal flush? From Laguna Niguel, California The number of ways to draw 3 cards out of the 47 remaining in the deck is combin (47,3)=16,215. One of those will be the three needed for a royal so the odds are 1 in 16,215. Straight flush hands that differ by suit alone, such as 7 ♦ 6 ♦ 5 ♦ 4 ♦ 3 ♦ and 7 ♠ 6 ♠ 5 ♠ 4 ♠ 3 ♠, are of equal rank. An ace-high straight flush, such as A ♦ K ♦ Q ♦ J ♦ 10 ♦, is called a royal flush or royal straight flush and is the best possible hand in high games when not using wild cards. The royal flush is the highest hand in poker. You need an Ace, a King, a Queen, a Jack and a 10. All the cards which make up the hand must be of the same suit. The order (from the highest to the lowest) of poker rankings is Royal Flush.

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.

Royal Flush Poker - Image Results

Royal Flush Poker Machine

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?

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.

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Royal Flush Poker Game

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.