What are the chances that Peach pulls out something rare?

Question

In Super Smash Brothers Mêlée (SSBM), Princess Toadstool (Peach) is a playable character. She has the ability to pull out turnips with her down special move, which she can throw as a projectile item. While the most common turnips that she pulls out are simple, happy-faced ones, sometimes she pulls out unhappier turnips which seem to do more damage, and even Mr. Saturns and Bob-ombs. How does this work? In particular, is it possible for her to pull out an indefinite amount of Bob-ombs in a row, or is there a limit, like Mr. Game-and-Watch's Judgment Hammer in either Mêlée or Brawl?

Answer 1

According to this, the chances for getting things work like this:

• First, a check is made to determine whether you get a turnip or an item. The chances of getting an item are 1/128; much rarer than any of the turnips.
• If you get a turnip:
  • The smiley, bored, sleeping, shocked, and happy turnips have respective chances of 35/58, 6/58, 5/58, 3/58, and 3/58. They all deal the same damage so altogether the chance is 52/58.
  • The winky turnip has a 4/58 chance. It deals slightly more damage (I don't have the numbers for this, since item throws deal varying damage based on their speed).
  • The dot-eyed turnip has a 1/58 chance and deals pretty good damage, something like slightly over double a regular one.
  • The "stichface" also has a 1/58 chance and will deal ridiculous damage (typically 35% or more).
• If you get an item:
  • There is a 3/6 chance of getting a Mr. Saturn. While he doesn't do much knockback, he does eat shields.
  • There is a 2/6 chance of getting a Bob-omb. Generally considered the "holy grail" of turnip pulls.
  • There is a 1/6 chance of getting a Beam Sword. People are mixed when they get this since it's just an okay item in Melee.

Unlike G&W's Judgement, any pull can follow any other pull; the game does not care what you got before. It is possible though ludicrously unlikely to (for example) get two Bob-ombs in a row.