There are varying shades of luck and even methods to apply randomness. One way of classification:

  * you can do what you want, but success chance is random
  * action choice is random, success is deterministic

I prefer the second approach. Your options are limited, but whatever you do, works. I think eurogames use the second way more often. Yes, the term "ameritrash" is intentionally derogatory (I didn't come up with it). Can you propose a better term ?