The top hands listed in the standard poker hand rankings occur very rarely in the game. The less likely the probability of making a certain hand, the higher that hand ranks in a game of poker.
Which of these monster hands wins when they go head-to-head? Does a straight flush beat four-of-a-kind?
The short answer is yes, but why does a straight flush beat four-of-a-kind? The poker hand rankings come down to probabilities, so let’s take a look at the math behind these two very strong hands:
Why Does a Straight Flush Beat Four of a Kind?
Four-of-a-kind and straight flush hands are among the rarest of occurrences in poker. A straight flush is mathematically harder to make than four-of-a-kind, however, and that puts the straight flush ahead of four-of-a-kind in the hand rankings.
The Math Behind a Straight Flush
A straight flush occurs when you put together five sequential cards of all the same suit. An example of a straight flush could look like this:
If you draw five random cards out of a 52-card deck, you have an 0.00139% chance of making a straight flush. That extremely low probability translates to 72,192.3-to-1 odds against drawing a straight flush.
The deck yields nine distinct ways to make a straight flush. Multiplied by the four suits, you have 36 total possible ways to draw a straight flush.
Texas Hold’em requires players to make the best possible five-card hand out of seven total cards. With all five community cards on the board, you have a 0.0279% chance of making a straight flush (3,589.6-to-1 odds against).
The Math Behind Four of a Kind
Like straight flushes, Four-of-a-kind hands are a rare occurrence in poker. To make four-of-a-kind, you must draw four of the same ranking card in a five-card hand.
An example of four-of-a-kind looks like this:
A standard poker deck yields 156 distinct four-of-a-kind hands. Multiplied by four possible suits for the kicker (the 2♣ in this case), you have 624 total possible ways to make four-of-a-kind.
Randomly drawing five cards from a 52-card deck gives us an 0.024% chance of making four-of-a-kind. This translates to 4,165-to-1 odds against drawing a four-of-a-kind hand.
In Texas Hold’em, the game requires you to make the best possible five-card hand out of seven total cards. With all five community cards on the board, you have an 0.199% chance of making four-of-a-kind (594-to-1 odds against).
While four-of-a-kind is an exceedingly rare hand in a poker game, a straight flush marks an even more elusive hand. Making a straight flush is mathematically less likely than four-of-a-kind, which is why straight flushes win if these two monster hands go to battle.