Using Advantage, Disadvantage, Expertise and "roll and compare" mechanics allows for improving hit chance and crit range, but doing so with dice has a fun, tactile side to it; simply having +1 to hit or "18-20 crit" on your sheet doesn't give you the same kind feel.
I also like Advantage/Disadvantage better (particularly as I have defined it in this game) rather than just bigger and more numbers being added to your roll. The nice thing with the "compare and contrast" mechanics, is that they can be layered over top of Advantage/Disadvantage, without skewing the numbers the way simply adding to the roll would. It also helps to mitigate the downside of Disadvantage, and further minimize the randomness of Advantage.
For example, if you're using "roll and compare" with a d8:
- With Disadvantage, you stand a fairly good chance of matching your d8 roll, assuming you don't roll doubles with the d20s to begin with. So while statistically the Disadvantage will give you a much higher chance of rolling unsuccessfully, that d8 can potentially turn that around
- With Advantage, you gain another safety net against bad rolls, without the swinginess that greatly expanding crit range (by adding dice) would bring into the game.
Trade-offs also work to keep things interesting; even something as simple as Power Attack is more interesting when the penalties and bonuses are subject to a roll of the die, rather than being known, flat numbers. There are limited ranges though, and the math isn't too tough to figure out, for those who want to crunch the numbers and optimize their actions.
Basically, I think it all plays off of that added rush from the "gambling" aspects of it. More dice-rolling means less of the same outcomes over and over, and more randomness -- but it has to be tempered by the design elements, to keep the math within acceptable ranges. This is what makes the process of design long and challenging, but also fun.
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