I'm working on a homebrew system. The base mechanic, without getting too involved on specifics, is roll a pool of d6s (1–5) and compare each vs. a target number (Generally 4–6); any that are equal to or higher count as a success and the more successes you get the better.

That is easy to calculate. What I'm having trouble with is how another proposed mechanic will affect the probabilities. If you are allowed/forced to add some (one or more) extra dice to the pool and ignore the same number of lowest results (for beneficial circumstances) or highest results (for detrimental circumstances), how will that affect the likelihood of getting a certain number of successes?

An example for clarification: You would roll to accomplish something and the appropriate stat has 3 dice. Every die that comes up 4+ is a success. 1 is more a technical success that comes with downsides, 2 is a decent success, 3 is success and then some etc. This aspect is already working as intended. The mechanic I would be introducing is either helping or hindering a roll by adding a die and dropping either the lowest or the highest respectively. E.g. An ally helps the character so the 3d6 now becomes a 4d6 with the lowest result being ignored.

I'm working on a homebrew system. The base mechanic, without getting too involved on specifics, is roll a pool of d6s (1–5) and compare each vs. a target number (Generally 4–6); any that are equal to or higher count as a success and the more successes you get the better.

That is easy to calculate. What I'm having trouble with is how another proposed mechanic will affect the probabilities. If you are allowed/forced to add some (one or more) extra dice to the pool and ignore the same number of lowest results (for beneficial circumstances) or highest results (for detrimental circumstances), how will that affect the likelihood of getting a certain number of successes?

An example for clarification: You would roll to accomplish something and the appropriate stat has 3 dice. Every die that comes up 4+ is a success. 1 success is more a technical success that comes with downsides, 2 successes is a decent success, 3 is success and then some, etc. This aspect is already working as intended. The mechanic I would be introducing is either helping or hindering a roll by adding a die and dropping either the lowest or the highest respectively. E.g., an ally helps the character, so the 3d6 now becomes a 4d6 with the lowest die result being ignored.

I'm working on a homebrew system. The base mechanic, without getting too involved on specifics, is roll a pool of d6s (1–5) and compare each vs. a target number (Generally 4–6); any that are equal to or higher count as a success and the more successes you get the better.

That is easy to calculate. What I'm having trouble with is how another proposed mechanic will affect the probabilities. If you are allowed/forced to add extra dice to the pool and then drop the highest/lowest die from the result for each die added this way, how will that affect the likelihood of getting a certain number of successes?

I'm working on a homebrew system. The base mechanic, without getting too involved on specifics, is roll a pool of d6s (1–5) and compare each vs. a target number (Generally 4–6); any that are equal to or higher count as a success and the more successes you get the better.

That is easy to calculate. What I'm having trouble with is how another proposed mechanic will affect the probabilities. If you are allowed/forced to add some (one or more) extra dice to the pool and ignore the same number of lowest results (for beneficial circumstances) or highest results (for detrimental circumstances), how will that affect the likelihood of getting a certain number of successes?

An example for clarification: You would roll to accomplish something and the appropriate stat has 3 dice. Every die that comes up 4+ is a success. 1 is more a technical success that comes with downsides, 2 is a decent success, 3 is success and then some etc. This aspect is already working as intended. The mechanic I would be introducing is either helping or hindering a roll by adding a die and dropping either the lowest or the highest respectively. E.g. An ally helps the character so the 3d6 now becomes a 4d6 with the lowest result being ignored.

So I'm working on a homebrew system. The base mechanic without getting too involved on specifics is roll a pool of d6s (1-5) and compare each vs a target number (Generally 4-6) any that are equal to or higher count as a success and the more successes you get the better. This is easy to calculate. What I'm having trouble with is how a proposed mechanic will affect the probabilities. If you are allowed/forced to add extra dice to the pool and then drop the highest/lowest die from the result for each die added this way how will that affect the likelihood of getting a certain number of successes?

I'm working on a homebrew system. The base mechanic, without getting too involved on specifics, is roll a pool of d6s (1–5) and compare each vs. a target number (Generally 4–6); any that are equal to or higher count as a success and the more successes you get the better.

That is easy to calculate. What I'm having trouble with is how another proposed mechanic will affect the probabilities. If you are allowed/forced to add extra dice to the pool and then drop the highest/lowest die from the result for each die added this way, how will that affect the likelihood of getting a certain number of successes?