The ultimate hand: A preface and primer

February 10, 2018

By Matthew E. Milliken
Feb. 10, 2018

Most Americans are obsessed with the best of the best. For decades, children have been encouraged to dream big: Growing up to become president, for instance, or the richest person in the world. Some of our most successful movies involve people striving to become — and succeeding at being — the most accomplished or powerful person in a given arena. The GodfatherTop GunThe Lion King, the Star Wars and James Bond and Harry Potter franchises, just about any superhero feature — the list goes on.

A lot of poker players revere the straight flush. This is the best hand in Texas holdem, consisting of five cards of the same suit in order. It’s the kind of thing players dream of hitting, and many movies with poker scenes cater to this fantasy. The high-stakes poker sequence in the 2006 movie Casino Royale, for example, shows James Bond hitting a straight flush and collecting a massive pot against incredible odds.

Let me get back to basics for those who may not know much about poker.

A holdem hand consists of the five best cards available to a player out of five community cards — sometimes known as the board, these are available for use by everyone participating in the hand — and two pocket cards, which can only be utilized by the player to whom they were dealt.

The pocket cards are kept face-down until all betting has concluded, introducing uncertainty into the game. You know what you have, but you can only surmise what your opponents might be holding. This mystery is what enables players to bluff — that is, to represent a strong hand by making or calling big bets. By knowing her opponents’ tendencies or deciphering a foe’s tells, a player can gain a huge advantage over everyone else at the table.

(Hand, by the way, is a term for both a round of poker and a player’s cards.)

The poker hands, in order of weakest to strongest, are:

• High card, e.g., a hand that includes a king.

• Pair, e.g., a pair of twos.

• Two pairs, e.g., a pair of tens and a pair of sixes.

• Three of a kind (sometimes called triplets or trips), e.g., three jacks.

• Straight, or five cards in a row, e.g., an ace, a two, a three, a four and a five. (That specific straight is called “the wheel.”)

• Flush, or five cards from the same suit, e.g., the seven, nine, ten, king and ace of clubs.

• Full house (a.k.a. a full boat or boat), or three of a kind plus a pair, e.g., queens full of threes, which would be three queens and a pair of threes.

• Four of a kind (a.k.a. quadruplets or quads), e.g., all four nines from a deck.

• Straight flush, e.g., the five, six, seven, eight and nine of hearts.

Probability dictates the relative strengths of these different hands. High card is the most common hand, comprising 1,202,540 out of 2,598,960 possible five-card hands, according to The straight flush is the least probable hand, made by just 36 configurations of five cards. The odds of getting a straight flush are more than 72,000 to one against, or more than five times less likely than the odds that a person will be struck by lightning over the course of a lifetime.

When two or more players have the same kind of hand, card ranks determine which one is the best: Ace-high beats every high-card hand; king-high loses to ace-high but is superior to every other high-card hand; queen-high loses to ace-high and king-high but beats all remaining high-card hands.

The same hierarchy determines priority for all other types of hands. A pair of aces beats all pairs; a pair of queens loses to aces and kings but beats all remaining pairs; a pair of twos loses to all other pairs. The ace-high straight beats all straights; the wheel, which is a five-high straight, loses to all other straights. The best flush is ace-high; the worst, seven-high. (Note that A-2-3-4-5 is a straight flush and A-2-3-4-6 is an ace-high flush, leaving 2-3-4-5-7 as the weakest flush and 2-3-4-6-7 as the second-weakest flush.) The only four-of-a-kind that beats quad kings is quad aces, while quad threes loses to every other four-of-a-kind except quad twos; and so forth.

As I said, many Americans are obsessed with the best of the best, and not all straight flushes are created equal. The very best possible single poker hand is a type of straight flush called the royal flush: The ten, jack, queen, king and ace from the same suit.

There are only four royal flushes, one for each suit. They make up one out of every 649,737 possible hands. (That’s 2,598,960 divided by four.) In other words, the probability that you’ll get one is slightly more likely than the probability of your killed by an asteroid impact.

I’ve had three royal flushes over the course of the last nine years. Over the course of my next few posts, I’ll describe each one.

Part 1

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