JDNYC wrote:
If you have a +1 to hit added to your die roll after all calculations are done, it's a 5% increase. It doesn't matter how you look at it or try to add other known or unknown variables (like your lottery example.)
Everyone has to roll a d20 to hit. A d20 has 20 sides. That means every time you roll a d20 you have an equal chance of getting one of those sides, regardless of the amount of times you roll it. Adding a +1 to that roll increases the number of sides that is counting as a successful hit by 1. That's an increase of 5%. 100% (total value of whole)/20 sides = 5% per side.
Let's see if this example is better:
You have a chicken and eat it.
I give you another chicken. You eat it too.
You say "I only ate one chicken more".
I say "You have eaten today double the food you had".
Are you right? Yes. Am I right? Yes.
Now let's say I don't know how many chickens you have eaten. If I give you one chicken, you can still say "I only ate one chicken more". But what determines the utility of a new chicken is how many chickens you ate before. If you didn't ate anything before, that chicken is really meaningful to calm your hunger; if you ate 20 chickens (well let's say 19 to avoid corner cases of critical chickens), the new one is not very useful to you.
So... if you have a 20-sided die, and you only hit with a natural 20, and then I buff you for a +1 to hit, you have 5% more chances of hitting than before, but you ALSO have doubled the die sides that mean a success hit.