Where Is The Line?

Pot odds are easy enough to figure out these days. There are a bunch of tools online that will simulate every possible outcome or just do the math for you. In the middle of a game, some odds are stamped in your memory. Then there's the monkey math method of outs x 2 x cards left to come to get a rough estimate. Some people actually realize that this is just based on the assumption that 50, 47, 46, and 45 aren't that different in terms of denominators.

But where's the line? If you're getting 1:1, do you call when you're only 45%? Is 2:1 worth it at 30%? Does 23% cut it at 3:1?

And I'm not talking about implied odds, even though they come into play in the beginning of this hand.

That royal flush the other day went something like this:

I've got QTd in position with 3 to act behind me and an M around 15. There's a raise to a total of 3x the BB, and I decide to call. I like my chances of getting more money in the pot if I hit a draw, and might even get this multi-way with the call. Nobody else calls.

The flop brings me the 2nd nut flush draw with an inside royal redraw. Essentially 12 outs twice.

The aggressor bets the pot, and I call, figuring him for the ace. I'm getting 2:1, this is a no-brainer. In hindsight, I think I should have pushed here.

The turn bricks and my opponent goes all-in. He's got exactly twice my remaining stack, so I'm looking at 1,985 to win 4,685 chips, or 2.36:1, or 29.76%.

But the chances of hitting one of my winning draws are only 27.27%. There are no more implied odds in this situation as he's all-in. Does his 2.49% edge really make a difference here?

I didn't think so. Especially given that it was the middle stages of a 45-man game and this was a good-sized pot that could give me a lot of power as long as I avoided the bigger stack 3 to my left. I called.

My royal hit on the river, but any diamond or king would have done. Naturally, my opponent typed "nice chase" followed by "wtf were you even doing in that hand?"

I chose not to answer him, but I did answer the question to myself. The only borderline decision made in that hand as far as I'm concerned was the call on the turn. I was thinking of pushing if he checked anyway, but his push confirmed that he was ahead. Is 2.49% enough to make you fold?