Don’t get me wrong, I’m not against randomness at all. It’s just pure randomness that is a fun-killer. If you don’t provide a way to tip the balance in your favor, it just seems unfair, because you remember losses easier than wins. Human reaction.
Example : Fallout combat system for ranged weapons with a hit ratio that you can increase by getting closer to the target, using a scope or taking more time to aim. All those options make risky shots a choice from the player, not an unfair random number generation by a senseless machine.
Counter-example : Item collection in My Country. Even if the game provides the list of actions that may give you a certain item, you can’t be sure you’re doing the right thing or the list is accurate unless you finally get the item. As long as you don’t get it, you’re frustrated because you don’t really know why it’s not produced. Is it the chances that are low by design, or is the list of actions to get the item wrong ?
Another example is Battle for Wesnoth combat system based on a Hit ratio. Any unit has fixed chances of dealing a fixed amount of damage, so it’s all or nothing. Numerous posts have been written on the game forums by players complaining that the random number generator (RNG) was favoring the enemy at their expense. The game developer team even hired a mathematician to prove that the RNG was unbiased but it didn’t help, complaints kept flowing. Of course, they missed the point, which is that a miss is more psychological harmful to the player than a hit is. After all, a warrior is supposed to hit its enemies.