Best Method for Dice Customization

[Walt Freitag]

Highlighting (e.g. coloring in or marking with dots) sides of already numbered d20s should be easier than putting your own numbers on a blank die. So consider getting some d20s numbered 0-9 twice (I still see these for sale occasionally so I imagine they're still manufactured), in white if possible, and marking one set of sides 1-6 with a color code meaning positive, the other set of sides 1-6 with a color code meaning negative. The color codes also make it immediately visually obvious which dice to add and subtract ("add all red sides, then subtract all yellow sides"), and when open ended rolls are to be made or continued.

- Walt

[Lee Short]

Highlighting (e.g. coloring in or marking with dots) sides of already numbered d20s should be easier than putting your own numbers on a blank die. So consider getting some d20s numbered 0-9 twice (I still see these for sale occasionally so I imagine they're still manufactured), in white if possible, and marking one set of sides 1-6 with a color code meaning positive, the other set of sides 1-6 with a color code meaning negative. The color codes also make it immediately visually obvious which dice to add and subtract ("add all red sides, then subtract all yellow sides"), and when open ended rolls are to be made or continued.

- Walt

Duh!  I can't believe I didn't think of that yet...my game started with a grainier skill system and dice with two +1s, two +2s, and one +3...so I got into the "I need custom dice" mode and never stopped to take a second look.  

I have already sent email to Koplow, and will report back what I find, even if I elect not to use them myself.  

thanks,
Lee

[Mike Holmes]

If yo uare highlighting, just make the 7-0 sides black. That will make them unreadable, as the numbers are in black (usually). Then go with red for negative (which is intuitive as it's the accounting color for negative, and leave the positive numbers in white.

I thought you had tried this already given the methods you mentioned, or I would have suggested it right off. The only problem is that marker tends to come off after a while requiring touchups.

BTW, if you wanted to use Paul's method, you could just use fudce dice and d6s in pairs. If the Fudge die of the pair comes up zero, the pair is discarded. Else you get positive or negative one through six. This has a slightly different distribution, but it might be better than what you had originally, and you don't have to find the old d10s. Another cool thing about this is that you can encode more information into the different pairs if you like.

Mike

[Lee Short]

I got a reply from Koplow.  The minimum print run is 10,000 dice, which would be $2470 + shipping.  Can't see coughing up that much dough for a vanity item.  The only way I'd consider it is if I thought I might be able to sell some of the dice to recoup my costs, but I just can't see that happening on a worthwhile scale.  

FWIW, heavy weekend playtesting has convinced me that the dice, as is, still have too high a variance.  I will be experimenting with similar dice with the +6 and -6 removed, which I think may be about right.  

Thanks for the input,
Lee

[Mike Holmes]

What sort of probabilities are you looking for? If you let us know what you wanted, we could probably come up wit a die convention that would suit. I am almost certain that I could reproduce the curves you are attempting to emulate using less dice or more common dice, etc.

Mike

[Lee Short]

What sort of probabilities are you looking for? If you let us know what you wanted, we could probably come up wit a die convention that would suit. I am almost certain that I could reproduce the curves you are attempting to emulate using less dice or more common dice, etc.

Mike

Basically, it must emulate Gaussian distribution as closely as possible.  In detail:  

-- must be open-ended

-- must be centered about 0

-- must have very low handling time.  Adding more than 4 10-sided dice together would be pushing the limit

-- must have an appropriately tight distribution to work with a system
    where skill ratings (-10 = clueless, 5 = apprentice, 25 = master ), and
     have the skill rather than the dice dominate event adjudication (I'm
     working on an essay to go in to my views on this in more details).  

