d66 dice rolls - linear or non-linear? OR 3d6 to replace d20

[jaz0nj4ckal]

Help with my math - Does the d66 dice roll system, 1/36 chance - does this create a true Linear scale?
Trying to run OD&D with just six sided (d6) dice.

I want to ditch the d20, so can I go the 3d6 route? Does that change anything with the bonuses/ Penalties? Do I match the percentage chance on a d20 with the nearest percentage on 3d6?


Thank you

 

[clearstream]

Help with my math - Does the d66 dice roll system, 1/36 chance - does this create a true Linear scale?
Trying to run OD&D with just six sided (d6) dice.

I want to ditch the d20, so can I go the 3d6 route? Does that change anything with the bonuses/ Penalties? Do I match the percentage chance on a d20 with the nearest percentage on 3d6?


Thank you

d66 is linear. 2d6 is non-linear (in the sense you mean. ) With d66 advantage and disadvantage will work as they do with d20. Mods however would need conversion (or be less effective. ) The scaling is 1.8. I'd possibly just double the mod.

 

[Celebrim]

Help with my math - Does the d66 dice roll system, 1/36 chance - does this create a true Linear scale?

Each result on d6/d6 is equally likely. The trick is mapping them to a linear scale correctly - if {1,1} is 1, is {2,1} a result of 3 or a result of 4? Or maybe 7? Is {2,2} counter-intuitively the result 5 or even more counter-intuitively the result 8? Another mapping of d6/d6, creates the sequence 11, 12, 13, 14, 15, 16, 21, 22, etc. The problem with this mapping is that while each result is equally likely, modifiers no longer work in any sort of intuitive manner.

It's a bunch of mental overhead, but the simplest mapping I can think of is do a literal base 6 conversion {3,5} = (3-1)*6+5 = 17, every time you rolled a dice. The only things you'll really need to change is you'll need to convert the to hit and saving throw tables over to the new dice. You might also consider changing the to hit and damage modifiers slightly, especially for Dex and Str bonuses since 'to hit' modifiers are now more granular and less important.

3d6 (Tri-6) systems are weirder than you might think. Linear bonuses do unexpected things, and they tend to have very small sweet spots owing to the limited range of values between 3 and 18 and the very tight grouping in the system. If you want to run OD&D, I'd definitely not go the route of Tri-6.

 

[jaz0nj4ckal]

The scaling is 1.8. I'd possibly just double the mod.

So you mean if D&D normally calls for a +2/-2 mod, you would make that a +4/-4 on a d66 dice roll?

 

[jaz0nj4ckal]

Each result on d6/d6 is equally likely. The trick is mapping them to a linear scale correctly - if {1,1} is 1, is {2,1} a result of 3 or a result of 4? Or maybe 7? Is {2,2} counter-intuitively the result 5 or even more counter-intuitively the result 8? Another mapping of d6/d6, creates the sequence 11, 12, 13, 14, 15, 16, 21, 22, etc. The problem with this mapping is that while each result is equally likely, modifiers no longer work in any sort of intuitive manner.

It's a bunch of mental overhead, but the simplest mapping I can think of is do a literal base 6 conversion {3,5} = (3-1)*6+5 = 17, every time you rolled a dice. The only things you'll really need to change is you'll need to convert the to hit and saving throw tables over to the new dice. You might also consider changing the to hit and damage modifiers slightly, especially for Dex and Str bonuses since 'to hit' modifiers are now more granular and less important.

3d6 (Tri-6) systems are weirder than you might think. Linear bonuses do unexpected things, and they tend to have very small sweet spots owing to the limited range of values between 3 and 18 and the very tight grouping in the system. If you want to run OD&D, I'd definitely not go the route of Tri-6.

So are you promoting that I use the d66 linear dice scale if I want to run my OD&D game with only d6 dice?

 

[Celebrim]

So are you promoting that I use the d66 linear dice scale if I want to run my OD&D game with only d6 dice?

No, I'm not promoting it. I can't think of a good reason to do it unless you are in jail or staying the winter in McMurdo and no one has a d20. But if you are going to do it, mapping d6/d6 to 1..36 is much better than 3d6.

