This is going to sound absurd given recent posts upon the subject of dice, but lest we forget that I use dice to play D&D every day, I do have some opinions on their effect in the game.
I see the poll I ran last week ended with 52% of the votes asserting that watching other people roll dice produced a lot of physical effect. I'm not certain the actual 'watching' is what people answered, but be that as it may, I'm willing to go along with there being psychological effects. I'm simply not sure it takes dice to get those effects ... but for the benefit of the majority, I'll talk a bit about the psychological effects I try to cause.
I don't know how I adapted to using dice to promote terror. It seemed to be something that came naturally. There is a sense of power involved in pointing to a random person during a game and commanding them to "roll a d6" without explaining why or what the die is for. The less they know, the better really. They should be able to figure out that its either initiative or surprise - but either way, the fact that is it probably one of those is a bad thing for the party, isn't it? Particularly for those voodoo artists who think they can make a d6 roll high or low at will. If they don't know what the die is for, which should they hope for? Is it to see if they are surprised, or is it to see if they surprise? They just don't know.
It is a powerful moment ... like god putting the finger on a player. "ROLL A D20, MINION," booms the voice. The chosen player feels a moment of tension as they search for the d20 of their choice. The fate of the whole party depends upon this roll. The other players lean in to see what will come up. The DM looks on benignly, his face revealing nothing. The die tumbles and falls, revealing a 17. The DM says "Oh." He does not explain the exclamation. He shakes his head, consults a book, then proceeds forward with whatever had been happening.
Infuriating, compelling, emotional. This is what dice give you.
For those who might think I don't understand this, I could only suggest you play in my world. Drama is built upon such things - and I love the production, manipulation and escalation of drama. It is a hammer banging on a drum shifting up to ramming speed; it is the unexpected interloper; it is the tiny thing you didn't notice that is just about to kill half the party. It is the statistical chance that the die will save the party vs. the statistical chance the die will kill the party. It is the HEART of D&D ... mwa-hu-hahahaha!!!!
Or, you know, it's just dice rolling on a table.
Don't get me wrong. The dice manufacture player involvement and perceived player agency. I'm just not sure they are the only way both can be accomplished.