A party meets a group of monsters. Dice are rolled, maybe some modifiers are tossed in. The winner goes first. I'd like to try a bid system for initiative: the side that's willing to pay the most in hp/luck/whatever, gets to go first. In my rules system it would work something like this:
"You're walking down the tunnel when you suddenly come face to face with some goblins. Anyone who wants to go first needs to pony up one Luck. Otherwise, the goblins get to go first." So the players think, how much of my resources would I give up in order to get the drop on these guys? You either let the other side go first, conserving your luck/energy, or you spring into action, getting the drop on the other side at the cost of lost resources.