alt Hacker NewsI think direct collision depends just on the geometric cross-section, no? Gravity can't repulse, so if you're on a direct collision path, nothing will move you off it. The whole slingshot thing is that you get close, you change path, but just because you pass close doesn't mean gravity will make you collide. I might be missing something...
If you have two stars moving directly and perfectly towards each other, and there are no other influences, then yes, they will collide.
In reality there will be always some sideways motion for each star relative to each other, especially in this kind of situation with a lot going on. The gravity of the bodies pull on each other as they approach, accelerating them towards each other, but their momentum is strong, and so gravity pulls them into an elliptical orbit (or hyperbola) and not into each other. There only needs to be a tiny relative sideways motion for this to happen.
In other words, gravity will not cause two stars passing very close to each other to collide, as one might expect. The stars really would to be aimed perfectly at each other to collide, which would be extremely unlikely with both stars feeling the faint pull of many distant neighbours.
I think I was being overly cautious when I suggested a direct collision was likely to happen. It's more accurate to say that an accidental confluence of the many complex gravitational forces and sheer number of stars could maybe allow collisions to happen somewhere in that system.