The geese can't win with 13 pieces. The geese win more than 50% of the games with 15 pieces. It would then seem that 14 geese is the sweet spot for making this game balanced and viable, eh?
Possibly, but it seems to me that it would depend on more information about what happens with 14 geese.
And on how much "more than 50%" the games are won by 15 geese. (E.g. if it's 51%, that's quite well balanced...)