Topic: Bell curved RM:)

[Jengada]

MisterK hit a very important point - there is a big difference between a bell curve in the raw roll and one in the action outcome (maneuver, attack, whatever). Looking specifically at the attack tables, you can monkey with the dice all you want but the nature of criticals, both their result distributions and the cumulative impact they have, is exceptionally non-Gaussian/nonlinear and will whack all of the raw roll normalization like a +10/round bleed, stunned no parry for 6 rounds crit.
The maneuver tables (RM2) are also exceptionally non-Gaussian as difficulty progresses from Routine to Absurd. There's a huge jump from Light to Medium. If you change the dice used and make them more Gaussian, that jump could get bigger or smaller. It will depend not only on the mean of your NdX+Y die choice but also the standard deviation of that.
In the end, you face the really high likelihood that "fixing" this will result in different die combinations for arms attacks, base attack spells, elemental attack spells, and maneuvers. And unless play-test the bejesus out of it like ICE did, drawing first on their original play-test groups, and then most recently using the power of the much bigger beta-test group for RMU, you're likely to suddenly find a player rolling something totally outside what you intended.
(I replaced stats and stat gain rolls 6 years ago with what seemed a very streamlined system. It worked well until, with the party at 11th level, it became clear it needs major repair. Once bitten, twice shy.)

 

[MisterK]

It would be easier to tinker with if all actions, including combat, required a single roll for resolution. It would be even easier if all actions had the same resolution mechanism (e.g., 101+ is a success, 100- is a failure, and you get an additional degree of success/failure per, say, 25 points above or below the threshold).

With a standard mechanism, and knowing the impact of skill modifier, you can start tinkering with the dice to get the bell curve you want (or don't want, if you don't like bells).

Right now, I'm halfway through with my RM hack : I have the single resolution mechanism, but damage still requires a second roll (I removed the RR roll and integrated the resistance in the casting roll, and you only need one roll regardless of how many skills are involved in the action - there is one main skill, and the others act as props). Oddly enough, the basic mechanism is not bell-curved (I still use a linear result), but the damage roll can be.

[Thot]

[...]
I want a bell curve in the rolls, so that you can be a bit more certain what the outcome of your actions can be. I don't want a general increase in successes.

My personal solution to that  is to just always allow any character to just "take the 50" instead of rolling D100. You forego the chance for a high roll, but also don't have the risk of unusual failure that way. Works like a charm.

[pantsorama]

I have thought about this a lot, and the solution I'd like to try is 4d30, and reroll any 1s or 30s - Note: not reroll all of them if there is a one or 30; roll just the di(c)e that rolled the 1(s) or 30(s).  For 1s you subtract from your total, 30s you add (with both rolls openended upwards if you roll a 30 on a reroll).  The keeps the long tails, and is only slightly more complicated at the table but that is easily automated away.  This has a ~12% chance of an openended roll, BUT it is not the full roll like in RM, so the higher chances is offset by the lower bonus/consequence.

I'd also leave success at 100 (maybe 110?), keeping partial at 76 (81?), but "absolute" I would lower to 150.  Same on the low end. This makes it basically unreachable for low skilled, but more reachable for the highly skilled. 

The problem with this is now how to give out skill points per skill rank.  When you work on the bell curve just starting out at average, small changes have outsized effects.  I haven't figured out the solution, but a +5 per rank is way too much in this system.  If you start at the middle of the bell curve, +5 to your roll gives you +10 chance of succeeding.  I haven't played around with it too much, but +3,+2,+1 is what I would try out at first. 

You can also even still keep the unusual result on the UM 66.  It will occur about 2% of the time, but I am OK with that.  If that is too high for you, just use a roll of 42 (1.2%), 69 (1.8%), or even 40 or 84 - which is right at 1%

That's the gist - and things like Knacks and talent and professional skill would also need a strong review.  I am eager to give it a look see, but I need to get my RMU game running first.

[Onirim]

You can achieve this with 3d10 in one color and 1d10 in another color.
Roll 3d10, take the middle result dice: this is your first digit.
In the same time, roll 1d10 (with the other color): this is your second digit dice.
So you have a bell curve (from high-low roll) for your first digit, and it's the more important thing. And you always get your second digit result.

Example:
3d10 > 3, 5, 8 = 5
1d10 > 9 = 9
So you've rolled a 59!

[jdale]

You can see the distribution that gets you by entering this in anydice.com:

output [middle 1 of 3d10]*10 + 1d10

It's not very bell-curved if you compare it to 3d100 / 3.

