Quote Originally Posted by daviddem View Post
you are OOP on the turn against an opp who can only have two hands (50/50 chance he has either). One of these hands has 100% equity against yours, and the other has 0% equity against yours. So obviously against this range you have exactly 50% equity.
1) Do you generally prefer to bet or check and why? If there is no straight answer, please say in what kind of circumstances you would prefer to bet or check (opp's style, board texture, whatever factors would influence your decision)
2) When you prefer one of these two options for whatever reason, how much do you prefer it? In other words, if you have 49% equity instead of 50, does that affect your decision? 45%? 40%?
1 - it depends on his what he does with each. the only way betting can NOT be of a lesser EV than checking is if he calls 100% of betsizes with all of his range on 100% of remaining streets in the hand (in this case, turn and river), in which case you have 50% equity over both those streets (hopefully you notice here that it's almost never so cut and dry as having either 100% or 0% equity when there are still cards to come, and this influences our decision, but it's helpful from a theoretical understanding perspective to use these exhaggerated examples) against his calling range and betting has a neutral expectation (ie it merely serves to increase variance). however, if he has 6 combos which have 100% equity against us, and 6 which have 0%, but he only calls with the range we beat 5/6 times, and never folds a better hand, our value-bet has a negative expectation in a vacuum, because when he calls, we lose that bet 7/12 times, and win only 5/12

2 - not sure exactly what you mean by this but i'll try to answer. pretend we are on the river in a certain spot (implication being hands of lesser value than ours have no equity, and hands stronger have 100% equity), if we have 50% or greater equity against villain's calling range to a particular betsize, the bet has a positive expectation. obviously if we beat 55% of his calling range, our EV is higher than if we only beat 51%. and 60% is better than 54% etc etc. note however that if villain ever bluffs us with a worse hand, this equity edge is negated, and so we want a slightly higher equity edge to compensate for the times we are incorrectly made to fold the best hand. i hope that goes some to way to answering your question.