Re: giving opponent correct odds to call
I didn't read the whole thread, but OP asks a pretty important question, so here's my certified answer (certified by me, that is):
First of all, in the situation that OP describes: if you bet less than 100$ in this situation then you are losing money, compared to betting 100$. It's better for you if villain folds than if he calls a 99$ bet. But it's better for you if he calls a 130$ bet than if he folds to a 140$ bet, so you need to figure out a reasonable amount over 100$ that will maximize your value (if you know exactly the probability that villain calls each size of bet you can compute it by maximizing profit when price-setting just like in economics).
To see the above is correct, just assume both us and villain are playing with out hands exactly face up.
But in poker something more interesting happens. Like EmptyPromises wrote above, villain actually has a range of hands, some of which have less than 20%, some of which have more, and some of which actually have us beat right now. To keep the discussion close to the original question, let's assume that we know for a fact that villain is on a draw with 20% equity, but we don't know which draw. Suppose for simplicity that we know villain is on exactly one of several draws, all equally likely, but we don't know which of them he is on, and suppose that the outs for these draws are all disjoint.
What happens now? Well, it actually depends on stack sizes. Suppose we are infinitely deep. Then it's not hard to prove that if villain has our hand pegged down and knows for a fact that we have none of these draws, then he has 40% "effective equity", meaning the situation is as profitable for him as if his equity was actually 40%. In this case, we'd actually want to bet 600$ into 300$, to deny him the "effective odds" (more like game-theoretic equity or such) from continuing with his draw(s). If his draws had more than 25% equity, the best move for us would actually be to check/fold! This is not a theoretical point: this comes up all the time. There are two ways to ameliorate it: one is to not look at pot odds but "effective odds" and thus to bet much bigger than we think denies villain his odds. But a much more important way is to make sure our range is not capped on the river, so that sometimes we have one of the draws he'll be repping. This is, for example, why it's important to bet our draws OTF even if villains are calling too much: to put them in our betting range, together with our made hands so as to not be exploitable on later streets.