THEORYMATH: Can you answer this for me?

[Visigani]

the Destiny Domain has a spell called "Choose Destiny" that allows you to roll a second time and take the better of two rolls for any d20 roll.


In terms of percentage, how much does this increase your chances for success on a given roll. In other words, if this were to add a fixed bonus to a d20 roll, what would that fixed bonus be?

 

[kitcik]

In terms of percentage, how much does this increase your chances for success on a given roll.?

It depends on what you need to roll.

Let's say you need an 11 or higher to succeed. That means there is a 50% chance of failure on one roll. The chance of failing both rolls is 50% x 50% or 25%, meaning the chance of success has increased from 50% to 75%.

Let's say you need a 17 or higher to succeed. That means there is an 80% chance of failure on one roll. The chance of failing both rolls is 80% x 80% or 64%, meaning the chance of success has increased from 20% to 36%.

In other words, if this were to add a fixed bonus to a d20 roll, what would that fixed bonus be?

This increased chance of success is NOT equivalent to any fixed bonus - it is dependent on the roll needed for success.

 

[Patryn of Elvenshae]

Kitcik's right about the difficulty of answering your initial question.

In a more general case, however, you can talk about the average improvement in your roll.

A single d20, over the long run, averages a result of 10.5.

2d20-L (2 d20 drop Low), over the long run, averages a result of 13.825, or roughly a +3.3 bonus.