CHASING THE BIG ONE
What are your true odds of hitting a royal flush?
By Henry Tamburin
Video poker players are forever hoping their next hand will yield a royal flush, because the payoff for a five-coin bet is an immediate 4,000 coins. A Strictly Slots reader sent a question about the player’s chance of hitting a royal if a player held three cards to the royal and drew two cards, or held two cards to the royal and drew three cards. We reached out to video poker expert, Henry Tamburin, to answer her question this month.
But before we explain that, have you wondered what your chances are of being dealt a three- or four-card royal on the initial deal? How about a five-card royal flush on the initial deal? The latter would be sweet, and as you will see shortly, the odds are long—but not impossible.
In Video Poker – Optimum Play by Dan Paymar, Table 2 (page 164) presents a summary of Pre-Draw Hands for 9/6 Jacks-or-Better. I’ve condensed that information into Table 1, showing all possible hands you might be dealt that contain anywhere from zero to five cards toward a royal flush.
As you can see in the table, your chance of being dealt a five-card royal flush on the initial deal (RF5) is a minuscule 0.00015% (1 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. Two weeks ago, 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 hand). I’m not writing about these two royal flushes to brag, but to make a point: even though the odds are long, getting a royal on the initial draw can happen to anyone at any time.
I’ll bet you didn’t know that once in every 2,777 hands you’ll experience the thrill of being dealt four cards to the royal. Moreover, a little less than every 100 dealt hands (92 to be exact) you’ll have a threecard royal flush. But let’s get to the question raised by the reader: namely, what are the chances of hitting a royal after I’m dealt an RF4, RF3, RF2 or RF1?
Suppose you are dealt these five cards: A-K-Q-J-5, where the first four cards are spades. Your heart starts pumping when you realize you have a four-card royal flush. You hold the four-card royal, say a quick prayer, and hope that you get the 10 of spades on the draw for the royal flush.
So what are your chances of getting the card you need? When you think about it, video poker is played with a standard deck of 52 cards (assuming you aren’t playing a joker-wild game), and five of the 52 cards were used on the initial draw. When you hit the draw button, you will get one card from the 47 unplayed cards and, of course, you’re hoping that card will be the 10 of the spades. In the pile of 47 unplayed cards, there is only one 10 of spades. If you draw that card, and only that card, you’ll get a royal flush. If instead, you draw any of the other 46 unplayed cards, you will not get the royal flush.
Therefore, the chance of hitting the royal flush when you hold a four-card royal flush and draw one card is 1 in 47. This means for every 47 times you hold four to the royal, on average you will hit the royal once, and not hit the royal the other 46 times—but notice I said “average,” meaning you could hit more than one royal or even no royals after every cycle of 47 draws.
While I’m on this subject of four to the royal, let me bring up a strategy point. Last night while playing video poker, I was dealt this hand: 10-J-A-K-Q, where every card was a diamond except the Ace of hearts. In other words, I was dealt a paying five-card straight that also contained the four-card royal flush in diamonds. If I held all five cards, I would have been paid $20 instantly for the five-card straight (dollar denomination machine).
Would you have taken the sure $20 payoff and held the straight? If you answered yes, you would have made a big mistake. When you are playing jacks-or-better and you are dealt this hand, the play that has the higher expected value is to hold the four-card royal flush, discard the fifth card, and draw one card and hope you get the card you need for the royal flush.
Sure, most of the time you will come up empty handed on the draw, but the payoff on the one time you get the card you need for the royal will more than make up for the times that you wound up with nothing. (BTW: When I hit the draw button, the Ace of hearts disappeared and up popped the Ace of diamonds, a 1-in-47 shot, for a $4K royal flush— proving the point that sooner or later you will get the card you need when you draw one card to a four-card royal flush).
Now let’s suppose you are dealt this hand: A-K-Q-6-3, where the first three cards are spades and the other two cards are of a different suit. Now what are your chances of drawing the two cards you need for the royal flush when you hold three to the royal? Mathematically, there are 1,081 different hands that you can make when you hold A-K-Q in spades and hit the draw button. Only one of those hands will result in a royal flush; therefore, the chance of hitting a royal when you hold three cards to the royal is 1 in 1,081 (0.09%).
Table 2 summarizes the chances of hitting a royal flush depending on how many royal flush cards you hold in the initial hand. In the case of holding two cards to the royal (RF2) and drawing, you’ll hit the royal once in every 16,215 tries. The chance of getting a royal when you hold only one high card (RF1) or no high cards (RF0) are slim but you might get lucky and beat those long odds. My father-in-law was once dealt five garbage cards, properly discarded all of them, and was dealt a royal flush on the draw… a 1-in-383,484 event.
QUICK TIP
DON’T CHANGE STRATEGY ON MULTI-LINE VIDEO POKER
Stick to single-line strategy—even on Triple Play—or risk bigger losses.
Many video poker players who play multi-line games (such as Triple Play) stray from the basic video poker playing strategy for a single-line game. That’s a big mistake. You should always use the same basic playing strategy for a multi-line game that you use for a single- line game. If you don’t, you risk losing more money in the long run. In fact, you should slow down your play on multi-line games because each error you make in playing strategy is magnified as the number of lines increases. Even though the playing strategy doesn’t change, the amount of bankroll you need increases when you play more than one line.
For example, for Triple Play, a rule of thumb is that you should have double the single-line bankroll.
