UA: Why 3d6 for the "Bell Curve" variant, instead of 2d10?

[malladin]

The mean (average) result of a d20 roll is 10.5, the mean result of a 3d6 is also 10.5, whereas 2d10 has a mean of 11.

3d6 also has a precident in other roleplaying games: Champions and GURPS also use 3d6.

Cheerio,

Ben

 

[Ranger REG]

For some reason I'm wondering if Steve Jackson is angry at Wizards for introducing his signature task resolution system.

Anybody wants to do a mathematical probability comparative analysis between the distribution of 2d10 and 3d6 with regards to the bell curve? I'm betting 3d6 is more true to the bell curve.

 

[swrushing]

Myself, I've long since come to the conclusion that "non-linear" is the better way to go. But, 3d6... ?! No, if you're going to go non-linear, then using 2d10 is better than using 3d6.

I long since came to the opposite conclusion and here's why...

3d6 is a linear die, s216 with success and fail values (DC) assigned to those 216 rolls.
2d10 is a d100, with success fail tags addes to those 100 results.

If the outcome is more predictable using d100 or d216 than in d20, it is because more of those 216 outcomes by percentage or more of those d100 outcomes by percentage were assigned that way.

For example, someone elsehwere recently complained that the d20 let him roll less than 5 too often... 20% of the time and that made a particular problem when he rolled two such low results in succession.

So he was going to 2d10 which made the less than 5 result only occur 6% of the time. Now he was happy.

So i asked, "why not just change the DC for that bad event on the d20 to "only on a 1" instead of "on a 1-4"? Then the % chance is 5% and you did not suddenly change the meaning of every other dc and skill check in the game. Did you really mean to change the spot check odds when you fixed the knockout percentage?"

Whether rolling 1d20, 2d10, or 3d6 you can... for the most part, assign a DC or required die roll so that you set the likelihood of something happening to whatever percentage you want. 9+ on 1s20 is 60%. 10+ on 2d6 is 62.5%. the predictability of the OUTCOME OF THE TASk is determined by the success/fail break points you set and not the die mechanic.

So, the "its more realistic" is really just saying "i like those odds more."

*************

The Dark Side of bell Curves...

Where does a bell curve fail you?

When you have non-perfect world tasks... you know, modifiers.

On d20... power attack shifting +1 from to hit drops the chance of a hit by 1 more miss in 20. It adds for this 1 more point to damage.

In 2d10, it still adds a flat 1 to damage, but it might drop your chance of hitting by 2% (1 in 50) or by as much as 10% (2 in 20.) Where it falls will not be determined by any normal rhyme or reasons such as "hurts more skill more" or even "hurts more skilled guys less" but by the fairly random "how close to the middle do you need to roll.

A +1 sword might add 2 more hits in 20 or it might add 1 more hit in 50. Moreover than benefit will chance from swing to swign.

-4 for non-proficiency can be as much as -36 out of 100... 18 in 50... nearly 1/3 of the possible rolls swpet away in one -4... or it might be as low as 14%, a little under 1/7 of the possible rolls swept away... and it will vary from attacker to defender maybe even round to round.

When you say "these tools give you a +2" in d20, you know what you are giving out... 2 more chances in 20... but with 2d10, you no longer know. Maybe its almost 4 more chances in 20 and maybe its only 1.

Thats why i prefer the linear... i can set Dcs easily enough and i know what my modifiers do to the odds consistently.

 

[Calico_Jack73]

i thought it was fairly clear... they wanted to give you a bell curve and wanted it sufficiently bell curvey to matter... so 3d6 (not at all unlike a d10+5) is a good commonly used very bell curvey one to pick.

Any time you are going to roll a single dice you won't have a bell curve at all. You only get one with more than one dice adding to a total. Your chance to roll the highest number on a single dice is the same chance of rolling the lowest or any other number for that matter. One dice = equal chance for any number = no bell curve.

 

[0-hr]

"new" Coke was made to taste more like Pespi so as to steal marketshare.
Maybe Monte is trying to weasle away some GURPS fans.


Isn't it also strange how close "Arcana Unearthed" is to "Unearthed Arcana"...

