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Doubles Pikachu's Attack and Special Attack stats in battle. If Pikachu or Raichu breeds while holding Light Ball, the Pichu that hatches will know the move Volt Tackle.
Light Ball can send Pikachu's Attack and Special Attack stats to sky-high levels—if you are mad enough to use Pikachu competitively, then this is the only item you should be using. This allows Pikachu to go mixed and dent many Pokemon that don't resist its STAB Electric-type moves, and actually present something of an offensive threat. Pikachu is quite slow and frail, though, so it can be tricky to sweep with it.
None in-game - obtain via Event Pikachu.