I love RNG. I do not like the fixed numbers at all. That's entirely predictable, and just no fun. This topic includes all forms of RMT so I'll just go with combat for now.
Combat: Every time a player enters combat, they should do so knowing that things could go terribly wrong. Or very fortunately right! But they should also have an idea of their potential victory, or defeat. And it all should be based on your ability vs. your opponent's.
I like the idea of randomized hit chances and damage, a base "fixed at present" number plus a randomizer. And I like the idea of Critical Hits and Fumbles. But all of this should be based on the current skills and stats. (I love the idea of adding stats to the formula, so an attack might be based on weapon skill plus Dexterity, Strength, or Agility, depending on the weapon. And that's compared to the defensive skill, Parry Skill plus Dexterity or Dodge Skill plus Agility. And then you compare the two and get a chance to hit. Similarly you do damage, mage spells, etc.)
Then Criticals come into affect. They too should be weighted by skill and ability from both sides.
So you have the usual attack chance and damage (both partially randomized), modified by the opponents abilities, and then the possibility of Crits that can make or ruin your day (but based on your known foundation of Skills and Stats. And ALL of the above is already modified by your, and your opponents, choices, skills, and natural ability in the form of Stats in coming up with the Die Roll.
So equal opponents have a basic, smallish chance of a Crit or Fumble, weaker opponents give you a better chance, and stronger opponents a weaker chance. This gives the player plenty of opportunity to recognize their chances of victory or defeat, and also the knowledge that they can always win, given luck vs. the opponent's power. As in "you mean there's a chance?" and "your chances aren't good."
Just for fun, lets add in "Luck, Be a Lady tonight."
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Once upon a time....