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You can acquire Apricorn items by shaking berry trees. Try the Forest of Focus.

If you feed the Cram-o-matic 4 coloured Apricorns, you’ll receive one of many Poké Ball items–the ball you get will be random. To determine what balls you may get, first you need to know that each of the 7 Apricorns has its own list of possible balls. Please refer to the tables below.

If you use the same Apricorn 4 times, you’ll only get the Poké Balls listed for that specific Apricorn. Meanwhile, if you mix and match different Apricorns, the game will randomly choose one of the lists–proportional to the ratio of Apricorns.

For example, if you combine 3 Red Apricorns and 1 Yellow Apricorn, there’s a 75% (3 in 4) chance of getting a ball from the red list and a 25% (1 in 4) chance of getting one from the yellow list. Your chance of getting a 1% rate item is still 1%, but you’re 3 times more likely to get a Level Ball (red), rather than a Moon Ball (yellow).

Note that giving the Cram-o-matic anything less than 4 Apricorns (eg. 3 Apricorns) will generate an item from the General Recipes instead.