Module 2 · Lesson 10 of 39 · Free
Finding the nuts on any board
On the river K♠ 9♠ 4♦ 2♣ 7♠ your K♥ K♦ make three kings, and still 45 different hands beat them: any two spades make a flush. The best hand anyone could hold on a board is the nuts, and five checks of the board, always in the same order, find it in seconds.
The hand
The river: K♠ 9♠ 4♦ 2♣ 7♠. You hold K♥ K♦ for three kings, and the Loose-aggressive player's cards are hidden.
Predict first
How many two-card hands make the nuts on this board?
- 1: A♠ Q♠, the highest flush
- 45: any two spades
- 9: the A♠ with any other spade
Show the answer
Answer: 9: the A♠ with any other spade
Only a flush beats three kings here, and every flush with the A♠ beats every flush without it. So whoever holds the A♠ and another spade cannot be beaten: 10 spades are unseen, and the A♠ goes with any of the other 9. A♠ Q♠ makes the highest flush, but A♠ 3♠ is the nuts too, because nobody else can hold the A♠.
Working it out
Run the checks from the top on K♠ 9♠ 4♦ 2♣ 7♠. A straight flush needs three cards of one suit within five ranks in a row: the K♠, 9♠ and 7♠ stretch over seven ranks, so none can be made. Four of a kind needs a pair on the board, and there is none. A flush needs three cards of one suit, and the three spades allow it, so the nuts is a flush with the A♠. Count the danger to your kings: 13 − 3 = 10 spades are unseen, and any two of them make a flush, 10 × 9 ÷ 2 = 45 hands. The A♠ with another spade, 9 hands, is the nuts, and the Q♠ with any spade but the A♠, 8 hands, is the second nuts: only the nuts beats it.
The checks always run in this order: a straight flush, four of a kind, a flush, a straight, then three of a kind. A full house is never the best hand possible, because a pair on the board that allows one also allows four of a kind. When none of the first four can be made, the nuts is a set of the top board card, three of a kind made with a pocket pair, such as K♣ K♥ on K♦ 8♠ 3♣. On the flop and the turn the same checks find the best hand at that moment, and each new card can change it: on the turn K♠ 9♠ 4♦ 2♣ your three kings were the nuts, and the 7♠ made a flush possible.
Formula
Checks in order: straight flush, four of a kind, flush, straight, three of a kind. With three cards of the suit on the board, nut flush hands = unseen cards of the suit − 1: 10 − 1 = 9
Check your understanding
The board is K♠ 9♦ 9♣ 6♥ 2♦. What is the nuts?
- Four nines, with 9♠ 9♥
- A full house, kings full of nines, with K K
- Three nines with an ace kicker
Show the answer
Answer: Four nines, with 9♠ 9♥
No suit appears three times, so no straight flush. The pair of nines on the board allows four of a kind, and only the last two nines, 9♠ 9♥, make it. K K makes the best full house, kings full of nines, but four nines beat it.
The board is J♠ 9♦ 8♣ 3♥ 2♠. How many two-card hands make the nuts?
Show the answer
Answer: 16
No suit appears three times and no rank twice, but three ranks lie within five in a row, so the nuts is the highest straight: Q J T 9 8, which needs a queen and a ten. There are 4 queens and 4 tens: 4 × 4 = 16 hands.
The board is J♥ 8♥ 7♥ 3♠ 2♣. Which hand is the nuts?
- T♥ 9♥
- A♥ K♥
- T♠ 9♦
Show the answer
Answer: T♥ 9♥
Three hearts lie within five ranks in a row, J 8 7, so a straight flush can be made: T♥ 9♥ fills J T 9 8 7 of hearts, and nothing beats it. A♥ K♥ makes only a flush and T♠ 9♦ only a straight.