1) The player understands the rules of when its random. If it is under the surface it will just confuse the player. The player must be willing to accept the outcome, even if unfavorable, because they were hoping for the alternative and were willing to sacrifice the cost regardless. But, one has to consider the psychology of such an action. Would it be when they are comfortable? Of course not. One would only resort to a gamble when all other alternatives have been attempted. Their back is against the wall and there is nothing left to lose. But the ability to then gamble makes all the difference. Because it adds an extra element when the alternative is simply losing outright. The system can still be deterministic. It gives rise to the "underdog story" that permeates most of our imaginative thinking and resonates within unique experiences where a player otherwise probably doomed anyway received a saving grace through a calculated risk that could have made defeat certain.
2) I feel that giving the player levers to influence the outcome adds complexity in its own right too, because now the player can somewhat determine the odds in some way. Do you have the resources? Then use them when it matters. It provides its own sense of strategy. Admittedly, this can lead to high highs and low lows since giving the highest sacrifice of risk and still getting the worst outcome will make anyone a little salty. I love X-Com, and the times I missed on 95% seem impossible..

But, again, as long as that is communicated upfront players who enjoy that unpredictability will still remember the highs when they achieved something against the odds.
^
Still, even the above stated randomness cannot be effective as a whole due to the emotional response of either extreme- which in too high of doses would be either stressful or even boring without a deterministic shell. I would call this nested randomness, which translates to:
Spectrum:
High End: Deterministic - Or at least very very close
Middle High - Slightly random output
Middle - Fully random output
Middle Low - Slightly random output
Low End: Deterministic - Or at least very very close