I need Bell Curve help!

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AslanC
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I need Bell Curve help!

Post by AslanC »

Okay using 2d10 as a rolling mechanic it scales like so;

2-1%

3-2%

4-3%

5-4%

6-5%

7-6%

8-7%

9-8%

10-9%

11-10%

12-9%

13-8%

14-7%

15-6%

16-5%

17-4%

18-3%

19-2%

20-1%

So here's why question.

What is a good range of mods for such a thing if an impossible task was a total roll of 30?

Any and all thoughts appreciated.

P.S. I suck at math which is why I am asking for help.
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serleran
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Post by serleran »

roughly half the average to 150% the average... so, 2 - 7. To get the impossible results would require a larger bonus, and a very good roll...
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Lord Dynel
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Post by Lord Dynel »

If an impossible task is attainable (I know, that sounds odd) then the lowest modifier would be +10. Anything lower than that would not produce the impossible result.

So if you meant for the impossible task not to be reached, I'd half that, to +5, and then think about a range of somewhere in the neighborhood of -2 to +2. So maybe as high as +7, or as low as +3 (very similar to serl's).

Say you choose +7, for example, is the max, high side. If you go high, you should consider going low - negatives in this case. I'd venture a -7 to +7 range (for 15 total modifier spots). More interestingly, -9 to +9, which would not only keep the "impossible," impossible, but would allow a unique modifier for each score in you above list. But that may be too close to your impossible number of 30 than you're willing to go.
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stoneshape
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Post by stoneshape »

Something to keep in mind here is that the standard deviation of 2d10 rounds out to 4.

Are you looking to replace d20 with 2d10 completely or just in certain areas?

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AslanC
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Post by AslanC »

It was an experiment in my mind about replacing 1d20 with 2d10, the math here and elsewhere shows that wouldn't work well.

C'est la vie
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Aramis
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Post by Aramis »

You might be interested in trying the 3d6 alternate system to d20s, especially for skill type rolls (i.e SIEGE checks). This adresses one of the weaknesses of d20s, which is that each result on the die is equally likely. Whereas in real life skill execution, our actions tend to group in the mediocre middle, with a few great and bad attempts as outliers.
As the d20 SRD wrote:
Bell Curve Rolls

Heres perhaps the most fundamental variant to the d20 rules: Dont use a d20! Instead, roll 3d6 whenever you would roll a d20, applying bonuses and penalties normally. The possible results when rolling 3d6 (or any other multiple dice) form a bell curvethat is, a range of odds that favors average results much more than extreme results.

Metagame Analysis: The Bell Curve

In general, this variant leads to a grittier d20 game, because there will be far fewer very good or very bad rolls. Not only can you no longer roll 1, 2, 19 or 20, but most rolls will be clustered around the average of 10.5. With a d20, every result is equally likely; you have a 5% chance of rolling an 18 and a 5% chance of rolling a 10. With 3d6, theres only one possible combination of dice that results in an 18 (three sixes, obviously), but there are twenty-four combinations that result in a 10. Players used to the thrill of rolling high and the agony of a natural 1 will get that feeling less oftenbut it may be more meaningful when it does happen. Good die rolls are a fundamental reward of the game, and it changes the character of the game when the rewards are somewhat stronger but less frequent.

Game balance shifts subtly when you use the bell curve variant. Rolling 3d6 gives you a lot more average rolls, which favors the stronger side in combat. And in the d20 game, thats almost always the PCs. Many monstersespecially low-CR monsters encountered in groupsrely heavily on a lucky shot to damage PCs. When rolling 3d6, those lucky shots are fewer and farther between. In a fair fight when everyone rolls a 10, the PCs should win almost every time. The bell curve variant adheres more tightly to that average (which is the reason behind the reduction in CR for monsters encountered in groups).

Another subtle change to the game is that the bell curve variant awards bonuses relatively more and the die roll relatively less, simply because the die roll is almost always within a few points of 10. A characters skill ranks, ability scores, and gear have a much bigger impact on success and failure than they do in the standard d20 rules.