You'll still need to do some work probably. My experience with D&D begins with AD&D, so I'm not familiar enough with the OD&D rules to tell you exactly what to do. But you'll need to do some scaling in the rules to account for ~18 being an average roll instead of ~10. You'll need to probably change the scaling on the to hit bonuses for high strength or dexterity. Magic item 'to hit' bonuses (but not damage!) and possibly other bonuses will need some scaling. For example, a +5 sword, might become +9 to hit/+5 to damage if you want it to have the same sort of impact. But that sort of big scaling is still a long ways down the road. You get a lot more granularity going to a 'd36', so you can have +1 swords and +2 to hit/+1 to damage swords and both make a good deal of sense.

 

[clearstream]

So you mean if D&D normally calls for a +2/-2 mod, you would make that a +4/-4 on a d66 dice roll?

Yes. It will turn out nearly the same and doubling is easy to calculate.

 

[WheresMyD20]

Trying to run OD&D with just six sided (d6) dice.

I want to ditch the d20

The closest approximation I can come up with using only 2d6 is to have one die be a normal 1d6 and the other die act as a control die. If the control die comes up 1 or 2, then read the normal 1d6 die as is (i.e. the roll result is a number from 1 to 6). If the control die comes up 3 or 4, then add 7 to the result of the normal die, producing a result between 8 and 13. If the control die comes up 5 or 6, then add 14 to the normal 1d6 die, producing a result from 15 to 20.

Using this method, you can produce a linear range of all the numbers from 1 to 20 except for 7 and 14.

If you want to get fancy, you can use some stickers on the control die to re-label it with two 0 sides, two 7 sides, and two 14 sides.

This method provides an approximation within -3.3% to +3.3% percentiles. A target number of 15 or better is 3.3%-tiles easier to roll (33.3% vs. 30%) and a target number of 7 or better is 3.3%-tiles harder to roll (66.6% vs. 70%). A target number of 11 is exactly the same (50% using either method). The average discrepancy is 1.5%-tiles.

 

[Nagol]

Each result on d6/d6 is equally likely. The trick is mapping them to a linear scale correctly - if {1,1} is 1, is {2,1} a result of 3 or a result of 4? Or maybe 7? Is {2,2} counter-intuitively the result 5 or even more counter-intuitively the result 8? Another mapping of d6/d6, creates the sequence 11, 12, 13, 14, 15, 16, 21, 22, etc. The problem with this mapping is that while each result is equally likely, modifiers no longer work in any sort of intuitive manner.

It's a bunch of mental overhead, but the simplest mapping I can think of is do a literal base 6 conversion {3,5} = (3-1)*6+5 = 17, every time you rolled a dice. The only things you'll really need to change is you'll need to convert the to hit and saving throw tables over to the new dice. You might also consider changing the to hit and damage modifiers slightly, especially for Dex and Str bonuses since 'to hit' modifiers are now more granular and less important.

3d6 (Tri-6) systems are weirder than you might think. Linear bonuses do unexpected things, and they tend to have very small sweet spots owing to the limited range of values between 3 and 18 and the very tight grouping in the system. If you want to run OD&D, I'd definitely not go the route of Tri-6.

The "simplest" mapping is to subtract one from each roll (or treat 6s as zero), resulting in 0-5 results and use a base 6 number system. This gets you 00 - 55 which maps directly to 0 - 35 when converted back to base 10.

 

[Celebrim]

The "simplest" mapping is to subtract one from each roll (or treat 6s as zero), resulting in 0-5 results and use a base 6 number system. This gets you 00 - 55 which maps directly to 0 - 35 when converted back to base 10.

Errrr....

Wouldn't it be even more simple to have a 01-56 mapping that maps directly to 1-36 by conversion to base 10.

I wonder why I didn't come up with that.

It's a bunch of mental overhead, but the simplest mapping I can think of is do a literal base 6 conversion {3,5} = (3-1)*6+5 = 17, every time you rolled a dice.

Oh yeah. I did.