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Systems & Settings => Rolemaster => Topic started by: DerGraumantel on June 02, 2023, 05:51:42 AM
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Now and then I feel that the resultdestribution in Rolemaster is too random and does not reflect realistic circumstances properly.
To fix this I want a more bell curve like roll distribution. Since I want to use all the original RM tables, I decided to simulate bell curve with to blank d20, that have numbers from 00 to 90 in differing amounts, for example 4 times 50 but only 1 time 00.
The dice are ordered. I just have to decide how often the different numbers should occur.
Has anybody tried that and has a good distribution?
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You could do 10D10 for a quick and dirty and well rounded curve, or 5D20 or maybe 3D30+10.
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I did an article about the matter back in 2009 for the guild compaion. Unfortuantely I don't think it was crawled before it disappeared from the front site. Not sure were the text is now on my hardrive...
The gist of the article was you can get a perfect bell shape in middle but no open ended tails or you can have realistic bell curve tails but slightly flat middle. RM dice mechanic aims for the latter and this give a chance of success that very closely maps to what you get with the real bell curve.
Assumptions about difficulties used at the game table and what makes a good gaming experience might lead to that Rolemaster curve is underiable at your gaming table, but be sure to compare the rate of success curve with your distritubution and the RM one. It is easy to delude yourself that you have a better looking distribution, but in reality have something that model the bell curve worse from a mathematic point of view.
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You could do 10D10 for a quick and dirty and well rounded curve, or 5D20 or maybe 3D30+10.
The problem with that is, that you end up with values between 10 and 100 (in addition to that being to many dice on the table, haha). That makes it hardly possible to use the RM tables. That is why I'm going for blank d20 where I put in the values.
I did an article about the matter back in 2009 for the guild compaion. Unfortuantely I don't think it was crawled before it disappeared from the front site. Not sure were the text is now on my hardrive...
Would love to read that!!!
I will try it out with the d20s once they are here, and share my results. I would say though, that with my method you still have the open ended tails since all results are possible.
My old Rolemaster Box came in fact with two d20 that had double numbers to simulate to d10:) What an artifact.
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You could do 10D10 for a quick and dirty and well rounded curve, or 5D20 or maybe 3D30+10.
The problem with that is, that you end up with values between 10 and 100 (in addition to that being to many dice on the table, haha). That makes it hardly possible to use the RM tables. That is why I'm going for blank d20 where I put in the values.
11D10-10 then. ;) But I find all this quite unwieldy.
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There is no player facing difference except the shape of the dice in my proposed system. Two D20, one with the tens, one with the ones. The only player facing difference is the shape, the distribution change is taken care of by the dice. But ehhh.... yes, I admit that I like making things difficult for myself.
Will be fun to try different distribution patterns and to decide about where on the dice which number should be.
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I use a bell curve for stat bonus generation: 3d10 - 15.
I've always thought about reducing the swinginess of RM by introducing a bell curve into the normal rolls, and with new online tools (like the Roll20 dice roller) it would be trivially easy. I was thinking of 2d50 or ([1d50 + 1d51] - 1).
I too would like to read Pastaav's article.
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In my opinion, the point is not so much to have a bell curve in the raw result, but a bell curve in the action outcome. Which is not necessarily the same, and in addition, has a different meaning for the various subsystems when they have different resolution mechanisms. Direct attacks are one (attack table + crit table), but non-elemental attack spells are another (BAR + RR), and static manoeuver resolution and moving manoeuver resolution (if you still use the MM table) are two more, each of which has its own implication on what "bell curve on the final result" means for tweaking the dice roll.
RM is not an easy system to tweak if you want a unified effect, because the various resolution mechanisms do not have the same action outcome curve.
If I wanted to do that, the first thing I would do would be to unify the resolution mechanisms into a single one. Then I would try to tweak this single resolution mechanism to alter the outcome probability curve.
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Anything that involves multiple rolls (e.g. SCR followed by RR) is moving you in that direction already. Three rolls gives a good curve, if you involve more (e.g. 10d10) the distribution gets really narrow.