 

[swrushing]

Any time you are going to roll a single dice you won't have a bell curve at all. You only get one with more than one dice adding to a total. Your chance to roll the highest number on a single dice is the same chance of rolling the lowest or any other number for that matter. One dice = equal chance for any number = no bell curve.

I have to assume that this is in response to me d10+5 reference...

Ways a d10+5 is like a 3d6 roll...

Both have ~80% of their possible results coming in an 8 number wide span (7-14.)
Within that 90% range, a +2 modifier is fairly static at about 20% (exactly 20% for the d10 and between about 15%-25% for the 3d6.)

So, if you make a 1 some sort of open ended failure and a 10 some form of an open ended success, you can get very close to the same results and keep constant modifiers.

Example:
Roll 1d10+5
on a natural one roll a second d10... 1 = a result of 3, 2-3 = a result of 4, 4-6 = a result of 5, 6-10 = a result of 6.
on a natural ten roll a second d10... 10 = a result of 18, 8-9 = a result of 17, 5-7 = a result of 16, 1-4 = a result of 15.

That will come not too far from a 3d6 in terms of results.

If thats not why you started telling me how bell curves are born based on my quote, I have no clue what you were referencing.

 

[MerakSpielman]

You could do 1d12 + 1d8

or 1d12+2d4

or 2d6+2d4

ok I'm getting silly. Shutting up now.

 

[Ranger REG]

Isn't it also strange how close "Arcana Unearthed" is to "Unearthed Arcana"...

Are you implying that the standalone ruleset that is Monte Cook's Arcana Unearthed is a bunch of jumbled-up, disorganized, mixed bag of mechanics?

 

[dcollins]

First of all, there are many good reasons for going with the bell curve roll, rather than a single, linear die roll, for saving throws, skill rolls, etc. On the following webpage, a guy explains those reasons well with his "Linear vs Non-Linear Dice" essay...

http://www.frontiernet.net/~jamesstarlight/LinearVsNonLinear.html

I just wanted to throw in a dissenting critical review -- as someone with a higher math degree, I've read that page and the past, and find it be off-the-mark. The writer seems to spill a great deal of ink trying to argue that "an 'average' is different from a 'mean'", which is not correct. It's perfectly valid to speak of an average/ mean/ expected result from a single linear die roll, and in fact that's what is usually meant by the words "on average".

 

[Unseelie]

I'm of the opinion that the Unearthed Arcana is not a well thought as it should've been.

One of the variants that initially sounds appealing to me, but ends up rubbing me wrong, is the "bell curve" variant that uses 3d6 to replace all d20 rolls. But why 3d6? To me, that's going from one extreme to another. Wouldn't 2d10 be a better alternative than 3d6?

First of all, there are many good reasons for going with the bell curve roll, rather than a single, linear die roll, for saving throws, skill rolls, etc. On the following webpage, a guy explains those reasons well with his "Linear vs Non-Linear Dice" essay...

http://www.frontiernet.net/~jamesstarlight/LinearVsNonLinear.html

Myself, I've long since come to the conclusion that "non-linear" is the better way to go. But, 3d6... ?! No, if you're going to go non-linear, then using 2d10 is better than using 3d6.

For one thing, with 2d10 you get almost the same range of numbers as you do with a d20; i.e. 2-20 with 2d10, compared to 1-20 with a d20; whereas with 3d6, you get a range of only 3-18.

For another thing, the bell curve created by using 2d10 is less extreme than the one created by using 3d6; i.e. with 2d10 you have better chances of rolling the numbers on each end of the range than you do with 3d6. So, although you are still making an impact on the game system by using 2d10, it's less than it would be with 3d6.

BTW: With the 3d6 bell curve variant, the threat ranges of criticals are increased by 1, right? But with the extreme bell curve created by using 3d6, increasing the threat ranges by 1 does not suffice, because you are still getting much less a chance for rolling within a weapon's increased threat range than you would be with a d20 rolling within the original threat range. However, with a 2d10 bell curve, increasing the threat ranges by 1 is adequate, because this way you are close enough to getting the same chance for rolling within a weapon's increased threat range as you would be with a d20 within the original threat range.

A two die bell curve is too steep in general, which means that bonuses and penalties have too much of an effect. A 3 die bell curve is much more natural.