Part: Part Four - Pot Odds & Hand Analysis

Counting outs and the price

Pre-flop
Blinds 100 / 200Pot 900 (4.5 BB)BTNA9 20,000 (100 BB)YOUto actMP 20,000 (100 BB)Solid MPraises 600 (3 BB)SB 20,000 (100 BB)posts 100 (0.5 BB)BB 20,000 (100 BB)posts 200 (1 BB)D

A solid player raises from middle position and it folds to you on the button with A♠9♠ - a suited ace that plays well in position.

Solid MP raises to 600 (3 BB); you hold A♠9♠ on the button. Best?

WhyA suited ace makes the strongest flush and dominates the weaker aces he's raising with, and holding the button lets you see his action first on every street. Flatting keeps his bluffs and dominated hands in the pot rather than blowing them out with a three-bet.
What happensThe blinds fold and you're heads-up in position - the exact setup that lets the later math actually pay. Pot: 1,500 (7.5 BB).
Flop
Heads-upPot 1,500 (7.5 BB)K72BTNA9 20,000 (100 BB)YOUnut flush draw (9 outs)MP 20,000 (100 BB)Solid MPbets 800 (4 BB)D

Flop: K♠ 7♠ 2♦ - you flop the nut flush draw, nine outs. He continuation-bets.

Nut flush draw (9 outs). He bets 800, so you call 800 to win 2,300 (~2.9-to-1). Best?

WhyNine spades give you roughly 35% to complete by the river - about four percent per out with two cards to come. You risk 800 to win the 2,300 already there; once your call goes in, the pot lays you a break-even point near 26%, so 35% sits comfortably ahead of the price, and the nut flush winning a big pot when it lands only widens the edge.
What happensYou call - not a gamble, but a spot where your equity outruns the price. Pot: 3,100 (15.5 BB).
Turn
Heads-upPot 3,100 (15.5 BB)K724BTNA9 20,000 (100 BB)YOUthe nut flushMP 20,000 (100 BB)Solid MPbets 1,500 (7.5 BB)D

Turn: 4♠ - you make the nut flush. He bets again.

You hit the nut flush and he bets 1,500 (7.5 BB). Best?

WhyYou now hold the mathematical nuts - no spade combination beats you. A king, two pair, a set, or a smaller flush all pay a raise, and slow-playing just risks a safe river killing your action, so build the pot while he still has a hand he can't fold.
What happensYou raise to 4,500; he calls with K-Q. The flop math you trusted is now stacking chips. Pot: 12,100 (60.5 BB).
River
Heads-upPot 12,100 (60.5 BB)K7248BTNA9 20,000 (100 BB)YOUthe nut flushMP 20,000 (100 BB)Solid MPchecksD

River: 8♦ - a blank. He checks.

Nut flush, he checks the river. Best?

WhyHe can still turn up with a king or two pair - hands that beat nothing yet call a reasonable river bet. Checking the nuts here simply refunds him the last street, so size a value bet to look bluffable and collect.
What happensYou bet 6,000; he calls and you win a big pot. Notice the win came from a call you'd already proven correct back on the flop.
Nine outs became about 35% equity, which beat the 2.9-to-1 price, so the call was correct before a single card fell. The flush arriving was the payoff, never the proof.

Count your outs, convert them to equity, and weigh that against the price plus what you'll win when you hit - call because the numbers clear, not because the hand feels good.