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In Generations III and IV, the Trainer Card also carries the Trainer's
score. A Trainer's score offers no specific purpose in the game and
appears to be only aesthetic. The score begins at zero and increases
every time a score-altering event occurs.
Berry is picked +1
Battled against a wild Pokémon +2
Battled against a Pokémon Trainer +3
Pokémon Egg is hatched +7
Pokémon is traded +10
Pokémon is evolved +20
Flag is obtained in the Underground +34
It carries on going until 9,999
Source: My points are 9,999 and has never risen since.