Why Does a Straight Flush Beat Four of a Kind

Why Does a Straight Flush Beat Four of a Kind?

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.

The straight flush and four-of-a-kind sit near the very top of the poker hand rankings. Both occur extremely rarely, and you’re likely winning the pot if you hold either.

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:

Why Does a Straight Flush Beat Four of a Kind

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:

Why Does a Straight Flush Beat Four of a Kind

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.

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About the Author

Geoffrey Fisk

Freelance writer and poker player based in San Diego, California.

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