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Cool concept! But I think I definitely got more jumps than I should, or is there something what resets the jumps? :D

It's probably not that you got more jumps -- my explanation of the mechanic sucked xD. 
As another player puts it -- your jumps only go down if you use all of them at once before touching the ground.
If you use 3 jumps before touching the ground, it goes down to 2 and you can never use a triple jump again and so on.