Hello, I'm fairly new to poker. I understand the basic idea of pot odds but I don't understand the justification.

For example, suppose you're heads up with an opponent and have an Ax suited and you have a flush draw on the turn with $100 in the pot and no tainted outs. Also, assume our opponent is really clever and knows if you hit your flush or not, so he will not call any raise if you complete your flush. Finally, assume this flush will be the nuts. So you have a 19.57% chance to win the pot. According to this idea of pot odds, you should not call a bet larger than 19.57% of his bet plus the pot. So you should only call if his raise is less than $24.33. Calling anything over $24.33 would give you "bad pot odds." However, if you look at your expectation...

EV = 0.1957*(124.33) + (1-0.1957)*(-24.33) = 4.763 > 0

So you could still call a raise greater than $24.33 and have a positive expectation. In fact, if you call any raise less than $32.14, you will still have a positive expectation.

In general, suppose we have a probability p of winning a hand and a bet b which is a fraction of the pot. Since the bet is a fraction of the pot, then the pot will be 1. So our expectation is

EV = p*(1+b) + (1-p)*(-b) > 0.

Assuming that p < 1/2, then we have

b < p/(1-2p).

The strategy of pot odds outlined on this site, and most other sites, states that you must only call bets that are less than p*(1+b) of the pot. So b < p*(1+b), giving us

b < p/(1-p).

Assuming we use this strategy, then b < p/(1-p) < p/(1-2p) whenever p < 1/2. So we're going to fold to bets that still give us a positive expectation.

So my question is why should I fold these hands to these bets when I still have a positive expected value?