Well Urmmmmm... its a weird question but to put it one way, you wouldn't hit any as our lovely black hole would consume this stick before you could hit any. Apart from that the chance is actually high, there are so many stars in our solar system (and even more near the centre) that you could hit on. But lets say if you to count the black hole, but it didn't get consumed, it would take so long (because of the black holes gravity) that you would die of old age before you managed to swing down through.
Edit anyone who can improve on my theory!