How does success chance change when a certain die result counts as multiple partial successes?

Question

Dice mechanism: count wins (> 4) of [Mod]d6 (AnyDice).

• Mod ranges from 1 to 10.
• Difficulty ranges from 1-10, 1 being trivial, 3 being moderate, 5 being difficult, and 6-10 being ever increasingly unlikely at all levels of mod.
• Game provides mechanisms for characters to "push themselves" to gain extra dice when their Mod < Difficulty (otherwise they would auto-fail), so a roll can always be attempted at the minimum possible dice pool size.

When counting wins, any die with a result of 6 counts as two wins. How does this alter the probability of success?

Answer 1

Here is a version of that Anydice program that counts 6 as two successes:

You can now get up to 20 successes in theory when you have 10d6. That means that the probablity shifts to larger numbers of successes. It looks like this:

compared to when you do not double on a 6:

For example, for 4d6, you have lower chances for 1 or 2 successes, but higher chances for 3 or 4 successes, and gain chances to even get to 5 to 8 successes.

For your difficulty classes this means the following success rates (rounded):

Class	2d6	4d6	6d6	8d6	10d6
Trivial (1)	56%	80%	91%	96%	98%
Moderate (3)	8%	33%	57%	74%	85%
Difficult (5)	0%	6%	20%	38%	56%
Unlikely (e.g 7)	0%	0%*	4%	13%	26%

Even with the full dice pool and doubling, getting anything that needs more than 5 or 6 successes is really hard. Getting 10 successes at best has a chance of about 2% with all 10 d6.