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Why a Full House Beats a Flush

And Other Thoughts on Why One Poker Hand Beats Another in Poker

by Randy Ray

Almost everyone, even non poker players, have some idea of poker hand rankings and which hands beat which other hands. But some people wonder why the hand ranks are set up the way they are. A good guess would be that the hands are ranked in order of how probable it is to get the hand. The less likely or common a hand is, the better it ranks.

Poker Hand Probabilities That guess is the correct answer by the way. So if someone asks you why a full house beats a flush, you can confidently answer that a full house beats a flush because the probability of getting a full house is lower.

The above assumes that you're dealing a 5 card hand from a 52 card deck with no wild cards. Wild cards and opportunities to improve your hand affect these probabilities, but for the sake of determining the hand ranking charts, this assumption is what determines the hand rankings.

Probabilities of Being Dealt Certain Hands

The chance of being dealt a hand with no pair is 50.1%. So roughly half the time, your poker hand will be garbage.

Pairs are the next most common hand and come up 42.2% of the time.

So 92.3% of the time, you'll have a pair or lower. This makes the better hands more exciting, don't you think?

Two pairs are dealt 4.8% of the time. 3 of a kind comes up almost as often, 2.1% of the time.

The rest of the hands happen less than 1% of the time. A straight happens 0.4% of the time, a flush happens 0.2% of the time, a full house happens 0.1% of the time, and a 4 of a kind comes up 0.02% of the time. A straight flush is even rarer, coming up only 0.002% of the time.

All of the above probabilities assume 5 cards dealt out of a 52 card deck. No wild cards, no chances of improving your hand.

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