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Yeah. I haven't thought about that mechanic, but I guess my initial reaction is: They are different and have different use cases. I've never really seen a reason to limit myself to only using a fixed set of mechanics. If it works for what you're doing right now, use it. If not, find something...

Here's a link to a Google sheet that calculates information for all the standard die sizes and different trigger numbers for the d20. There's not much explanation, so if it needs more, let me know.

Assuming that after each round, the dice pool is 5/6 as large as the previous round, the number of turns until no dice are left is given by t=log⅚(1/2n), where n is the number of dice. This is a huge approximation because it yields fractional dice numbers for each round, but they largely agree...