Situations are taken from 5c/10c NL tables.
1. Hero is CO, dealt AQ. 2 callers, Hero raises to 60c, BB calls, all others fold. Flop comes down rubbish, say T 7 3. Pot is $1.30 - $1.40. Before you can make a continuation bet, BB bets 10c (i.e. completely out of proportion to the pot). Should you ignore this and make a standard continuation bet (which would be going all-in, since 2/3 pot = 90c > half of remaining stack), fold since you've technically missed the flop, or call?
If you call, the turn comes down more rubbish, say a 5, and BB bets 10c again, now what? What if the turn comes down K and BB bets 10c? What about river?
(I've seen people min-bet at each round with complete rubbish, trying to get opponents to fold, and after flopping the nut flush, so...)
2. You are late/blinds, with a hand to raise with, say AJ/AQ. Couple of callers, then someone min-raises from a middle position. Should you treat this as a raise, and fold, or as 2 callers, and adjust your raise accordingly?
If you have a hand like QQ or AK, again in late/blinds, couple of folds, a min-raise, everyone folds up to you, should you bet (4+2)BB? 3-bet? Pushing all-in from 2BB to 20BB seems a bit extreme, and will probably scare an Ax/KT/QJ out.