Why increase pointer by two while finding loop in linked list, why not 3,4,5?

Question

I had a look at question already which talk about algorithm to find loop in a linked list. I have read Floyd\'s cycle-finding algorithm solution, mentioned at lot of places

Answer 1

If the linked list has a loop then a fast pointer with increment of 2 will work better then say increment of 3 or 4 or more because it ensures that once we are inside the loop the pointers will surely collide and there will be no overtaking.

For example if we take increment of 3 and inside the loop lets assume

fast pointer --> i  
slow         --> i+1 
the next iteration
fast pointer --> i+3  
slow         --> i+2

whereas such case will never happen with increment of 2.

Also if you are really unlucky then you may end up in a situation where loop length is L and you are incrementing the fast pointer by L+1. Then you will be stuck infinitely since the difference of the movement fast and slow pointer will always be L.

I hope I made myself clear.