Part: Part Two - Playing Styles & Starting Requirements

A big pair against a 3-bet

Pre-flop
Blinds 100 / 200Pot 2,600 (13 BB)COQ♠Q♦● 20,000 (100 BB)YOUyou opened to 500BTN● 20,000 (100 BB)3-bettor3-bets 1,800 (9 BB)SB● 20,000 (100 BB)posts 100 (0.5 BB)BB● 20,000 (100 BB)posts 200 (1 BB)D

You open to 500 from the cutoff with Q♠Q♦. The button - a competent, fairly aggressive player - three-bets. The blinds fold.

You opened pocket queens and a capable button three-bets to 1,800 (9 BB). Best play?

WhyQueens are far too strong to hand over to a single three-bet, and flatting just plays a bloated pot out of position where you'll be guessing on half the flops. Four-bet: you're ahead of most three-betting ranges and you clarify where you stand - the only thing that should give you pause is him shoving all his chips back in.
What happensYou four-bet to 4,400 (22 BB). He calls. Pot: 9,100 (45.5 BB).
Flop
Heads-upPot 9,100 (45.5 BB)K♦9♣5♥COQ♠Q♦● 20,000 (100 BB)YOUoverpair? - no, a king flopsBTN● 20,000 (100 BB)3-bettorto actD

Flop: K♦ 9♣ 5♥ - an ugly card. A king is right in the range that calls a four-bet (A-K, K-K). You're first to act with about 14,000 (70 BB) behind.

A king flops - a card that hits his calling range hard. With Q-Q, best?

WhyThe king is about the ugliest card in the deck for you - it's the top of the range that flat-called your four-bet, the A-K and K-K, and almost nothing worse keeps going if you fire. Check: hold the pot small and keep a cheap fold available, rather than betting straight into the hands that just improved.
What happensYou check. He bets 4,500 (22.5 BB).
Turn
Heads-upPot 13,600 (68 BB)K♦9♣5♥3♠COQ♠Q♦● 20,000 (100 BB)YOUsecond-best one pairBTN● 20,000 (100 BB)3-bettorbet 4,500 (22.5 BB)D

He bets on the king-high board. The turn is irrelevant to your decision - the question is whether queens are good.

Facing a 4,500 (22.5 BB) bet on a king-high board in a four-bet pot. Your queens are…

WhyIn a four-bet pot the continuing range is tiny and top-heavy, and a king-high flop is the texture that fills it in - his bet is the kings and ace-kings you were already worried about, not a bluff you can look up. Queens were a monster two minutes ago and a bluff-catcher now. Fold and keep the stack; overpairs come with no no-fold guarantee.
What happensYou fold and he shows A-K, exactly as the board warned. You gave up a pot but only the minimum - reading the run-out saved you the whole stack a stubborn overpair ships here.
You got the value in with queens pre-flop, then read the four-bet pot instead of your raw hand strength when a king landed. In a pot that narrow, a king hits his continuing range far harder than yours - folding an 'overpair' there is what separates a big pair from a punted stack.

Big pairs make money two ways - getting value in when they're ahead, and folding when the board and the betting say they're not. Four-bet them pre-flop; don't marry them when an overcard smashes the exact range that called.