It goes without saying that three-of-a-kind does not beat a straight in poker. It has to do with math and hand rankings. Less common is a straight, five consecutive cards (like 5♠ 6♥ 7♦ 8♣9 ♠), which only accounts for 10,200 = \binom{4}{1}^{5} in a deck of cards. On the other hand, three-of-a-kind has 54,912 combinations, which are more probable to be made. Thus, making the straight a more rare hand. This makes straights the superior hands when it comes to Texas Hold’em, with players having a 4.62% chance of landing one compared to three-of-a-kind which is at around 4.83%.
Three-of-a-Kind vs. Straight
Many people, when they hear three-of-a-kind and see a straight, may presume ‘Well, five cards in order has to be weaker than three of the same card, correct?’. Three separate instances of the same card, this seems like it should be impossible, right? However, the straight is really the one that comes out ahead — and figures never lie.
Let’s break it down. What are the chances of hitting a straight? From a standard 52-card deck, there are only 10,200 ways to make straights. Sounds like a lot, right? However, stack it up against three-of-a-kind, of which there are 54,912 possible combinations, and all at once our straight doesn’t seem quite as impressive. All but a fifth as common actually. How come straights beat three-of-a-kind in poker rankings?
A buddy of mine, I recall, lost multiple hundred greenbacks betting for or against the Yankees to win that series. He had trips, still the most arrogant person in this world, thinking HE won. Later, his opponent turned over a straight, and he just went like ohhhh. Oh, and I CANNOT BELIEVE I LOST TO A STRAIGHT! Well, believe it. The fact is that straights are just more powerful — mathematically.
The probabilities of getting three-of-a-kind from the seven cards are at 4.83%, and hitting a straight is only 4.62%. Sure, while they are quite close, Hold’em wins out when it comes to the straight, and that makes straights a bit tougher to attain, hence them holding more power in rankings.
Now, imagine experiencing the following: you are sitting at a card table with an impressive threesome, grasping, believing that it is a winning hand. A moment later, however, the lone opponent tables a seven-high straight. What do you do? Some things, you just got to learn — straight beats three-of-a-kind; and although your hand may look really pretty before the flop…
Why Is a Straight Stronger Than Three-of-a-Kind
Alright, why the hell would a straight beat three-of-a-kind? I understand — it sounds strange at first. Three-of-a-kind sounds pretty strong, right? But the true answer is in math and usage.
Consider, for example, the ranking of poker hands. As in poker, the more difficult hand to make beats an easier one. It’s not just how badass or classy your hand looks but rather how uncommon it is. And guess what? Straights are so rare that three-of-a-kind beats one.
The truth of the matter is, there are 10,200 ways a straight can be made in a typical 52-deck card. These are fewer than the 54,912 ways to make three-of-a-kind. And that is why they rank higher. In poker, rarity matters, which is why straights beat three-of-a-kind: Straights don’t come that often (% of hands) as Trips do!
Well, the obvious response to that might be “But it seems like straights are everywhere at all these events!” Yeah, okay, true, in some games that may feel like it — but over the long term, real straights are more uncommon. I recall one poker night where a guy hailed his three-of-a-kind as the ultimate winner before he was pipped by an underdog straight. As unlikely as that sounds, it is the rules… and the math supports this.
You have a 4.62% chance of making an open-ended straight from seven cards in Texas Hold’em. This comes with a 4.83% chance of three-of-a-kind. Though the numbers are close, that slight gap is enough to vault straights up on rankings. And as we know in poker, even the tiniest of odds can turn into a big difference.
Frequency of Straight and Three-of-a-Kind in Poker
Well, let us just take a look at some numbers since in poker, more matters. Knowing how often those hands appear can significantly change the manner in which you play and even help make your decisions at the table better.
Let’s start with straights. A straight, which as you might know, is 5 cards in a row. What are the odds to hit a straight in 52-card play? There are 10,200 different combinations. They are much rarer when compared to the whole spectrum of possible poker hands.
Three-of-a-kind is almost the opposite, though. There are 54,912 possible ways to create a three-of-a-kind hand, which is over 5 times the amount of combos as a straight. This large frequency discrepancy is the reason why straights always outrank flushes on a poker hand chart. Less common = more valuable.
I just can remember one time where a buddy of mine was sure he had the best possible three-of-a-kind, and lost to a straight. He couldn’t believe it and thought he got a bad beat. The reality of the situation was, he hadn’t accounted for how often those hands came. Straights are only so frequent, and thus stronger when they appear.
How to Recognize a Straight and Three-of-a-Kind
The difference between a straight and three-of-a-kind is the most vital distinction to understand when learning poker. Both of these hands are strong, and to prepare you for that, I am hereby explaining the formation behind each hand.
The straight was unremarkable. A straight consists of five connected cards. For example, 5-6-7-8-9. The important part? They do not have to be the same type of card. A straight can be of different suits, as long the cards are in a sequence. For instance, 7♥ 8♠ 9♦ 10♣ J♠ is a straight. Easy, right? That’s essentially a straight of five cards.
The trick is to get the order correct. If you’re ever stumped, just look for all five consecutive cards, irrespective of suit. One of the toughest things about straights is that they can be semi-deceptive, especially when so many cards are spread out on the board.
Now, onto three-of-a-kind. This one is a bit easier to catch. Three-of-a-kind is a hand where you have three cards of the same type. For example, if you have three 8s, so the 8♣. Then the full one is really easy. It’s that straightforward. Unless the other two cards in front of you aren’t forming specific combinations such as a full house (3-of-a-kind plus a pair).
I have seen people in the game landlocked on a straight when it was really broken or run with their thinking that three-of-a-kind is underwhelming. Always double-check your cards. Straights running five cards are always straights, anything below that and they weren’t even close to it. A three-of-a-kind is simply when you have a set of matching cards – no excuses.
Leveraging the Power of a Straight
As it pertains to poker, an understanding of what a straight can do for you gives serious competitive edge. While hands such as a broadway outside straight can get you paid, there are much more effective ways of utilizing our equity with the solid hand that is an open-ended straight!
Well, to begin with, you need to realize that there are fewer hands where straights can be made compared to another hand like… three-of-a-kind. This means that even when you do hit one, the odds are good so you are usually a huge favorite to win it, but don’t be too results-oriented. You need to know when to bet big and when to go stealthy. It can be difficult not to have your straight-card value face up, especially if there’s been no strength shown on the community cards. Take the opportunity to surprise them and squeeze as much value out of this deal as you can.
But timing is everything. If the straight is out there, such as if the board comes with five cards in sequence, other players might wonder whether you have it. Well, in that case, you’ll need to play it smart. Your first raise shouldn’t scare everyone off — you’re trying to build the pot without tipping them off that you have a monster hand. Another tactic is to be choosy, take it easy in the beginning, and save your hand for when you need a home run.
Keep in mind that straights are always weak to hands like flushes or full houses. Therefore, while a straight is strong, it’s not invincible. Once the board grows those big hands, you have to think twice about where your set is at. If you consider someone else has the flush, slow down, do not risk too much.
Players make the same mistake with straights; they can be over-confident and power cards home to find themselves beaten by a full house or flush. Don’t fall into that trap. Beep-boop: Play your straight like it was always coming, but be wary of the board.