[jdale]

I have thought about this a lot, and the solution I'd like to try is 4d30, and reroll any 1s or 30s - Note: not reroll all of them if there is a one or 30; roll just the di(c)e that rolled the 1(s) or 30(s).  For 1s you subtract from your total, 30s you add (with both rolls openended upwards if you roll a 30 on a reroll).  The keeps the long tails, and is only slightly more complicated at the table but that is easily automated away.  This has a ~12% chance of an openended roll, BUT it is not the full roll like in RM, so the higher chances is offset by the lower bonus/consequence.

Ignoring the open-ended aspect, that gives a range from 4 to 120, with a mean result of 62, which is a bit of a departure.

[pantsorama]

I have thought about this a lot, and the solution I'd like to try is 4d30, and reroll any 1s or 30s - Note: not reroll all of them if there is a one or 30; roll just the di(c)e that rolled the 1(s) or 30(s).  For 1s you subtract from your total, 30s you add (with both rolls openended upwards if you roll a 30 on a reroll).  The keeps the long tails, and is only slightly more complicated at the table but that is easily automated away.  This has a ~12% chance of an openended roll, BUT it is not the full roll like in RM, so the higher chances is offset by the lower bonus/consequence.

Ignoring the open-ended aspect, that gives a range from 4 to 120, with a mean result of 62, which is a bit of a departure.

Right - that is why I brought up changing the target numbers for success, partial success, etc.

[Onirim]

You can see the distribution that gets you by entering this in anydice.com:

output [middle 1 of 3d10]*10 + 1d10

It's not very bell-curved if you compare it to 3d100 / 3.

No, it's not 3d10 + 1d10
It's 3d10 for the tens (middle dice) and this is a belly bell curve.
The other 1d10 is for the ones it's not added, it replaces the last digit, because you don't need to make a bell curve with the last digit, it's not really useful. And you don't want to go to 110. So replacing it, not adding it btw.

This is a bell cuve and the last 1d10 replace the ones last digit, and is not added to it. Annot do this in Anydice

[jdale]

[middle 1 of 3d10] means (for anydice.com) that you roll three d10s and pick the middle value. E.g., you roll a 2, a 4, and a 7, so the result is 4.

[middle 1 of 3d10]*10 makes that the tens digit. E.g. you roll the 2, 4, and 7, it picks the 4, and then multiplies by 10 to get 40.

Then add the 1d10 for the ones place. So if you had 40 at the previous step, and then roll a 6 on the last 1d10, the result is 46.

I am pretty sure that is how to express the die rolling mechanic you are suggesting. If you paste the whole thing into the box at anydice.com, click Calculate and then click Graph, you'll see a plot of the resulting distribution.

There's one quirk that these are really 0-9 dice and not d10s, but 00 means 100. I ignored that with the result the curve is offset 10 to the right. The shape is still correct. If you want to correct for that (except the 00 result), you can use this instead:

output [middle 1 of 3d{0,1,2,3,4,5,6,7,8,9}]*10 + 1d{0,1,2,3,4,5,6,7,8,9}

There's a way to fix 00 but I stopped before I figured that out.

[pantsorama]

[middle 1 of 3d10] means (for anydice.com) that you roll three d10s and pick the middle value. E.g., you roll a 2, a 4, and a 7, so the result is 4.

[middle 1 of 3d10]*10 makes that the tens digit. E.g. you roll the 2, 4, and 7, it picks the 4, and then multiplies by 10 to get 40.

Then add the 1d10 for the ones place. So if you had 40 at the previous step, and then roll a 6 on the last 1d10, the result is 46.

I am pretty sure that is how to express the die rolling mechanic you are suggesting. If you paste the whole thing into the box at anydice.com, click Calculate and then click Graph, you'll see a plot of the resulting distribution.

There's one quirk that these are really 0-9 dice and not d10s, but 00 means 100. I ignored that with the result the curve is offset 10 to the right. The shape is still correct. If you want to correct for that (except the 00 result), you can use this instead:

output [middle 1 of 3d{0,1,2,3,4,5,6,7,8,9}]*10 + 1d{0,1,2,3,4,5,6,7,8,9}

There's a way to fix 00 but I stopped before I figured that out.

Technically you need to add a -10 to the equation to bring the bell curve absolute ranges back in line, but essentially this is the way to represent to probability distribution in anydice, yes.

[pantsorama]

So you get something like

output ((([middle 1 of 3d10]*10)-10) + 1d10)

Oh - one other point.

If you want to keep open ended rolls, you might want to expand the range of dice results that will trigger an open ended roll.  Especially in the 3d100/3 model.  The chance of rolling open ended (high or low, but not both) on that model is about 1 in 2000 - a far cry from the 1 in 20 chance we have now.