Would the player be allowed to flee the random encounter and avoid it altogether? Would the enemies disappear after fleeing from them or would they be persistent?
Could the player exit and then reenter the area where the roll occurs to force more encounters? If it's based on a timer I can imagine someone who works from home, for example, could just leave the game running throughout the day - as ridiculous as it may sound.
I'm just throwing around ideas as if I were tasked with developing this.
