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Here are the little sister gift levels. At top levels, there's a small chance of winning Protect. This can obviously be changed to a different TM but I figured that was a nice, appropriate one.
Maybe that should be changed though. Once you max out her friendship, she always gives Protect and the 2% slot is used for something even rarer (maybe divided equally between evo stones?).
I figure every time you call, you have an appropriate percentage chance of getting the item for your current BBP level (i.e. one item a day).