3 · LEARN THE USEFUL MATH · LESSON 11 OF 29 · 6 min
Count outs carefully
An out is an unseen card that could improve your hand enough to win. With four hearts in your hand and on the board, nine hearts remain in the deck. But if the board pairs, some of those flush cards may still lose to a full house.
You have A♥ 8♥ and the flop is K♥ 5♥ 2♣. Nine hearts remain, but the chance of winning is not simply nine divided by the remaining cards because your opponent may already have a strong hand or improve too.
Separate cards that improve you from cards that win
Count visible cards first. A suit contains 13 cards. If your two hearts and two hearts on the flop give you four, nine hearts remain unseen. With 47 unseen cards after the flop, the chance that the very next card is a heart is 9/47, about 19%. That is a chance to make a flush on the turn, not automatically a 19% chance to win the hand.
Some apparent outs are dirty. If the board is paired, a heart can complete your flush while also giving an opponent a full house. If an opponent might hold a higher heart, a low flush can lose to a higher flush. A card that pairs one of your ranks may improve you to a pair but still leave you behind. Remove or discount such cards before comparing your chance to the call price.
For a quick estimate with two cards still to come, players often use about four percentage points per clean out. With nine clean outs, that suggests roughly 36% by the river. The exact chance of seeing at least one of those nine cards is about 35% when no cards are removed beyond the five you can see. Future bets and opponent redraws can make a simple 'by the river' estimate misleading for a flop call.
List the nine unseen hearts in the prepared draw spot. Then name one opponent hand that would make a heart less valuable than it first appears.
Count clean outs, not merely cards that make a prettier hand.
MAKE THE CALL
With four hearts visible between your cards and the board, how many hearts remain unseen?
Start with a prepared decision, then play the rest of the hand with practice chips. Turn on guidance to see the trainer's reasoning.