As it says above, the tendency on 3d6s would be that average tasks would succeed much more often, difficult ones would fail more often. Things like magic bonuses and monster or character level would be more emphasized, the importance of a good or bad dice roll would be de-emphasized

So it is up to you which set of distortions you prefer

Information on it from the d20 SRD is here:
http://www.d20srd.org/srd/variant/adven ... eRolls.htm
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AslanC
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Post by AslanC »

This is mostly the same as 2d10 by the way which is also a bell curve.

The problem isn't that, it is that I don't want to add other dice for other tasks, and well Bell Curve doesn't work well for rolling up the scarcity of magic items.

Thanks for the replies though
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Post by Lord Dynel »

Aramis wrote:
You might be interested in trying the 3d6 alternate system to d20s, especially for skill type rolls (i.e SIEGE checks). This adresses one of the weaknesses of d20s, which is that each result on the die is equally likely. Whereas in real life skill execution, our actions tend to group in the mediocre middle, with a few great and bad attempts as outliers.


As it says above, the tendency on 3d6s would be that average tasks would succeed much more often, difficult ones would fail more often. Things like magic bonuses and monster or character level would be more emphasized, the importance of a good or bad dice roll would be de-emphasized

So it is up to you which set of distortions you prefer

Information on it from the d20 SRD is here:
http://www.d20srd.org/srd/variant/adven ... eRolls.htm

GURPS uses the 3d6 system. It's one of the things I like the most about that system.

Sorry you didn't find what you were hoping for, Aslan.
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CharlieRock
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Post by CharlieRock »

There are times when the CK just has to go "don't roll, it's not going to happen."
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Post by Fizz »

AslanC wrote:
It was an experiment in my mind about replacing 1d20 with 2d10, the math here and elsewhere shows that wouldn't work well.

Actually, i've experimented with it as well, and liked how it works. But you do have to keep in mind what it does. Things that are easy become very easy, and it makes things that are difficult become very difficult.

One way to compare 2d10 to 1d20 is by looking at the percentages. Consider the odds of rolling a 20 on a d20- 5% chance. With 2d10, to get approximately the same odds you use a range of 18-20. There is a 6% chance of an 18 or better: 3%+2%+1% = 6%.

Also remember, you're never trying for exactly a set number, you're always trying to beat the target number. So you have to consider the odds of not rolling the number exactly, but of rolling that number or higher.

Consider this chart. The left column is the result, the middle is for 2d10, the right is for 1d20. The percentages are the changes of getting that result OR Better.

1: n/a-, 100%

2: 100%, 95%

3: 99%, 90%

4: 97%, 85%

5: 94%, 80%

6: 90%, 75%

7: 85%, 70%

8: 79%, 65%

9: 72%, 60%

10: 64%, 55%

11: 55%, 50%

12: 45%, 45%

13: 36%, 40%

14: 28%, 35%

15: 21%, 30%

16: 15%, 25%

17: 10%, 20%

18: 6%, 15%

19: 3%, 10%

20: 1%, 5%

So, the odds of rolling a 14 or better are 28% with 2d10, or 35% for 1d20.

As you can see, the middle range (9 to 13) is pretty comparable, and they start to diverge at either end. So really you just need to be careful about extreme tasks.

Rather nicely, the CB for a Prime remains the same- a 45% chance of rolling a 12 or better in either system. But for non primes, it's much more difficult with 2d10- only 6% chance of rolling an 18 or better, compared to 15% in 1d20.

To resolve this, it's best to adjust the CB for non-primes. The Prime bonus (+6) is based on the standard deviation of 1d20. The standard deviation of 2d10 is about 4. That's a difference of 2. So your CB for non-primes should be 16 instead of 18. Sure enough, the odds of rolling a 16 or better on 2d10 are 15%- the same as rolling an 18 on 1d20.

I've found the 2d10 system works rather nicely. It gives more consistent results than 2d10 and makes the extreme results truly rare and exciting.

Hope that helps!

-Fizz

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AslanC
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Post by AslanC »

Fizz wrote:
Hope that helps!

Thanks Fizz.

That's a really a good indepth take on it.
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jaguar451
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Post by jaguar451 »

Thanks Fizz. Nice analysis. I do like reducing random chance a bit, making skill more important.... 2d10 does look like an interesting middle ground between 3d6 and 1d20....

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