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10

Let's first simplify the problem by setting X = A − B. It should be clear that the success rate of d20 + X vs. a plain d20 is the same as for d20 + A vs. d20 + B. Similarly, the success rate of d20 + X vs. 10 is the same as for d20 + A vs. 10 + B. It turns out that, for X close to 0, both of these methods give similar odds, with the roll vs. 10 ...

3

It makes things easier for the side rolling dice Unless the net difference between A and B is equal to -5 when it’s the same or less than -5 when it’s worse. How much better varies with the modifier. Here is an anydice program you can play with. Your intuition that because one has a higher average (both median and mean) was pretty good but that’s only part ...

-1

Subtract success counts from multiple success count pools Roll two pools of dice, and count "successes" a la white wolf, 40K, shadowrun, etc, in both of them. Then subtract the smaller form the larger. This is, in effect, what wargames like 40k are doing when you roll hit pool, wound pool, save pool, etc. Consider the anydice formula output [absolute [...

1

You could use a d100 and have custom intervals determinign the outcome. E.g: 1-20: encounter difficulty 1 21-35: encounter difficulty 2 and so on With this method you can create any distribution you like.

0

Use a different a die for fumble chance. I know this isn't allowed by your constraints, but I found it interesting in my (failed) exercise to devise a unique answer. Starting from 1d6 and working up to 1d20, use a "power" die (or "drama" die, whatever, where a 1 on that die is a fumble). $\begin{array}{|c|c|} \hline \textbf{Dice} & \textbf{... 4 You can exactly simulate a 50% exponential decay with a few "exponentially exploding" d8s. You can generate values from 1-10 with at most three rolls. To treat a d8 as exponentially exploding, use these values for the faces: 1-4 → 1 5-6 → 2 7 → 3 8 → Explode! 3 plus another roll of the die. Or just 4 if you don't want to roll any ... 1 Similar to the dice subtraction suggestion, you could use "distance to the center of a normal-ish distribution", where you use the unsigned distance. As an example "absolute 3d6 - 10": Roll 3d6, add them up, and either subtract 10, or subtract the total from 10, whichever gives a positive number - (anydice link) And here's the graph for "abs 4d6 - 14".... 7 Use integer division; that is, division where you keep only the whole number part. For example, d6/d6 or d10/d10 https://anydice.com/program/1a38f Those are quite easy to calculate, or, since the outcome is very limited, you can just print a cheat sheet with the results. 13 Difference between the highest two of a pool You can use a fairly simple roll to achieve this. You roll$X$d$N$where$X > 2$and$N\\$ is the length of your range. You then take the two highest results and take the difference between them (take the difference so it is positive). You can test the probabilities with this Anydice function: function: ...

39

Steal the "Disadvantage" method from 5e. Take any number of dice, where the highest number on the die is the range you want (i.e. - a d20 for 1-20), and roll them all. Use the lowest value. More dice skew the lowest value closer to 1. Anydice link For a quirkier method that would be mildly more mysterious to any on-lookers Absolute Value and Dice ...

4

You need logarithmic dice. Roll, say, a D100 and a D 6, read the dice with the D6 as (1-2-3 = 0, 4-5 = 1, 6 = 2) as the mantissa (whole number portion) and the percentile as the decimal, so you get a result that looks like, say, 0.69 or 1.24, then use an antilog function (on a calculator, it looks like 10^x, usually) to convert your result into an actual ...

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