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)
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.
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.
| 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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