Let’s face it. What all video poker players hope (and pray) for is that the next hand will give them a royal flush because that results in an immediate 4,000 coin payoff. But did you ever wonder what the chance that this will happen when you hold, say, four cards to a royal flush?  How about holding three cards to a royal?  And what is the chance of being dealt a royal flush on the initial deal? I’ve summarized the answers to these questions below and they may surprise you.

Note: There are many different video poker games but by way of example, I’m going to focus solely on Jacks or Better in this article. Also, keep in mind that a high card in video poker is a Jack, Queen, King, and Ace (a ten is considered a low card).

First off, it’s important that you understand how the cards are dealt in video poker. Even though there isn’t a casino dealer dealing the cards, a computer chip that resides inside the video poker machine simulates what a live dealer would do if she were dealing the cards. It works like this.

A standard 52-card deck is shuffled and when a player hits the deal button on the machine, the shuffling stops and five random cards are dealt to the player (i.e., these are the five cards that appear on the video poker screen on the initial deal.) While the player decides which cards he wants to keep (or hold), and which he wants to discard for replacement cards, the remaining 47 unplayed cards are shuffled. Let’s assume a player decides to hold the first four cards on the screen and discard the fifth card. He hits the hold button beneath each of the four cards that he wants to keep and then hits the draw button. The fifth card is removed and a single, randomly selected replacement card (from the shuffled 47 unplayed cards) is dealt to the player, which completes his hand. The key points to remember are this:

• Video poker plays like a five-card draw poker game. You get one opportunity to improve your poker hand.
• The card(s) in your initial hand that you discard can’t appear again on the secondary draw.
• Once the hand is completed, all the cards are reshuffled for the next hand.

OK, let’s now look at the facts on what your chances are to hit a royal flush depending upon how many cards to a royal flush you were dealt in your initial hand.

(Note: I’m going to assume a player is playing at a leisurely pace of 600 hands per hour for the examples that follow. Moreover, the data on the odds of hitting a royal came from Dan Paymar’s book, Video Poker – Optimum Play (second edition)

ON THE INITIAL DEAL

Your chance of being dealt a five-card royal flush on the initial deal is a minuscule 0.00015 percent (or 1 chance in 649,740). You might think that with those long odds, you’ll never be lucky enough to be dealt a royal flush. However, never say never.

Once I was dealt a 10-J-Ace-Q-K in spades on the deal for an instant royal flush. It happened quickly because I was playing fast. (I had the speed of the cards being dealt on the screen on the fast setting). I knew something good happened when the machine locked up and music started playing. My second dealt royal flush was even more memorable. I was showing my father-in-law how to play a Triple Play game when I was dealt a royal flush on the bottom hand (and of course, I automatically wound up with a royal on the second and third hands). As I said earlier, never say never.

## ON THE DRAW AFTER DISCARDING ALL FIVE CARDS

If you are holding five “garbage” cards and discard all of them for five new ones, the chance that it will result in a royal flush is 1 in 383,484. Although this has never happened to me, it happened once when my father-in-law tossed away all of his initial five cards and was dealt a royal flush. (Again, even though the odds are long, never say never!)

## FOUR CARDS TO THE ROYAL FLUSH

Lucky you if you were dealt four cards to the royal flush right off the bat. This doesn’t occur very often: on average once every 2,777 hands (about once every 4.5 half hours of play). However, every time you are dealt four cards to the royal flush, the chance you will get the one card you need for a royal on the draw is a relatively measly 1 in 47.

Note: Coincidentally, during my last five-hour playing session prior to writing this article, I was dealt four cards to the royal flush a surprisingly five times. This is about six times more than what I should have statistically received during five hours of play.  Did I luck out and hit the royal flush at least once? Keep reading for the surprising result.

## THREE CARDS TO THE ROYAL FLUSH

You’ll be dealt three cards to a royal flush once in every 92 hands, on average, (or about 13 times every two hours), Unlike the 1 in 47 chance above, now the chance of hitting a royal flush, when holding only three cards to the royal, is 1 in 1,081.

Note: Now for the rest of the story of my recent playing session, After being dealt four cards to the royal flush five times, and coming up empty handed each time, I was dealt (for the first time) three cards to the royal. And, as you probably guessed it, I held the three cards to the royal, hit the draw button, and up popped the two cards I needed for the royal flush. As I said earlier, never say never.

Sidebar: I wrote an article previously about my very long royal flush drought. The above royal flush finally ended my drought, which lasted 22 months and approximate 310,000 hands since my previous royal.  I’ll discuss how to survive long royal flush droughts in a future article.

## TWO CARDS TO THE ROYAL FLUSH

You can expect to be dealt a two-card royal flush once in every 13 hands on average (or about 46 times per hour). Even though the frequency of being dealt a two-card royal is great, the odds of drawing a royal from it are long:  one in 16,215. (However, I remember twice in my playing career converting a hand containing two cards to the royal into a royal flush so I’ll say it again, never say never.)

## ONE CARD TO THE ROYAL FLUSH

You’ll average being dealt only one high card on the deal about 100 times per hour. Far fetch as it may seem, it’s possible to hold one single high card, hit the draw button, and be dealt the other four cards you need for a royal flush. But don’t count on this happening very often because the odds are 1 in 178,365. (I can only recollect one-time holding a single high card and being dealt the other four cards I needed for a royal flush.)

The following table summarizes the above; namely, the odds and frequency of being dealt the cards you need for a royal flush on the initial deal, and what your chances are of converting the initial hand into that glorious royal flush. Good luck!

Initial  Hand     Chance in % Which Equals: Frequency* Chance of Getting RF
RF5 0.00015 1 in 649,740 1 per 1083 hours Got it!
RF4 0.036

1 in 2,777 1 per 46 hours 1 in 47
RF3 1.09 1 in 92 13  in 2 hours 1 in 1,081
RF2 7.7 1 in 13 46 per hour 1 in 16,125
RF1 16.7 1 in 6 100 per hour 1 in 178,365