When we have six terms of which three are negative and three are positive.
When we have seven terms of which three are negative and four are positive.
So the probability increases.
It occurs me that a line of an odd number of distinct objects has a middle point. Whereas, an even number does not.
If you look at the inclusion/exclusion principle of counting from which the derangement sum is derived then I think you will have a better understanding of the sum.