Over in this thread,

Mike Holmes wrote: What I had also originally suggested (and I can't remember if it's in there or not) is that the player who gets the edge die should narrate getting some situational advantage to represent it.

That's a good idea. For face to face games. It essentially inserts a situational trait to be called on during the reroll.

I've considered gimmicks that always give the edge die to the side that rolled the lowest number of dice. It seems like it keeps the spirit of giving it to the side that did marginally better (since tying with fewer dice is that) the edge and probably escalates tension better. Did you guys play with that?

Chris