[RPG] When rolling with disadvantage what is the chance to get a 1?


When you roll with disadvantage is the chance to get a 1 5+5 for 10% or 5X5 for 25%? Just sat down and rolled 100 times with disadvantage got 18 natural 1s and 0 natural 20s. Still don't know.

Best Answer

The odds of a natural 1 are 9.75% and the odds of a natural 20 are 0.25%.

When you roll 2d20 you have 400 possible combinations of numbers. For a natural 20 there is exactly 1 possible way to get a 20 when rolling with disadvantage (20 on both dice) so the probability of getting that value is 1/400 (or .0025 or .25%)

For a natural 1 there are 3 different possibilities that can result in a 1 when rolling with disadvantage, 1-1, 1-X, and X-1 (where X is not 1). There is 1 way to get 1-1, 19 ways to get 1-X and 19 ways to get X-1. Adding all of those up we get 39 different ways to get 1, so the probability is 39/400 (or .0975 or 9.75%).

As a note your 5% + 5% comes close, but you are double counting the 1-1 combination.