Anyway... if you take the average of 3 d10's, which approximates a bell curve (with limited resolution), the distribution is
1 1.00
2 4.60
3 10.90
4 18.70
5 22.30
6 20.50
7 13.60
8 6.40
9 1.90
10 0.10
You don't have that kind of resolution on a d20, where the minimum is going to be 5%, so maybe:
1 1 face
2 1 face
3 2 faces
4 3 faces (alternate: 2)
5 3 faces (alternate: 4)
6 3 faces (alternate: 4)
7 3 faces (alternate: 2)
8 2 faces
9 1 face
10 1 face
That's going to be a fairly subtle effect overall. Open-ended up goes from 5% chance to 2.5% chance. You can't really narrow it more on a d20.
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If you go the bell curve route you’ll need to increase the skill bonuses and other rolls to have results that make sense.
One of the issues with RM is and has always been that most normal player PC levels 6-10, PCs are pretty incompetent. The success percentage for most skills from level 6-10 would be below average for reasonably routine things PCs would be called upon to perform.
We tried to use bell curves , the methods above like 10d10 using a Roll20 macro and what we ended up with was a very high failure rate
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If you go the bell curve route you’ll need to increase the skill bonuses and other rolls to have results that make sense.
One of the issues with RM is and has always been that most normal player PC levels 6-10, PCs are pretty incompetent. The success percentage for most skills from level 6-10 would be below average for reasonably routine things PCs would be called upon to perform.
We tried to use bell curves , the methods above like 10d10 using a Roll20 macro and what we ended up with was a very high failure rate
You cannot fix 10d10 by having higher bonuses since there is no bell-curve tails (aka it is not a good approximation of the normal distribution at all).
The effective range of 10d10 is about 35-75. The likelihood you end in the range 50-60 is like 45%. The likelihood you end in range 45-65 is about 75%. The maximum skill difference between lowest level character and highest level character and the target number for success need to be in the same ball park for it to work so adding too many dices will mess things up a lot.
RMFRP Gamemaster Law section 9 has a good base discussion of these matters but there are loads of resources online to calculate dice probabilities and see if you have a proper bell curve that approximate the normal distribution or just something that looks like a bell at particular zoom level.
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I like Anydice. https://anydice.com/
You can simulate the d20 with repeated numbers by entering this:
output d{00,10,20,20,30,30,30,40,40,40,50,50,50,60,60,60,70,70,80,90}+d10
I suggest clicking the Graph button to see how it looks. It's not a very smooth distribution but it is higher in the center and lower at the sides. And as noted, it halves the chance of open-ended results.
The average of three d100 rolls gives a better distribution but obviously not as convenient at the table. Open-ended becomes about a tenth as likely. 3d30+4 is better, but you completely lose the open-ended ranges.
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If you go the bell curve route you’ll need to increase the skill bonuses and other rolls to have results that make sense.
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.
I like Anydice. https://anydice.com/
You can simulate the d20 with repeated numbers by entering this:
output d{00,10,20,20,30,30,30,40,40,40,50,50,50,60,60,60,70,70,80,90}+d10
This is great, thank you for that!!!
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If you go the bell curve route you’ll need to increase the skill bonuses and other rolls to have results that make sense.
One of the issues with RM is and has always been that most normal player PC levels 6-10, PCs are pretty incompetent. The success percentage for most skills from level 6-10 would be below average for reasonably routine things PCs would be called upon to perform.
We tried to use bell curves , the methods above like 10d10 using a Roll20 macro and what we ended up with was a very high failure rate
You cannot fix 10d10 by having higher bonuses since there is no bell-curve tails (aka it is not a good approximation of the normal distribution at all).
The effective range of 10d10 is about 35-75. The likelihood you end in the range 50-60 is like 45%. The likelihood you end in range 45-65 is about 75%. The maximum skill difference between lowest level character and highest level character and the target number for success need to be in the same ball park for it to work so adding too many dices will mess things up a lot.
RMFRP Gamemaster Law section 9 has a good base discussion of these matters but there are loads of resources online to calculate dice probabilities and see if you have a proper bell curve that approximate the normal distribution or just something that looks like a bell at particular zoom level.
Point taken. So maybe 5d20 would be a better representation. Or since we’re using Roll20 3d33. We can also fix the open in up and down rolling.
