Quote:
by saying "4x only if all in"
are you saying if would call a all in on the turn?
If you are on the flop, then your concern is what will happen on the turn, not what will happen on the turn and river, because you may face a bet again on the turn.
So for example :
$20 in the pot, heads up. Villain bets $10 on a flop of Kh8h2s. You have AhTh.
You are getting 3:1. You want to hit nine hearts (2h is a bit dubious because it pairs the board and does not give you the nuts, but we will ignore that for now). We know five cards, so there are 47 remaining. That is 9:38, or 4.25:1 against hitting your flush. So you aren't really getting the odds to call, unless your ace is good or your opponent will pay off if you hit.
Now over two cards you are about 2:1 against hitting your flush. So if you were all in for that $10 it would be an easy call getting 3:1. For 3:1 you need only 25% equity to call all in.
Please note in the below simulation we have basically no hidden outs, although we could get runner TT or runner QJ.
Hold'em Simulation ?
990 trials (Exhaustive)
board: Kh8h2d
Hand Equity Wins Ties
AhTh 37.27% 369 0
AsAc 62.73% 621 0
But with only one card to come, we have only 20% equity :
Hold'em Simulation ?
44 trials (Exhaustive)
board: Kh8h2d4d
Hand Equity Wins Ties
AhTh 20.45% 9 0
AsAc 79.55% 35 0
Dependent probability tells us that if you have an 80% chance of something, then the chance of hitting it in two tries is 80% squared, or 64%, or 2:1 against. So over multiple tries the probability of hitting something goes up (or conversely the probability of not hitting it goes down).
Basically, when you are on the flop, your concern is how often will you hit your hand on the turn, and then what will happen. 20% equates to 4:1, but it is not quite so simple as we are not getting the direct odds to call so we should fold, because what if we hit our flush and then our opponent calls a bet on the turn or river? Or what if he bets and then calls a raise? Or what if we call on the flop, and then he checks the turn and we get a free river? So there are a lot of possibilities, and your task is basically to model them all as much as you can. In the 3:1 example with the nut flush draw you probably could call, even though you are not getting the 4:1 pot odds that equate to your probability of hitting the turn, because at least some of the time almost any opponent will be calling something on the turn or the river. Even if they are folding 90% of the time, that other 10% of the time they might be stacking off. Against a very loose or suspicious opponent, who will happily call two large bets with top pair even though the flush came, then you can draw more liberally than you can against a weak tight nit who will sigh fold if you do hit your hand. And if your opponent is very aggressive and could be bluffing and willing to barrel off on the flush card then you get implied odds there as well.