Can you call when the pot odds don't favour you?

Question

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

or

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?

Answer 1

Yes, you can and you should. The concept you're describing is called implied odds (the estimated profit you'll make if you make your hand).

Notice is a much less concrete value as it is an estimation of whether your opponent will call when the draw comes and the amount he'll be willing to pay. There's also the concept of reverse implied odds which are the odds or you completing your draw and still loosing (for example against a bigger draw or a full house)

Answer 2

I only read a part of your question but you can indeed call when odds are not in favor. Implied pot odds is what it's called. Basically you calculate that what you payed too much, you will receive back at the next street(s). An example:

Hero and Villain play a pot. On the turn you have a flush draw (giving you 9 outs). This is more or less 19% chance of hitting it. Villain bets exactly half the pot size (but he puts in half of his stack as well). Knowing this, you might want to call in some cases cause you know that on the river he can't fold to you with only this much chips left (less than half of his original stack).

In numbers: Villain has a stack size of 1200... All the action before the turn costs him 400 chips. You called everything so the pot is now 800 chips. At the turn Villain has 800 chips left and puts 400 in the pot for half the amount of his money and half the pot size. This makes the pot 1200 (giving you 400/1600 odds). Your outs are about 19%, but your odds are 25%, which is EV-... However, knowing that at the river Villain will only be able to commit another 400 chips, giving you maximum 400/2400 odds, you should call.

If you know Villain is really aggressive and pushes a lot on the river, it's even more interesting for you because you can earn ALL his chips, even if he has a large stack...