What are your true odds of hitting a royal flush?
By Henry Tamburin
Video poker gamers are perpetually hoping their subsequent hand will yield a royal flush, as a result of the payoff for a five-coin wager is a right away 4,000 cash. A Strictly Slots reader despatched a query concerning the participant’s probability of hitting a royal if a participant held three playing cards to the royal and drew two playing cards, or held two playing cards to the royal and drew three playing cards. We reached out to video poker professional, Henry Tamburin, to reply her query this month.
However earlier than we clarify that, have you ever puzzled what your chances are high of being dealt a three- or four-card royal on the preliminary deal? How a few five-card royal flush on the preliminary deal? The latter can be candy, and as you will note shortly, the percentages are lengthy—however not unattainable.
In Video Poker – Optimum Play by Dan Paymar, Desk 2 (web page 164) presents a abstract of Pre-Draw Fingers for 9/6 Jacks-or-Higher. I’ve condensed that info into Desk 1, displaying all doable palms you could be dealt that comprise wherever from zero to five playing cards towards a royal flush.
As you’ll be able to see within the desk, your probability of being dealt a five-card royal flush on the preliminary deal (RF5) is a minuscule 0.00015% (1 in 649,740). You would possibly assume that, with these lengthy odds, you’ll by no means be fortunate sufficient to be dealt a royal flush. Nevertheless, by no means say by no means. Two weeks in the past, I used to be dealt a 10-J-Ace-Q-Ok in spades on the deal for an immediate royal flush. It occurred rapidly as a result of I used to be taking part in quick. (I had the pace of the playing cards being dealt on the display screen on the quick setting.)
I knew one thing good occurred when the machine locked up and music began taking part in. My second dealt royal flush was much more memorable. I used to be displaying my father- in-law tips on how to play a Triple Play sport once I was dealt a royal flush on the underside hand (and naturally, I mechanically wound up with a royal on the second and third hand). I’m not writing about these two royal flushes to brag, however to make a degree: although the percentages are lengthy, getting a royal on the preliminary draw can occur to anybody at any time.
I’ll wager you didn’t know that after in each 2,777 palms you’ll expertise the fun of being dealt 4 playing cards to the royal. Furthermore, rather less than each 100 dealt palms (92 to be precise) you’ll have a threecard royal flush. However let’s get to the query raised by the reader: particularly, what are the probabilities of hitting a royal after I’m dealt an RF4, RF3, RF2 or RF1?
Suppose you might be dealt these five playing cards: A-Ok-Q-J-5, the place the first 4 playing cards are spades. Your coronary heart begins pumping whenever you notice you’ve a four-card royal flush. You maintain the four-card royal, say a fast prayer, and hope that you just get the ten of spades on the draw for the royal flush.
So what are your probabilities of getting the cardboard you want? When you consider it, video poker is performed with an ordinary deck of 52 playing cards (assuming you aren’t taking part in a joker-wild sport), and five of the 52 playing cards had been used on the preliminary draw. While you hit the draw button, you’re going to get one card from the 47 unplayed playing cards and, in fact, you’re hoping that card would be the 10 of the spades. Within the pile of 47 unplayed playing cards, there is just one 10 of spades. For those who draw that card, and solely that card, you’ll get a royal flush. If as a substitute, you draw any of the opposite 46 unplayed playing cards, you’ll not get the royal flush.
Due to this fact, the possibility of hitting the royal flush whenever you maintain a four-card royal flush and draw one card is 1 in 47. This implies for each 47 occasions you maintain 4 to the royal, on common you’ll hit the royal as soon as, and never hit the royal the opposite 46 occasions—however discover I stated “common,” that means you may hit multiple royal and even no royals after each cycle of 47 attracts.
Whereas I’m on this topic of 4 to the royal, let me carry up a technique level. Final night time whereas taking part in video poker, I used to be dealt this hand: 10-J-A-Ok-Q, the place each card was a diamond besides the Ace of hearts. In different phrases, I used to be dealt a paying five-card straight that additionally contained the four-card royal flush in diamonds. If I held all five playing cards, I’d have been paid $20 immediately for the five-card straight (greenback denomination machine).
Would you’ve taken the certain $20 payoff and held the straight? For those who answered sure, you’ll have made an enormous mistake. When you find yourself taking part in jacks-or-better and you might be dealt this hand, the play that has the upper anticipated worth is to carry the four-card royal flush, discard the fifth card, and draw one card and hope you get the cardboard you want for the royal flush.
Positive, more often than not you’ll come up empty handed on the draw, however the payoff on the one time you get the cardboard you want for the royal will greater than make up for the occasions that you just wound up with nothing. (BTW: After 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 purpose that in the end you’re going to get the cardboard you want whenever you draw one card to a four-card royal flush).
Now let’s suppose you might be dealt this hand: A-Ok-Q-6-3, the place the first three playing cards are spades and the opposite two playing cards are of a different swimsuit. Now what are your probabilities of drawing the 2 playing cards you want for the royal flush whenever you maintain three to the royal? Mathematically, there are 1,081 different palms that you could make whenever you maintain A-Ok-Q in spades and hit the draw button. Solely a kind of palms will lead to a royal flush; due to this fact, the possibility of hitting a royal whenever you maintain three playing cards to the royal is 1 in 1,081 (0.09%).
Desk 2 summarizes the probabilities of hitting a royal flush relying on what number of royal flush playing cards you maintain within the preliminary hand. Within the case of holding two playing cards to the royal (RF2) and drawing, you’ll hit the royal as soon as in each 16,215 tries. The possibility of getting a royal whenever you maintain just one excessive card (RF1) or no excessive playing cards (RF0) are slim however you would possibly get fortunate and beat these lengthy odds. My father-in-law was as soon as dealt five rubbish playing cards, correctly discarded all of them, and was dealt a royal flush on the draw… a 1-in-383,484 occasion.
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DON’T CHANGE STRATEGY ON MULTI-LINE VIDEO POKER
Follow single-line technique—even on Triple Play—or danger greater losses.
Many video poker gamers who play multi-line video games (resembling Triple Play) stray from the fundamental video poker taking part in technique for a single-line sport. That’s an enormous mistake. It’s best to at all times use the identical fundamental taking part in technique for a multi-line sport that you just use for a single- line sport. For those who don’t, you danger shedding extra money in the long term. In truth, you must decelerate your play on multi-line video games as a result of every error you make in taking part in technique is magnified because the variety of traces will increase. Although the taking part in technique doesn’t change, the quantity of bankroll you want will increase whenever you play multiple line.
For instance, for Triple Play, a rule of thumb is that you must have double the single-line bankroll.
