The ins and outs of that most elusive of hands

1. Video Poker Royal Flush
2. Straight Flush Poker Hand
3. Flush Poker Hand

Five cards all of the same suit, but not in order, such as 4-6-9-J-A of spades. There is no primacy of suits; if two or more players have flushes, the player with the highest card in their flush wins. If those cards match, then the next highest card determines the winner and so on.

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?

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.

The odds of flopping a royal flush given two suited broadways → 0.005% or 1 in 19,600.

The Royal Flush is actually a type of straight flush. It is created when we hold T,J,Q,K,A all of the same suit.

To flop a Royal Flush, it is necessary to start the hand with precisely two suited cards between Ten and Ace. Regardless of which two of these cards, we hold the probability of flopping the straight flush will be the same.

This is because either way, we’ll need the flop to come down as three precise cards.

Odds of Making a Royal Flush on the Flop

Since there are exactly 19,600 different possible flops that can be dealt, the odds of flopping the Royal Flush are precisely 1 in 19,600. (To learn how the number of different flops can be calculated, check out the 888poker article on straight flush odds in poker.)
Odds of flopping the Royal Flush with two suited cards between Ten and Ace =

1/19,600 = 0.00005 or roughly 0.005%

Odds of Flopping the Royal Flush Straight Draw

Flopping the Royal Flush is virtually impossible. A slightly more likely possibility is that of flopping the Royal Flush straight draw.

We’d only need two specific cards to fall for this to be the case.

For example, imagine we hold the TdJd.

Flops that give us the Royal Flush draw with TJs

QdKdx (47 possible flops)
AdQdx (47 possible flops)
AdKdx (47 possible flops)

The third card can be any one of the remaining 48 cards left in the deck (aside from the card that actually gives us the straight flush.

This means 141 different possible flop combinations give us the straight flush (47 * 3).

Odds of flopping a straight flush draw with two suited cards between Ten and Ace = 141/19,600 = 0.0072 or roughly 0.72%.

That’s still less than 1% chance of flopping a Royal Flush draw even after starting out with a suited connector, but it is 141 times more likely than flopping the Royal Flush itself.

Similar logic can be applied to calculating the possibility of flopping straight flush draws when starting out with a suited connector. Although there are typically more ways to flop a straight flush draw than a Royal Flush draw.

For example, starting with T9s, there are 9 different ways of flopping a straight flush draw, making the probability three times more likely than flopping a Royal Flush draw with a holding such as QTs

Odds of Making the Royal Flush Postflop

There will be two primary types of Royal Flush draw we’ll flop. The gutshot Royal Flush draw and the open-ended Royal Flush draw.

Gutshot Royal Flush draws have 1 out in the deck, while open-ended Royal Flush draws have 2 outs in the deck.

Odds of Hitting on the Turn or River

Odds of catching the gutshot Royal Flush on the turn 1/47 = 0.0213 or roughly 2.1%

Odds of catching the open ended Royal Flush on the turn 2/47 = 0.426 or roughly 4.3%

Odds of catching the gutshot Royal Flush on the river 1/46 = 0.0217 or roughly 2.2%

Odds of catching the open-ended Royal Flush on the river 2/46 = 0.0435 or roughly 4.4%

Odds of Hitting by the River

To calculate the probability of hitting by the river, we’ll employ the trick of calculating the chance of not hitting and then subtracting from 100%.

Odds of not catching the gutshot Royal Flush on the turn 46/47

Odds of not catching the open-ended Royal Flush on the turn 45/47

Odds of not catching the gutshot Royal Flush on the river 45/46

Video Poker Royal Flush

Odds of not catching the open-ended Royal Flush on the river 44/46

Odds of not catching the gutshot Royal Flush on the turn or river = 46/47 * 45/46 = 0.9574 or roughly 95.7%

Straight Flush Poker Hand

Odds of not catching the open-ended Royal Flush on the turn or river = 45/47 * 44/46 = 0.9158 or roughly 91.6%

Odds of hitting the gutshot Royal Flush by the river = (100 - 95.7%) roughly 4.3%

Odds of hitting the open-ended Royal Flush by the river = (100 – 91.6%) roughly 8.4%

Implied Odds Analysis of a Royal Flush

A Royal Flush always carries excellent implied odds when hitting. This is because our opponent is usually forced into stacking off with very strong worse hands - such as worse flushes and full houses.

Royal Flushes made with two of our hole cards always carry better implied odds than straight flushes made with one of our hole cards. When using just one of our hole cards, it means there will be four cards to the Royal Flush already on the board.

This scenario decreases the chance that our opponent will pay us off with worse holdings. It will be impossible for our opponent to make the nut flush since the highest possible card of the correct suit makes the Royal Flush, and we hold it ourselves.

Basic Strategy Advice

Unless all five cards of the Royal Flush appear on the board itself, it is impossible to ever chop with the Royal Flush. It is always the best hand, and we should be looking to invest as much of our stack as possible (preferably all of it).

Flush Poker Hand