Maybe only one such reroll for each of us, and they can be transferred to someone else?  It's a little different than saying "X per group" because forums slow down any sort of voting mechanic, but if each player is responsible for one such reroll, they get to make the decision themselves.<br/><br/>The transfer would be something like, if TheHangedMan already used his but seriously needs another, I could say I'm giving mine.<br/><br/>Refreshing on conclusion of an adventure seems pretty fair to me.