I'll take a stab at this.
Now, RNGesus is an interesting guy. Even when he decides to be nice to you, he still messes with you a bit.
Every one is born with a Special stat set at 0. What this means is that RNGesus hasn't done anything nice for you, ever. And because of this, he's more likely to do something nice for you in the future. But again, even if/when he decides to be nice, he's still mean.
So you find your first treasure room. Obviously, you pray to RNGesus for good luck before entering. As you enter, he has a decision to make.
Does he give you a sweet item? Or a shit item?
And since there's so many items in game he can't decide which to give you so he decides to roll a die. It's a special die, in that the amount of faces it has is tied to the amount of items that a) you have unlocked and b) are in the Item Room pool.
So let's say there are 50 possible items. He rolls a 50-sided die. At this point, there's as good a chance of getting Polyphemus as there is of getting The Poop.
If his die ends up picking a non-special item, he goes ahead and gives it to you. Your Special stat stays the same, because he was not nice.
If, however, it ends up picking a special item, he decides to reroll a d100, just to mess with you. He looks at your special stat, sees that he hasn't done anything nice for you, and decides that you deserve this special item, but he still doesn't want to just give it to you. So he decides that, if he rolls a number from 1-83, he'll give it to you. If he rolls a number higher than that, he'll pick a different item.
Let's say he rolls a 36, so he gives you the item. Now he's done something nice for you, so he increases your Special stat and it's less likely in the future that he'll do something nice.
You're on the next floor and you find another item room. You enter it, and the process repeats.
However, this time, if his die picks a special item, he looks at your special stat and realizes that he was just nice to you! So he decides that you probably shouldn't get another special item (but he'll still give you a chance). Because your Special stat is one, he plugs it into his handy equation and comes to the conclusion that if he rolls a number between 1-23, you'll get the item; otherwise, you won't. If you're unlucky, your Special stat stays the same; otherwise, it increases by one. The process repeats for every time an item spawns.
Note: This may be out of date
RNGesus knows that not all special items are created equal. Because of this, he doesn't really consider giving you My Reflection as being super nice, so he doesn't change your Special stat by as much. He's still less likely to be nice to you in the future, but he's much more likely to do so than if you had gotten a better Special item.
Note: This is for sure out of date; Bloody Lust is no longer a special item
In the original game, Samson was pretty stacked from the start. Since he started off with such a good item (Bloody Lust), RNGesus figured that he didn't have to be as nice to Samson as he was to everyone else. So he set his starting Special stat at 1, making the chances of special items spawning much less.
That's pretty much the basics. There are some nuances to it (to be honest, I'm not entirely sure how Devil Deals work with the Special stat) but this should give you a solid foundation.
Sorry if it's a bit long.