I kind of like Betrayal at House on the Hill's method better.
Each whenever. You add a d6 to the dice pool and roll. If the total is over X the thing happens.
If you remove the d6's, then you could be waiting for many turns to roll that last 6. It could be 1 turn or 100 turns. It would be pretty rough if you plant a bomb and roll a Yatzee on the next turn.
By adding dice, you have a minimum and maximum time frame, and more of a bell curve as to when it will happen.
And if you want more/less uncertainty, you can increase/decrease the die size.