I found a question a while back on a forum while searching for an answer. The question was about optimizing an archer build in D&D Fifth Edition. Back in the 2E and 3.5E days I was a min-maxer, because those systems lent themselves really well to that style of play. 5E can as well, though not to the same extent.
Anyway, the long and short of it is I ended up diving deep down a rabbit hole that I haven't escaped from (and likely never will.) The result? I rediscovered my lost love of dice rolls.
And that's just one page! Of dozens!
So why roll all these dice, eh? Why not just use a random number generator or something, hmmmmmm?
Dice rolling is different from random number generation. There's the physical properties of the dice themselves that need to be taken into account. The amount of bounce, the friction or lack thereof, the material the dice are made of, any imperfections they might have, the surface upon which the dice are rolled, the way the dice are thrown from the hand, whether one is using a dice tower or not, a dice tumbler, etc.
Lots and lots of variables.
Ultimately I decided that I can't trust that the calculations for overcoming a certain DC (Difficulty Class) or AC (Armor Class) will be reflected by a computer's random roll compared to my random roll on the table.
I know, I know, it sounds crazy. But it's what I care about for some reason, so... read on if you want!
A QUICK NOTE: I'm not going to cover the basics of D&D in this post. Maybe somewhere down the line I will. Just keep in mind that for nearly everything in the game, the DM will ask the players to roll a 20-sided die and the results will be determined from there (after several positive or negative modifiers.)
Let's say I want to cast a spell I don't know from a scroll I found. There's a mechanic for doing that, being an ability check against a DC set by 10 + the level of the spell. A level three spell would be a DC 13, a level 5 spell would be DC 15, and so forth. My character will have a 16 in Intelligence for this exercise, resulting in a modifier of +3. So I roll a d20 and add 3 to the result to see if I can cast Fireball from a scroll.
Sweet, an 18 is pretty good!
So my total is 21, which definitely clears the DC of 13 for a third level spell. That means my first level character just successfully cast a third level spell, which he shouldn't be able to do until level five!
That's how a regular roll usually goes, though. So what can be done to alter this roll? Gaining levels works; every four levels or so a character usually gets the chance to increase an ability score by two or take a feat. Increasing an ability score by two grants an additional bonus to that ability's modifier. So 14 is +2, 16 is +3, 18 is +4, and so on. But what else can be done?
Well, there's an easy advantage to gain while rolling dice, namely the Advantage mechanic. At its purest, a roll with advantage means you roll 2d20 and take the higher of the two dice.

Disadvantage means you take the lower of the two rolls.
One rolls with advantage when the DM says to roll with advantage, as determined by the very same DM. Likewise, the DM decides when you roll at disadvantage. There are ways to play the system though, and insure those advantaged rolls.
For instance, if a character is hidden from their target's sight and manages to hit them with a ranged weapon, that attack would have advantage. However, if the attack were made at long range, the roll would have disadvantage that counteracts the advantage, meaning the attack is made normally.
A rogue, level 2, can use the class feature Cunning Action as a Bonus Action to hide during combat. If they hide successfully, they get advantage on their next attack. They also get a sneak attack, which does lots of extra damage which gets better with higher levels.
If you happen to be a spellcaster and you have access to Enhance Ability, you can give yourself advantage (and another small bonus) to any ability checks or saving throws with an ability chosen at casting. There are many, many other ways to reliably gain advantage or to counteract disadvantage.
So by taking all of these things into account, I can determine how well my character concepts will perform at the table.
But really I just like rolling dice and I need a reason or something.
There's more where this came from, let me know what you think! I'll try and respond to comments, but my family and job have me pretty busy so forgive me if I take a while to respond to you.