Texas Holdem Royal Flush Probability

4/1/2022by admin

Texas Holdem Royal Flush Probability Average ratng: 9,5/10 7384 votes

The probability of being dealt a royal flush is the number of royal flushes divided by the total number of poker hands. We now carry out the division and see that a royal flush is rare indeed. There is only a probability of 4/2,598,960 = 1/649,740 = 0.00015% of being dealt this hand.
The only way you could possibly make a straight flush is if your hand becomes: 8♥ 9♥ T♥ J♥ Q♥ 9♥ T♥ J♥ Q♥ K♥ 2). The only way you could possibly make a royal flush is if your hand becomes: T♥ J♥ Q♥ K♥ A♥ I'm having a difficult time in figuring the probability of this.
That doesn’t mean you should be playing any two cards, as the same odds apply for players with a higher hole cards. On a flush draw! Your chances of making a flush after the flop when on a flush draw are at 34.97%! It’s a great feeling when you’re on a flush draw on the flop, and one third of the times, you’ll make the hand!

Playing poker is about playing the odds. The following list gives the odds for outcomes in Texas Hold’em hands. When you realize how heavily the odds are stacked against you, you may want to rethink going all-in before the flop with two suited cards. Use the odds to your advantage:

1 percent (1-in-100): Percentage of time that no player holds an Ace or a King at a table in a 10-handed game
1 percent (1-in-100): Percentage of time that if you hold two suited cards, you’ll flop a flush
6 percent (about 1-in-20): Percentage of time that five community cards will give pocket suited cards a flush
6 percent (about 1-in-20): Percentage of time that you’ll be dealt a pocket pair
8 percent (about 1-in-12): Percentage of time that you’ll hit at least trips after having a pair on the flop
12 percent (about 1-in-8): Percentage of time that you’ll flop trips if holding a pocket pair
12 percent (about 1-in-8): Percentage of time that two more cards will flop in the same suit as a suited pocket pair
19 percent (about 1-in-5): Percentage of time that the five community cards will at least trip your pocket pair
32 percent (about 1-in-3): Percentage of time that you’ll pair one of your cards on the flop (with no pocket pair)
33 percent (about 1-in-3): Percentage of time that you’ll make a full house or better after having trips on the flop
35 percent (about 1-in-3): Percentage of time that you’ll make a flush on the turn or river if you have four cards to a flush after the flop

There are very few feelings in poker that beat the one of flopping quads or a straight flush. There you are, sitting with the absolute nuts and your only job is to figure out how to milk your opponents most money you can.

But if you’ve been playing poker for a little while, you’ve probably realized these rare hands don’t come around nearly as often as you’d like.

This is because the odds of being dealt a royal flush or other top-ranking hands are quite small. If you want to know more about exact numbers and the math behind rare hands in Texas Hold’em, keep on reading. Committing these facts to memory will probably make those rare occasions when you actually do manage to make one of these hands even more exciting and profitable.

Royal Flush (Straight Flush)

Six Plus Hold’em is an exciting and fun poker variant based on Texas Hold’em where the game is played with a deck of 36 cards as opposed to the usual 52 cards in traditional hold’em. Deuces through fives are removed from the deck giving the game its name Six Plus Hold’em/6+ or Short Deck Poker. In Texas Hold’em, a player makes the best 5 card hand from 7 cards available to them, 2 hole cards and the 5 cards that make up the board (flop, turn and river). To calculate the probability for being dealt a royal flush in ONLY 5 cards, we can fi.

A royal flush is essentially the best possible hand that you can get in poker, but it’s still just a straight flush. So the odds of being dealt a royal are exactly the same as being dealt any other straight flush. You just need to have two hole cards that can make a royal, i.e., anything between a 10 and an Ace.

In this article, we’ll focus on the instances where you’ve got to use both of your cards to make your straight flush since doing it with just one card is neither as rare nor as lucrative, as you’ll have a four-straight, four-flush board that most players will tread very lightly on.

For two cards to be able to make a straight flush on the flop, they need to be suited and connected. However, not all of the starting hands meeting these criteria have the same odds, as some of them have more options than the others. Below is the table showing chances of flopping a straight flush with different types of suited connectors.

Hand	Number of possible combos	Percentage
A2s	Just one (2-3-4)	0.005%
Suited connectors (i.e. 78s)	Four (4-5-6, 5-6-9, 6-9-10, 9-10-J)	0.02%
One-gappers (i.e. 68s)	Three (4-5-7, 5-7-9, 7-9-10)	0.015%
Two-gappers (i.e. 69s)	Two (5-7-8, 7-8-10)	0.001%

If you’ve been wondering why that straight flush never comes in when you decide to peel the flop with your suited connectors, the table above probably offers a bit of a new perspective. The odds of this happening, even with the best possible candidate, are very slim.

Making a Straight Flush on Turn or River

More often than flopping a straight flush, you’ll actually flop a straight flush draw. It will be either an open-ended draw (with two possible cards to complete it) or a gutshot draw where only one card from the whole deck can improve you to straight flush.

Once you do flop that draw, the odds of making the hand actually improve quite significantly, even though they’re still low.

Draw type	Chance to improve on the turn	Chance to improve by the river
Gutshot	2.1%	4.3%
Open-ender	4.3%	8.4%

So if you have an open-ended straight flush draw on the flop, you have decent odds of hitting by the river. If your opponents will let you and if you account for the implied odds when you do hit this highly unlikely hand, these types of draws are sometimes worth chasing.

Probability Of A Royal Flush In Texas Holdem

Quads (Four of a Kind)

Quads are another rare Hold’em hand although not nearly as rare as a straight flush. You’ve probably seen quite a few of these during your time playing poker and have had them at least once or twice yourself as well.

Once again, I’ll focus on odds of making quads when you are dealt a pocket pair as that’s the kind of quads you want to have and that you can extract some value from.

First of all, if you run the numbers, the overall odds of making quads with a random pocket pair if you were to just deal five cards (flop, turn, and river) are 0.816%. This is not a very useful stat, though, as you’ll rarely get to see all five cards unless you improve on the flop (i.e., flop a set).

Below are some more useful numbers.

Texas Holdem Royal Flush Odds

Odds of flopping quads	Odds of turning quads (after flopping a set)	Odds of getting quads by the river (after flopping a set)
0.245%	2.1%	4.3%

If you compare these numbers with the aforementioned ones for the straight flush, you can see why you’ve likely seen quads much more often than straight flushes.

And, if you were wondering what the odds are of flopping quads with just one card (i.e., when not holding a pocket pair), that would be 0.001%.

In Conclusion

Rare poker hands are at the top of hand strength charts for a reason. They’re very hard to get and when you do get them, you’ll almost always end up winning a pot. Even when you do lose with one of these hands, you might end up a winner as many cardrooms and casinos offer nice bad beat jackpots to tackle these precise scenarios.

Having seen these numbers, you’ll probably have a somewhat better idea of how (un)likely you are to be dealt a straight flush or quads during any individual session. Admittedly, this information won’t help you get any better in flopping royals. However, knowing the exact odds could save you a lot of money in the long run as you’ll know when to hold’em and when to fold’em.

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