I'm not sure if this riddle is "closed" or something, but I'll try to back up @OmegaKrypton's one, since I came up with the same ending conclusion.
Adding up what you're left with each time just doesn't "mathematically" work. In fact, while the sum of what you gave each time inevitably adds up to your initial total, the sum of what you are left with works differently.
Let's make some examples:
Since this is valid for every N total, we can use a smaller number to clarify better: let's pick 5.
If we apply the same rules:
Give 2, left with 3. Give 1, left with 2. Give 1, left with 1. Give 1, left with 0.
Summing up, the "given total" adds up to 5, of course. But the "left total" sums up to 6.
Now, let's try this setup.
Give 2, left with 3. Give 1, left with 2. Give 2, left with 0.
Now the sums, are both equal to 5. This means that, while the total of what you give is always "correct", the sum of the values you are left with, depends on how you distribute the starting value over time. In other words, according on how many steps you take to make 50 reach 0 (and on how much you take away from 50), the value you'll get will inevitably change.
Hope this is worth to read!