Why does this recursion return 0?

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Your base case is return 0. After the line return n * bounce(n - 1) where n is 1, bounce(0) will be executed, returning 0 and multiplying all your previous results by 0.

Following the calls, we see:

  • 5>=1, so return 5*bounce(4)
  • 4>=1, so return 5*4*bounce(3)
  • 3>=1, so return 5*4*3*bounce(2)
  • 2>=1, so return 5*4*3*2*bounce(1)
  • 1>=1, so return 5*4*3*2*1*bounce(0)
  • 0<1, so return 5*4*3*2*1*0

meaning everything gets zeroed out at the end.
You want the base case to be 1 for that reason.

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