Say you're drawing to a made hand in a $10-$20 limit hold'em game and you have N outs.
On the turn, one line of thought is that you should only call if the pot odds are in your favour, i.e. if there is X in the pot and
X > (46 - N)/N * 20
However, this seems to ignore the fact that you can probably extract an extra bet if you make your hand. Taking that into account your EV is
EV = N/46 * (X + 20) + (46 - N)/N * (-20)
so you should call if
X + 20 > (46 - N)/N * 20
X > [ (46 - N)/N - 1 ] * 20
i.e. you can effectively subtract 1 from the required pot odds to account for the fact that you can extract an extra bet when you make your hand. If you think that that there's only some probability p of extracting that extra bet, you could subtract p from the required pot odds instead of subtracting 1.
This seems to have the largest effect when the pot is small and you have many outs, for example if you have 9 outs (flush draw) you would normally require pot odds of 4.1 : 1 to call, but this suggests that folding with less than 3.1 : 1 is actually throwing away value. If you have 15 outs (both straight and flush draw) you would normally require 2 : 1 but this suggests that if you don't call when you have better than evens, you are throwing money away.
Is my analysis here correct, and if so, why is the advice that you should call only if the pot odds justify it so prevalent? Is there a name for this concept of extracting extra bets from your opponent when you make your hand?