Imagine, for a moment, a 20 x 20 grid of blocks.
Now, pretend that I'm rolling a 13 or higher at D&D at advantage.
I can evaluate this by coloring the blocks 12 or lower on each axis one color, and the remaining bricks another.
So, my chances start at 13, 14, 15, 16, 17, 18, 19, 20, or 40% chance to hit.
With advantage, I subtract my 144 bricks that miss, and get 256. This works out to be a 64% chance to hit. That is the magic of advantage. I also have a 39/400 chance of getting a critical hit - which is similar to the 1 in 10 - with the counting boxes approach (the 39 is because two 20's is the same, mechanically, as 1).
I can repeat this with Disadvantage by noting that there is a 64-brick block from 13 to 20 and putting that over 400. and seeing it takes me to a 15% chance of success and a 1 in 10 chance of a critical failure, and a 1 in 400 chance of a critical success.
Just by counting the bricks.
#dnd #dnd5e #dungeonsanddragons #ttrpg
Note: I'm aware calculus, statistics, etc. exist - this is intended to be an easy to understand, reproducible proof that anyone with a piece of quad rule / graph paper can reproduce in minutes to understand the outcome.
And yes, this works in 3 dimensions as well - or an arbitrary number of dimensions (dice). The theory - I'm rolling a position in a finite n-dimensional grid, where n is the number of dice, and either my position is inside a box or outside works at any number of dimensions.
In general, if you are doing "you can certainly try," instead of just saying no, you should know - whatever the odds - the dice can and will betray you.
Which is why you only ask for or allow a roll as a DM when you want the player to have some chance to succeed. If 1 in 400 is too great of an odds, it is time to just tell the player no.
@sylvietg I've thought about this a lot.
In general, unless there is a level of immediate stress involved I don't call for checks.
I look at the players stats, and if a roll of 10 could succeed I generally lean in favor of auto success.
Outside that I call for rolls.
@sylvietg as for long shots, you have to think about the edge case of nat 20s and rule of cool.
If a hypothetical roll of a nat 30 (nat 20+10) couldn't do it I call no go.
If the player could hypothetically succeed on a nat 30, I'll let them roll for that 5% chance.