Lightning thief: what is percys plan to get past cerberus? why dosnet it work?

Percy's plan was to throw a stick for Cerberus to fetch but it doesn't work since it fell into the river Styx. Then annabeth came in and used a ball to play with Cerberus and it does work since she went to a dog obedience class. This allows Percy and Grover to sneak past Cerberus