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Why does GP jump to a random number when breeding? I breed sibling pairs and it's anywhere from 15-25, how are the calculations done?

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A foal's GP is calculated by the average GP and BLUP of your breeding pair, and then includes a random increase proportional to the top GP of the game. If the GP of the breeding pair is further away from the top GP, the bigger the gains. Because of this random increase (it used to be -/+ 4%, but they've changed that not too long ago), you could breed the same pair multiple times and have a different GP in each foal within a specific range. Only with twins could you expect identical GP.

You may like to do a browser search for a Howrse GP calculator to help with any specific figures you're working with.