# Is one Proficiency die better than two Ability dice?

My GM often allows me and the other players to roll one skill or another for various checks (Coordination or Athletics is a common option; the character either balances across an obstacle or bypasses it with brute strength).

My character has three Ability dice in Athletics, and one Proficiency die and one Ability die in Coordination. Subtracting the one Ability die in common between those skills, I am left with the question; which is better? Two Ability dice or one Proficiency die?

I am defining better as "Which option is most likely to produce the most Success." I am not concerned with the amount of Advantage produced, and I am only concerned with Triumph in so much as it counts as a Success.

For the uninitiated in FFG's Star Wars, the dice have no numbers, only faces with outcomes on them. The outcomes available on Proficiency and Ability dice are Success, Advantage, and on Proficiency die, Triumph.

An Ability die is a d8 with the following faces:

• 1 Blank face
• 2 faces with one Success
• 1 face with two Success
• 2 faces with one Advantage
• 1 face with one Success and one Advantage
• 1 face with two Advantage

A Proficiency die is a d12 with the following faces:

• 1 Blank face
• 2 faces with one Success
• 2 faces with two Success
• 1 face with one Advantage
• 3 faces with one Success and one Advantage
• 2 faces with two Advantage
• 1 Face with Triumph (which counts as Success, but does addition, unrelated, things)

If we're utterly only paying attention to Successes, and treating Triumph as one Success, then we can just write out the dice like this in AnyDice format:

ABIL: d{0, 1, 1, 2, 0, 0, 1, 0}
PROF: d{0, 1, 1, 2, 2, 0, 1, 1, 1, 0, 0, 1}

output 2dABIL named "2x Ability"
output 1dPROF named "1x Profession"


If we produce an at-least graph of the results, we see that 2 Ability dice is a pretty clear winner over 1 Proficiency dice. They have a 75% chance of at least 1 success (vs just 66.66...% chance for 1 Proficiency), a 37.50% chance for at least 2 (vs 16.66...% chance), and from there they just get better with the ability to hit 3 and 4 successes.

Making things far more transparent: 2 Ability dice will equal or exceed 1 Proficiency die 77.08% of the time (see here).

• Beat me to it by 5 AnyDice programs... (I got 7d87) – MrLemon Mar 8 '16 at 9:01

Two ability dice are better.

An Ability die produces an average of 5/8ths of a success each time it is rolled (there are 5 success symbols, and 8 faces).

A Proficiency die produces an average of 10/12ths of a success each time it is rolled.

As such two ability dice will give you an expected value (in successes) of 5/4ths while one proficiency die will only give you an EV of 5/6ths.