How can I determine the rolling curve of this roll under system?


The system

  • The system relies on Traits and Skills (which both range from 0 to 6).
  • Players rolls a number of d6 equal to the Skill they’re using.
  • Any dice result equal or under the related Trait value is considered a success.

Example : Bob attacks an orc. He has a Melee Skill of 3 and a Strength Trait of 4. He rolls 3d6 and the results are: 2 5 3. He has 2 successes.

Special cases

  • The result of a dice is 1, the dice counts as 2 successes.

Example : Bob attacks again. He still rolls 3d6 and the results are: 1 3 6. He has 3 successes.

  • The character does not have the required Skill, he rolls 1d6, only a result of 1 counts as 1 success (instead of 2), other values are failures.

Example : Bob tries to parry. Since he does not have the Parry skill, he rolls 1d6 and the result is a 2. He fails.

My questions

How can I make sure that progression is "coherent"?

How are highly skilled characters better than those with good Traits? Is the last assumption even correct?

What would the success curve (skill over trait over difficulty) look like?

I’ve tried various things over excel and anydice but cannot comprehend the statistics or get formulas to work.

Finally, sorry for any grammar mistake, english is not my first language and thanks for the help.