[davebwell]

question (1) suppose there is $100 in the pot on the turn and the effective stacks remaining are $25. Further suppose you know each others hands with certainty and you are a 50.1% to 49.9% favorite to win the pot at showdown. clearly the opponent has the pot odds to call any bet you make. If you both check you fold the river anytime he hits his draw and he folds anytime he misses it. So the current pot is a wash. However, if you bet the $25 to win his remaining $25 you have a 0.2% advantage which is an average of $0.05 per hand so you are better off betting even though he has the odds to call.