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If you go the bell curve route you’ll need to increase the skill bonuses and other rolls to have results that make sense.
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.
I like Anydice. https://anydice.com/
You can simulate the d20 with repeated numbers by entering this:
output d{00,10,20,20,30,30,30,40,40,40,50,50,50,60,60,60,70,70,80,90}+d10
This is great, thank you for that!!!
Just changing the Bell Curve in the rolls will result in more action failures if the actual skill totals aren’t increased as well. A 5-6 level character getting mainly die results if 40-60 will fail on a regular basis and rarely reach 111 unless it’s a spell they’ve dumped a huge number of points in. Spell casting will also result in a lot of nearly failing. Definitely won’t be fast casting any spells that are near their level.
There will be an unintended consequence of the rolls being near the average or mean.
We’ve tried it. The low skill proficiency of PCs through 6-7th level for mediocre tasks would make relatively simple things fail far too often.
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The difficulty becomes important though. If you have a +30 bonus and no modifiers, with the renumbered d20 method you only have a 20% chance of succeeding (vs 30% normally). But if the maneuver is Easy (+20), you're back at 50%, same as normal. If the maneuver is Routine (+30), now you have a 70% chance of succeeding, better than normal (which would be 60%).
I think that's the intent here. Things that are long shots get even longer, but things you should normally be able to achieve will be more reliably achieved. You need to take that into account when designing challenges for the PCs. The PCs should also be looking for ways to improve the odds, e.g. complementary skills, or doing what they can to lower the difficulty. (E.g., you want to climb a rope? Take the time to put knots in it. Searching for traps? Get more light. Etc.)
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The difficulty becomes important though. If you have a +30 bonus and no modifiers, with the renumbered d20 method you only have a 20% chance of succeeding (vs 30% normally). But if the maneuver is Easy (+20), you're back at 50%, same as normal. If the maneuver is Routine (+30), now you have a 70% chance of succeeding, better than normal (which would be 60%).
I think that's the intent here. Things that are long shots get even longer, but things you should normally be able to achieve will be more reliably achieved. You need to take that into account when designing challenges for the PCs. The PCs should also be looking for ways to improve the odds, e.g. complementary skills, or doing what they can to lower the difficulty. (E.g., you want to climb a rope? Take the time to put knots in it. Searching for traps? Get more light. Etc.)
Your example exemplifies the whole issue with the prevalent incompetence. The fact that an easy task will be failed 40% of the time means that PCs even at levels where they should be competent fail to be reliably so.
Without total randomness working in their favor, PCs simply aren’t very good at doing stuff. No way should PCs be failing easy tasks at 5-6th level a third of the time. It shouldn’t require stacking talents and having multiple training packages for a 5th level PC to be consistently good at stuff that fits into the easy category.
This is an old design flaw that’s remained in the game for years. It’s exacerbated if the dice rolls have a true bell curve.
I may be a little confused regarding changing to d20, since a d20 doesn’t yield any different distribution than a d100 except being less granular. It’d require something like 2d50, 3d33 or 5d20 to yield any kind of curve - unless I’m missing something.
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Your example exemplifies the whole issue with the prevalent incompetence. The fact that an easy task will be failed 40% of the time means that PCs even at levels where they should be competent fail to be reliably so.
Without total randomness working in their favor, PCs simply aren’t very good at doing stuff. No way should PCs be failing easy tasks at 5-6th level a third of the time. It shouldn’t require stacking talents and having multiple training packages for a 5th level PC to be consistently good at stuff that fits into the easy category.
This is an old design flaw that’s remained in the game for years. It’s exacerbated if the dice rolls have a true bell curve.
