Reading the board: the best five cards from seven

In Texas Hold'em you hold two private cards and share five community cards, so every player has seven cards to choose from. Your hand is the best five of them. Most of the time the answer is obvious, but the awkward cases (three pairs, a six-card straight, a board that already makes a hand) are where players misread a showdown and where the app's "name the best hand you can make" question earns its keep.

Where the 21 comes from

Choosing five cards from seven is the same as choosing the two to leave out, and there are 7 × 6 ÷ 2 = 21 ways to do that. You never need to test all 21, but the count shows how they split, and the split depends on how many of your hole cards are used.

• Both hole cards: you add three of the five board cards. There are 10 ways to pick three from five.
• One hole card: you pick which of your two cards (2 ways) and four of the five board cards (5 ways), so 2 × 5 = 10.
• No hole cards: all five board cards. There is exactly 1 way, and it is called playing the board.

10 + 10 + 1 = 21. Using neither hole card is rarely the best choice, but it is always on offer, and it matters more than people expect.

Playing the board

If the five community cards are K♠ K♦ K♣ 5♥ 5♠, the board is a full house, kings full of fives. A player holding 2♦ 3♣ has no better five than those, so they play the board. So does everyone else whose hole cards cannot improve it. Two players who both play the board have identical hands and split the pot.

A player holding A♥ A♣ on that board can do better: K K K A A, kings full of aces, beats kings full of fives. The board's own pair of fives is the weak spot, and a pocket pair of aces replaces it.

Rules that pick the five

Once you know the hand type, a few rules decide which five cards represent it.

1. Pair plus kickers. Take the pair, then the three highest remaining cards. On a board of K♠ 9♦ 6♣ 4♥ 2♠, a player with K♦ Q♣ holds K K Q 9 6. A player with K♥ J♣ holds K K J 9 6. The queen beats the jack, so the first player wins. The 4 and 2 never matter.
2. Three pairs. With K K 8 8 4 4 A, you play two pair, kings and eights, and the ace is the kicker: K K 8 8 A. The third pair is ignored. If the seventh card were a 3 instead of the ace, the best kicker would be a 4, taken from the unused pair: K K 8 8 4.
3. Two sets of trips. With 9 9 9 5 5 5 A, the hand is a full house, nines full of fives. The spare trips supplies the pair, and the ace is left out.
4. A flush of six or seven. If six of your seven cards share a suit, you play the highest five of them. The sixth, lowest card is dropped, and it can change who wins when two players have flushes.
5. A run of six. With 4 5 6 7 8 9 among the seven, the straight is 5 to 9, not 4 to 8. Aces work at either end, so A 2 3 4 5 is a straight, but with a 6 as well the best straight is 2 to 6.
6. A flush and a straight together. A straight flush needs all five cards in the same suit. Having a flush in one suit and a straight made with different suits does not make one. Check the suited cards on their own, and if they do not form a straight, play the flush, since a flush beats a straight.

The same logic applies at the very top. If the board is four nines and a 7, any hole card above the 7 becomes your kicker, and an ace is the best you can have. Anyone without one plays the board.

Why Omaha is different

Everything above rests on a freedom that Hold'em gives you: use two, one or none of your hole cards. Omaha removes it. Each player has four hole cards and must use exactly two of them with exactly three board cards, which gives 6 × 10 = 60 combinations instead of 21. A board with four suited cards and just one suited card in your hand is not a flush in Omaha, as the post on Omaha's exactly-two rule explains. In Hold'em, that same hand is a flush, and so is a board that is a flush on its own.

Reading the board before the maths

Counting outs and pot odds both start from knowing what you hold now. The "Reading the cards" lesson in Holdem Coach: Poker Trainer shows your cards and the shared cards and asks you to name the best hand you can make, which is the first step before the arithmetic in the pot odds post. Likewise, the "Which hand is in front?" lesson shows two hands and asks which is more likely to win, and the kicker rules above are what settle the close ones.

Get the five cards right and the rest of the decision, whether to call, raise or fold, starts from a correct picture of your hand.