Tournaments refresh every 24 hours. You will be put in a bracket of 99 other players randomly, and that bracket will be gone and reformed with another 99 players randomly the next day.
Every time you fight in the Arena/Pit for either Unfair Challenge or Versus modes, you will gain Pit Points. Pit Points are basically just another word for your tournament points that are reset the next day along with your bracket.
Depending on how many Pit Points you have when the clock strikes for reset will determine how many exclusive Pit rewards you receive the next time you log in. The tiers are Gold/Silver/Bronze, and being higher within any of those ranks will not yield more items than being lower in one of that same rank IE. a "high" Gold player will receive 3 items, and a "low" Gold player will receive 3 items.
You WILL receive Pit Points even if you lose a Versus battle, or if you lose the Unfair Challenge after winning the first fight.