Frank's discussion is spot on ... and, yet, I find myself in sharp disagreement with the subject title.
Clearly he addresses those who, for example, given an particularly adverse spate of hands, are inclined to question the randomness of a machine. His point is very apt, as it is for any number of other examples.
However, in my own play, I'm very keen on understanding (and attaining an acute gut grasp) of a very specific aspect of randomness -- "variance" (a measurement of the dispersion of random events).
I see a sharp intuitive sense of the relationship between variance and bankroll risk as being a key element of satisfying play (yielding an insurance that play expectation and reality are reasonably in synch). (As an aside, I really refer specifically to overall result dispersion rather than just the single point statistic "variance", which at times needs to be tweaked to be of practical use.)
For example, when I play a 50-play or 100-play machine, I want to promptly evaluate an appropriate risk level that optimizes my coin-through within the bankroll constraints with which I'm comfortable. Likewise, when I approach any other unfamiliar play with which I'm not totally familiar, it's equally important that I acquire a firm grasp of the related variance so that I can size my wagers accordingly and ideally avoid an after the fact "buyers remorse" due to loss experience in excess of comfort levels.
It's not my intent to belabor the point ... just to suggest that there are aspects of randomness that adept players will seek to understand.
- H.
