Ok, so, I'm new (level 13) reading the rules (spread through the rules, the FAQ, and some other places), and... I want to make sure I'm not missing anything in the translation.
~ Every day, there is an hour long tournament every other hour that lasts for an hour.
~ Every room with the trophy icon is taking part in the SAME tournament.
~ Also, there's a week-long ELO tournament going on.
~ ELO and ELO (no random) are taking part in the SAME week long ELO tournament.
~ Survivor Type ELO does not count towards the weekly ELO tournament.
~ ELO and ELO (no random) are taking part in the week long ELO tournament, and every other hour, the other hourly tournaments at the SAME TIME.
~ You get the biggest rewards in hourly tournaments by KOing your opponents with pillz left over. You also get really good (albeit halved) points just for leveling characters. In addition the fewer stars (levels) you have when you win, the more points you get (though, this bonus isn't as big as the ones for left over pillz and leveling).
~ You get the biggest rewards in ELO for winning (especially against those with ELO ratings higher than yours).