With an allocation of size n, you have capacity for n-1 characters and the trailing 0, and the trailing 0 does not count as a character. If you double the size of the allocation to 2n, the capacity increases to 2(n-1) + 1.

So why does it increase the size of the allocation to 2n + 1?

Allocation size is capacity + 1. If you double the allocation size to 2 * (capacity + 1), the new capacity is 2 * capacity + 1.

Surely 2 * (capacity + 1) = 2 * capacity + 2

That is the new allocation size. The new capacity is one character less. The allocation must include space for the trailing 0, which is not a part of the string and is hence not included in the length/capacity numbers.

I see, thanks for your patience :)

Great thread, I was scratching me head a bit too.