Here is a solution for survivals >75%

Every 4 four people a group according to "从高到矮排队".
The people in position 1, 5, 9, 13, ...could be killed.
But the rest of people must be survivals.
They should have an agreement at gathering before queueing. If colors of 2,3,4's cap are white more than black, 1 should say white. If colors of 2,3,4's cap are black more than white, 1 should say black.
So 2 should clearly know what color his cap is, and 3 knows earlier, 4 know too.
5th person is just like 1st person.....
So the assured survival rate is 3/4= 75%.
If 1, 5, 9 .... happen to say the color which matches their cap color, they are survivals too.
So this strategy has survival rate greater than 75%.