The dice in Mat's head seem to rattle quite often. I was wondering if there was any discernible pattern to them? Such as "once they start, the event is X hours away" or something like that? He doesn't seem to try to determine anything other than what will make them stop.
No, there isn't any consistent timeline for when they start to when they stop.
They seem to start when events are set in motion that can lead to an important moment in time where a decision must be made or chance has to go his way. They're related to his ta'veren nature, which doesn't really operate on a fixed timeline.
In the series, we see some times where the dice roll for a relatively short amount of time, to essentially spanning entire books. Although the amount of time passing in each book varies greatly, it's clear that there are variation in how long the dice roll.