you mention your third star alliance allowed baggage. please note you do not have an allowance for a third baggage, what star gold allows you is one additional piece of baggage, on top of your normal allowance (which is currently one piece, for most cheap fares)
therefore, 1 bag allowed by ticket plus 1 bag allowed by star gold = 2 free bags, not three
where the confusion might come is that until 2018 both av and cm allowed 2 free bags plus 1 star gold - 3. sadly, no longer so