Part: Part Four - Pot Odds & Hand Analysis

A river bluff-catch

Pre-flop
Blinds 100 / 200Pot 1,300 (6.5 BB)BBAJ 20,000 (100 BB)YOUto actBTN 20,000 (100 BB)Aggressive buttonraises 600 (3 BB)SBfoldsD

An aggressive, high-bluff button raises to 600 and you defend the big blind with A♥J♠.

Aggressive button opens to 600 (3 BB); you hold A♥J♠ in the BB. Best?

WhyCall. A-J offsuit defends fine against a wide button-stealing range - and against an aggressive player you'll often get to make a profitable bluff-catch later.
What happensYou call. Heads-up to the flop.  Pot: 1,300 (6.5 BB).
Flop
Heads-upPot 1,300 (6.5 BB)J73BBAJ 20,000 (100 BB)YOUtop pair, jack kickerBTN 20,000 (100 BB)Aggressive buttonbets 800 (4 BB)D

Flop: J♦ 7♣ 3♠ - you flop top pair, jack kicker. You check, he c-bets.

Top pair vs an aggressive button who c-bets a ton. Best?

WhyCall. Against an opponent who barrels and bluffs too much, calling keeps his bluffs in - you're turning your top pair into a bluff-catcher and planning to pay him off only when the price is right.
What happensYou call.  Pot: 2,900 (14.5 BB).
Turn
Heads-upPot 2,900 (14.5 BB)J735BBAJ 20,000 (100 BB)YOUtop pair, jack kickerBTN 20,000 (100 BB)Aggressive buttonbets 1,100 (5.5 BB)D

Turn: 5♥ - a blank. He bets again, smallish. You call.

He keeps firing on a dry board. With top pair, jack kicker, best?

WhyCall. Nothing has changed your read: he over-bets bluffs and barrels. Continue calling as a bluff-catcher and let the river price set your final decision.
What happensYou call.  Pot: 5,100 (25.5 BB).
River
Heads-upPot 5,100 (25.5 BB)J7352BBAJ 20,000 (100 BB)YOUa bluff-catcherBTN 20,000 (100 BB)Aggressive buttonbets 2,000 (10 BB)D

River: 2♣ - bricks. He bets 2,000 into 5,100, so you call 2,000 to win 7,100 (~3.5-to-1). You need to be good ~22% of the time.

Getting ~3.5-to-1 against a habitual bluffer who barrels missed draws here. Best?

WhyCall. The price (~3.5-to-1) means you only need to be good about 22% of the time. Against an aggressive player whose triple-barrel range here is well over a quarter bluffs - busted draws and pure air - your top pair beats enough of it to make the call clearly profitable, even though it only beats his bluffs.
What happensYou call; he shows a busted draw.  The pot-odds math made it an easy call.
You computed the price (~3.5-to-1, needing ~22%), compared it to how often this player bluffs, and called - bluff-catching is pure pot-odds math against an estimate of his bluff frequency, not a guess.

To call a river bet you need to win only as often as the price requires (bet/(pot+2×bet)) - call when your read says the opponent bluffs more often than that threshold.