2d10 is just 1d20 with some scaling.
Namely, DCs are ~0.5 lower, modifiers are SD(1d20)/SD(2d10) =~ sqrt(2) larger.
(VAR(1d20) is 399/12, VAR(2d10) = 2VAR(1d10) = 192/12, so VAR(1d20)/VAR(2d10) = 399/192 =~ 2. SD is the square root of variance.)
Select "Graph" "At least" to see how the two lines are basically on top of each other. I just moved the average, and scaled modifiers. (I threw in some x10 to make everything integers).
The place where they differ is in the "crit hit"/"crit miss" range; the outermost 5%, which in d20 is the "auto fail on 1" and "auto succeed on 20" area.
For 3d6, the average is the same, but the modifiers are effectively 2x larger than 1d20. So you can emulate the same thing by simply doubling all modifiers from a d20 system (and doubling DC distance from 10).
Ie, for 5e D&D, you'd add (attribute-10) to your d20 check, count proficiency as x2. DCs would double away from 10 (then subtract 1 for rounding purposes).
Strength 18, athletics(+3 prof) against DC 16.
With 3d6 they'd have a +7 against a DC 16, needing an 9+. The P(3d6>=9) is 74%.
Or 1d20+14 vs DC 21, needing a 7+, or 70% success chance.
3d6-2 strength no proficiency against DC 10 is a 37.5% chance.
Or 1d20-4 vs DC 9 needing a 13+, 40% success chance.
3d6 is "just" doubling modifiers and scaling DCs similarly.
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Multiple dice get interesting to me when you start playing with the dice themselves. Simply adding them up, the central region (where almost all rolls end up) is close enough to linear that we can ignore the missing twist (remember, we care about cumulative probability, not chance of an exact roll, and cumulative probability makes things more linear). Only the tails are significantly different, and those can be handled with a crit mechanic that gets the feel you want anyhow.
When you start playing with pairs of dice in your roll doing something (or similar) then rolling more than one die starts being more fun and interesting.
As an example, I have messed around with a percentile system. You roll 2d10, and you read the percentages both directions.
If you succeed with doubles that is a critical success. (so roll two 9s against a 45% difficulty)
If both directions beat your target number, that is a full success. (roll a 6 and a 7 against a 45% difficulty)
If one direction beats your target number, that is a partial success. (roll a 4 and a 7 against a 50% difficulty)
If both directions fail to beat your target number that is a (full) failure. (roll a 6 and a 7 against an 80% difficulty)
If you fail with doubles that is a critical failure. (So roll two 1s against a 27% difficulty).
Because there is very limited correlation between reading your 2d10 in each direction, this mechanic is quite similar to rolling twice. The chance of a crit is 10% of the base chance of a success/failure. If a failure is 0, partial is 1, and full is 2, and you ignore crits, the expected yield is 2 times the target percentage; at low percentages this is dominated by partial successes, at higher by full successes.
You can emulate this with a 1d20 type system by always rolling 2d20 and checking both against the target number, sort of like advantage or disadvantage. Doubles are less likely (5% times success or failure chance) than the above percentile system; if we add in "a critical is either doubles, or an extreme value (20 or 1) together with a full success or failure" you recover roughly the 10% of nominal success rate is crit rate.
You do need mechanics for partial/full successes for this to work. But I think it moves narrative forward better than a standard pass/fail system.
Namely, DCs are ~0.5 lower, modifiers are SD(1d20)/SD(2d10) =~ sqrt(2) larger.
(VAR(1d20) is 399/12, VAR(2d10) = 2VAR(1d10) = 192/12, so VAR(1d20)/VAR(2d10) = 399/192 =~ 2. SD is the square root of variance.)
AnyDice
AnyDice is an advanced dice probability calculator, available online. It is created with roleplaying games in mind.
anydice.com
Select "Graph" "At least" to see how the two lines are basically on top of each other. I just moved the average, and scaled modifiers. (I threw in some x10 to make everything integers).
The place where they differ is in the "crit hit"/"crit miss" range; the outermost 5%, which in d20 is the "auto fail on 1" and "auto succeed on 20" area.
For 3d6, the average is the same, but the modifiers are effectively 2x larger than 1d20. So you can emulate the same thing by simply doubling all modifiers from a d20 system (and doubling DC distance from 10).
Ie, for 5e D&D, you'd add (attribute-10) to your d20 check, count proficiency as x2. DCs would double away from 10 (then subtract 1 for rounding purposes).
Strength 18, athletics(+3 prof) against DC 16.
With 3d6 they'd have a +7 against a DC 16, needing an 9+. The P(3d6>=9) is 74%.
Or 1d20+14 vs DC 21, needing a 7+, or 70% success chance.
3d6-2 strength no proficiency against DC 10 is a 37.5% chance.
Or 1d20-4 vs DC 9 needing a 13+, 40% success chance.
3d6 is "just" doubling modifiers and scaling DCs similarly.
---
Multiple dice get interesting to me when you start playing with the dice themselves. Simply adding them up, the central region (where almost all rolls end up) is close enough to linear that we can ignore the missing twist (remember, we care about cumulative probability, not chance of an exact roll, and cumulative probability makes things more linear). Only the tails are significantly different, and those can be handled with a crit mechanic that gets the feel you want anyhow.
When you start playing with pairs of dice in your roll doing something (or similar) then rolling more than one die starts being more fun and interesting.
As an example, I have messed around with a percentile system. You roll 2d10, and you read the percentages both directions.
If you succeed with doubles that is a critical success. (so roll two 9s against a 45% difficulty)
If both directions beat your target number, that is a full success. (roll a 6 and a 7 against a 45% difficulty)
If one direction beats your target number, that is a partial success. (roll a 4 and a 7 against a 50% difficulty)
If both directions fail to beat your target number that is a (full) failure. (roll a 6 and a 7 against an 80% difficulty)
If you fail with doubles that is a critical failure. (So roll two 1s against a 27% difficulty).
Because there is very limited correlation between reading your 2d10 in each direction, this mechanic is quite similar to rolling twice. The chance of a crit is 10% of the base chance of a success/failure. If a failure is 0, partial is 1, and full is 2, and you ignore crits, the expected yield is 2 times the target percentage; at low percentages this is dominated by partial successes, at higher by full successes.
You can emulate this with a 1d20 type system by always rolling 2d20 and checking both against the target number, sort of like advantage or disadvantage. Doubles are less likely (5% times success or failure chance) than the above percentile system; if we add in "a critical is either doubles, or an extreme value (20 or 1) together with a full success or failure" you recover roughly the 10% of nominal success rate is crit rate.
You do need mechanics for partial/full successes for this to work. But I think it moves narrative forward better than a standard pass/fail system.