Let's put aside the dice manipulations discussed in this thread for a moment. The details are going to vary between editions but in RMU, a 5th level character can have up to 10 ranks in a skill (a couple more for cultural skills), so that's +50, plus a stat bonus, plus a professional bonus if relevant. For a skill they are not training intensely, have no cultural background in, have no talents for, not a professional skill, they might have 5 ranks for +25, so perhaps +30. Easy is +20, so +50 on the roll. If they can't find a +5 complementary skill bonus they aren't trying, so +55. If the skill is something they can make gradual progress on (a percentage maneuver), they are almost assured success, it's just a question of how long it takes. If partial success is possible, the chance of actual failure is only 20%. It's only unforgiving maneuvers that are pass/fail that they will have the higher 45% chance of failure for. The character with 2 ranks/level, if it's not a professional skill, will have maybe +55, +20 for Easy, maybe +5 complementary skill bonus, so +80. If partial failure is possible, they will only truly fail on an open-ended down roll. Even if it isn't, the chance of failure is only 20%. A professional skill could have another +10 and the stat bonuses will likely be higher, so it's quite possible they will only fall short of Success on an open-ended down roll.
You mention training packages. If you are looking at RMSS, you are starting with your culture ranks, and you have your professional bonuses up front. Plus your stats will be very close to their potentials by 5th level. Bonuses will generally be higher. Near success on 91 will usually let you succeed in one additional round. 5th level RMSS characters are very competent.
I may be a little confused regarding changing to d20, since a d20 doesn’t yield any different distribution than a d100 except being less granular. It’d require something like 2d50, 3d33 or 5d20 to yield any kind of curve - unless I’m missing something.
The OP proposed replacing the tens die with a d20 numbered unevenly, e.g. 00,10,20,20,30,30,30,40,40,40,50,50,50,60,60,60,70,70,80,90. So that increases the chance of results in the 30-79 range, and decreases the chance of results in the 1-19 and 80-100 range. It's not a very smooth bell curve and the impact is much smaller than rolling three dice. I posted above how to plot that distribution on Anydice. That's what I was referring to.
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Your example exemplifies the whole issue with the prevalent incompetence. The fact that an easy task will be failed 40% of the time means that PCs even at levels where they should be competent fail to be reliably so.
Without total randomness working in their favor, PCs simply aren’t very good at doing stuff. No way should PCs be failing easy tasks at 5-6th level a third of the time. It shouldn’t require stacking talents and having multiple training packages for a 5th level PC to be consistently good at stuff that fits into the easy category.
This is an old design flaw that’s remained in the game for years. It’s exacerbated if the dice rolls have a true bell curve.
I agree with you regarding actions that are assumed everyone could perform to a certain extend. For these actions I wrote another topic, called Rudimentary Rolls that is supposed to take care of what I call everyman skills. In short I use stat checks based on the RR table for that.
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This is an old design flaw that’s remained in the game for years. It’s exacerbated if the dice rolls have a true bell curve.
The open ended roll of RM has very attractive properties for a game. It is very good approximation of the real bell curve in the range -100 to +200 and in the middle you have linear relationship between bonus and chance of success. If you get a +10 in bonus it for normal cases really mean improved successrate of +10.
The method with one d20 and d10 that is discussed in this thread means you get more probability mass in the center and that you either need a lookup table for that different bonuses give in successrate or do some calculations in your head. You get less randomness in the outcome so if you want that kind of experience it might be worth living with the downsides, but it is not given this makes the game more fun.
The fundamental problem with RM1 and RM2 and early versions of RMSS IMHO was that the range of difficulties suggested by the game as not at all aligned with the -100 to 200 range so that an easy difficulty does not by mean the task is easy by any reasonable metric. The solution was introduction of the moving maneuver chart and similar tables to effectively change the target number to beat to make probabilities to make sense.
RMSS eventually fixed the issue with School of Hard Knocks that revised the difficulties to be dependent on powerlevel but most importantly to have difficulty penalties that in scale are aligned with the bell curve formed by open ended dice mechanics.
I may be a little confused regarding changing to d20, since a d20 doesn’t yield any different distribution than a d100 except being less granular. It’d require something like 2d50, 3d33 or 5d20 to yield any kind of curve - unless I’m missing something.
Correct a flat d100 and a flat d20 is just a difference in granularity. Adding more dice will give you curve...but unless you make the skill bonus and penalties to align with expected statistical outcome from your sum of dice you won't have a good approximation of the bell curve (aka normal distribution). The 10d10 we talked about early can work as real bell-curve provided you set the range of possible skill bonus to be minimal and choose a suiting target number to beat.
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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.)
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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.
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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.
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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.
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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!
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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.
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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.
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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.
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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 :)
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[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.
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[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.
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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.