These are the rules for crimefighting, exactly as stated in-game:

Select 5 Superpower Cards to begin the game. Each villain has their own hand of 5 cards (though unlike you, they may have multiple copies of the same card!). Learn what each villain uses, so you know the best cards to counter theirs! Each turn, you simply choose one of your cards to play. You'll have to read the INFO on the card items to know what each card does. You can't check it during the game! Cards can never be played twice in a row, so they will be disabled for 1 turn after use. Your card and your opponent's card take effect simultaneously. However, if you play the right type of card, you will cancel out your opponent's card! Remember this chart:

Crimefight rules

It's like Rock, Paper, Scissors, but with a fourth item. A lemur perhaps. If you play a card, and your opponent plays a Lightning card, your card is the only one that has any effect this turn! if you play Lightning and your opponent plays , both cards take effect, because those two elements do not directly interact. So always try to play the element that will beat what your opponent plays. it'll be like they never even get a turn! The goal is to reduce your opponent's Life to zero. Do that, and you'll win a prize! But whether you win or lose, or even if you run away mid-fight, the 5 cards you played the game with will be used up. So go out, find some cards, and fight some crime!