I've been getting curious about dice and the math behind them.
I was wondering if you know of any usual combinations of dice, or usual methods of counting them that you can use in order to get strange results?
Pic related. If you roll three d6s that are marked with {0,0,1,1,2,2}, then it basically makes a curved version of a d10's results
+r@nsf3r dot sh
11nVOW/Bain_Introduction_to_Prob_and_math_stat.pdf
Chapters 2 covers random variables (a die is a discrete uniform random variable) and chapter 4 covers joint distributions (multiple dice)
It's an undergrad text, so it should be too difficult to understand.
Check for astragalomancy, roll 5 d4(sides 1,3,4,6).
Defining values at the edges of the spectrum as exponential can lead to highly unusual results.
Splitting a task up into a few rolls can lead to unpredictable results. For example, I heard of an adventure that was played in a world where magic could become unpredictable. Whenever you used a spell or a magical item, you had to roll 4d100. Roll 1 was for the deviation from the intended effect. Roll 2 was for whether the resulting effect was beneficial or malignant. Roll 3 was the severity of the resulting effect, Roll 4 was the scope of the effect.
The party entered the game world through a portal and found a magic book that was supposed to tell them about the game world. But the player who activated the book rolled:
> 01 on d100: complete deviation from the intended effect
> 01 on d100: the effect was completely malignant
> (1)00 on d100: maximum severity
> (1)00 on d100: scope was the entire game world.
The book malfunctioned, opening a sphere of annihilation that destroyed the entire game world over the duration it was supposed to work, which was five minutes. DM let the party escape back through their portal.
I've recently been trying to come up with some sort of weird probabilities you roll a d2, d3, d4, d5, and d6 at the same time.
The reason for this is because you can use dice shaped like the platonic solids in order to roll this, just by rearranging the numbers on the races. Take a look:
>altered d4 = d{1,1,2,2} = d2
>altered d6 = d{1,1,2,2,3,3} = d3
>altered d8 = d{1,1,2,2,3,3,4,4} = d4
>altered d12 = d{1,1,2,2,3,3,4,4,5,5,6,6} = d6
>altered d20 = d{1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5} = d5
But even though this starts out promising, I haven't found any probabilities that seem very interesting yet.
I made some experiments on manipulating minimum values.
Disadvantage roll
Neutral roll
Advantage roll
Here's a weird distribution you can get with just three d6s
you would need to decide which dice to multiply, and which to add, though.
this one doesn't need marking and is smoother
Roll 3d6, take the highest. If there are any pairs, add the SINGULAR value of the dice to the third die.
Second line is doing the same thing with d10s
damnit
Whoops, forgot to give a link: www.anydice.com
Yes, either rolling them separately or using color coded dice would help.
But why? Where do you need weird distributions, that are hard to grasp intuitively?
You presume that the standard d100 or bell curve are intuitive.
An equal chance to roll 0 as it is 50 is quite swingy, and does not represent the consistency that a skilled individual can provide.
The bell curve is sort of okay, but is heavily affected by even a single additive bonus.
Stranger distributions let you control probability more organically than a list of exceptions and bonuses. for example makes it more likely to get average rolls, and if you ever "crit", there's a system in place to determine just how amazing the crit is that is faster than using exploding dice.
If I need to roll 40% or less on d100, I can intuitively tell that I have almost fifty-fifty odds of succeeding. If I need to roll 5 or more on this system I have no idea is it likely or unlikely to happen, because it's much more complicated process.
Let me ask you a question:
How often do you find yourself having to roll a 216-sided die, but you only have three d6s? Basically every single day, right?
Well, good news! By relabeling your d6s, you can easily make them give a value from 1 to 216, with equal odds for each answer.
>not choosing stats the hardcore way
>1d20 down the line
Just learn to count in base 6, faggot.
Rolled 3, 15, 16, 4, 5, 7 = 50 (6d20)
Billy, the retarded archer. Now if only he could lift the bow...
Intuitive to understand, but not intuitive in depicting a realistic situation. Knowing how to do a task properly doesn't just give you 10% chance of doing it better.
Sure, it's simple enough for the player, but you've frontloaded the trouble onto the GM and how to gauge DCs.
Naw, my method's superior.
Base 6 is best base.
You can instantly tell what number something is divisible and if a number is prime (all prime numbers over 3 are one more or one less than six)
Rolled 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1 + 20 = 47 (20d2 + 20)
Wait, let me try that again
Rolled 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2 + 20 = 46 (20d2 + 20)
Huh, that was supposed to be 20d2-20. It changed to + for some reason
+-20
...
...
...
...
I would argue that it is easy for a GM to decide the appropriate DC with linear system and that is a big reason why they are used (unfortunately). I can easily think - DC 10 = normal person succeeds half the time.
My favourite skill check system is CoC's. What is yours out of curiosity?
>My favourite skill check system is CoC's.
I don't know if you're deliberately not distinguishing between corruption of champions and call of cthulu, but it got a chuckle out of me.
I'm still shopping around, but I really like the idea of "saving" particular dice results to use in clutch moments and/or as a sort of mp bar.
Anydice is a cool website. Too bad it doesn't cover vector-valued random variables. I mean, you can project them into the reals, but it's just not the same thing.
I'm home brewing a system and ended up deciding to go with 2d10 for the beta because modifiers can range from -5 to +5 before it gets stupid. Previously I wanted doubles on the dice to matter, but I decided that rolling a 10 matters.
Another conflict resolution mechanic I've considered: you roll Xd10 dice. The X is your rank, it tells you how well you possibly could succeed. For example: animals and small children would roll 1d10 for intelligence checks, while adults would roll 2d10. You have a variety of options in this system, such as: flat modifiers, increasing/decreasing the number of dice, matching repeated values, matching sequences, etc. I feel like this is a good system to use if there's a lot of variety of power and skill levels.
>216-sided die,
>have three d6s
216 probabilities is not the reason 3d6 is used
>Base 6 is best base.
Base 3 is the best base
0/0, 1/0, 2/0, 1/2 doenst work
0/1, 0/2, 1/1, 2/1, 2/2,
55.555555555....% of the stuff work
you are making the division at base 10
I think the result would still be the same
While I can understand messing around with this stuff because it is fun (if you like stats), I am just not sure what you would achieve by introducing it in a real TTRP.
The skill check probabilities are supposed to be relatively transparent.
I mean, that's the general idea. That people have a notion of their odds of succeeding at their endeavours.
As we (usually) do in real life.
Further, I'm just not sure what a more wonky prob-distribution would add to the game.
Would it be play-creating? Would it make things more engaging?
As general rule of thumb, when I homebrew for my running campaigns, I try to simplify the math involved in applying my cool items / enemy abilities / etc.
Because the math bit is rarely the fun bit, once the game is rolling, and because more complex = higher chance I'll fuck it up in the moment.
What do you see these weird distributions being used for?
Call of Chthulu. Have never heard anything about the other before.
I mean, I don't play MAID every day, but sometimes, sure.
>The skill check probabilities are supposed to be relatively transparent.
thats is not the case with 3d6 and people still use it
It is relatively transparent. 10.5 is the average. The further from that point you get the more unlikely until you reach 1/216 at the ends.