-- ideally, I would like it to be scalable for tasks with more or less randomness
   (longer timed task means random factors tend to cancel means less
   net randomness).  The basic mechanism is for very short duration
   tasks (under 1 minute) (more on this, too, in my essay)  

FWIW, here's the distribution for the original (up to +/-6) dice:

net -15:   incidence 0.119360                cum 0.464520            
net -14:   incidence 0.152000                cum 0.616520            
net -13:   incidence 0.197080                cum 0.813600            
net -12:   incidence 0.528980                cum 1.342580            
net -11:   incidence 0.877720                cum 2.220300            
net -10:   incidence 1.260060                cum 3.480360            
net -9 :   incidence 1.667860                cum 5.148220            
net -8 :   incidence 2.096580                cum 7.244800            
net -7 :   incidence 2.558860                cum 9.803660            
net -6 :   incidence 4.828960                cum 14.632620            
net -5 :   incidence 5.271340                cum 19.903960            
net -4 :   incidence 5.635340                cum 25.539300            
net -3 :   incidence 5.984760                cum 31.524060            
net -2 :   incidence 6.287500                cum 37.811560            
net -1 :   incidence 6.597820                cum 44.409380            
net 0  :   incidence 11.147500               cum 55.556880            

Given the scale, it should have been apparent that 7% chance of a 10 or greater variation was too much.  

Without the 6's it looks like:

net -15:   incidence 0.034140                cum 0.100580            
net -14:   incidence 0.053480                cum 0.154060            
net -13:   incidence 0.078900                cum 0.232960            
net -12:   incidence 0.110360                cum 0.343320            
net -11:   incidence 0.147800                cum 0.491120            
net -10:   incidence 0.542200                cum 1.033320            
net -9 :   incidence 0.967100                cum 2.000420            
net -8 :   incidence 1.415000                cum 3.415420            
net -7 :   incidence 1.893160                cum 5.308580            
net -6 :   incidence 2.363120                cum 7.671700            
net -5 :   incidence 5.927240                cum 13.598940            
net -4 :   incidence 6.374980                cum 19.973920            
net -3 :   incidence 6.783980                cum 26.757900            
net -2 :   incidence 7.155040                cum 33.912940            
net -1 :   incidence 7.573260                cum 41.486200            
net 0  :   incidence 17.001240               cum 58.487440    

This gives a 2% chance of a variation of 10 or more -- more in line with  what I'd like, I think (but I'll have to wait for playtesting to see for sure).  

Lee

[Mike Holmes]

Hmm. Right off the bat, looking at this, I'd go with one +d10 and one -d10. That is roll two different colored D10s, and subtract on from the other. Roll any ten again and add it to the appropriate side. Not a bell, but not bad approximation for only two dice. Then have something special happen on 00 (task is interrupted by act of god, for example, or automatic spectacular success if you like such).

Here's the distribution. The chance for a 19 or higher is actually 1.6% total for all results.

Code:

0    9.00%
1    8.00%
2    7.10%
3    6.20%
4    5.30%
5    4.40%
6    3.50%
7    2.60%
8    1.70%
9    0.80%
10   0.90%
11   0.90%
12   0.80%
13   0.70%
14   0.60%
15   0.50%
16   0.40%
17   0.30%
18   0.20%
19   0.10%
20   0.00%

The chance to get over ten is about five percent, so this is less than you're original seven, but higher than your later system.

For a more weighted center, go with the same system with a third die. The "neutral" die replaces the lower of the positive or negative dice if it is higher than that die. This skews things towards the center, uses only three standard d10s, gives you a bell, and has the following distribution:

Code:

0    16.20%
1    10.09%
2    7.96%
3    6.11%
4    4.54%
5    3.25%
6    2.24%
7    1.51%
8    1.06%
9    0.89%
10   0.81%
11   0.64%
12   0.49%
13   0.36%
14   0.25%
15   0.16%
16   0.09%
17   0.04%
18   0.01%
19   0.00%

Which looks very much like what you're going for.

Mike

[Lee Short]

That looks good, but I think the handling time will be too large for my present gaming group.  I will give it a test run with a couple of my players, though.  

My current group is 7 players, and at least 5 of them have never taken calculus, just to give a feel for the level of math skills.  We play once every 3-4 weeks, and the campaign has called for very few skill rolls so far.  Given these parameters, I think that the handling time for your method would be much larger than I am willing to tolerate.  It would have worked well for my college gaming group (gamed every week, everyone with math SATs over 700).  

thanks,
Lee

[Mike Holmes]

That looks good, but I think the handling time will be too large for my present gaming group.  I will give it a test run with a couple of my players, though.  

???

Your old system required you to add and/or subtract three dice potentially. The more complicated one that I suggest requires you to do two comparison tests, and do one subtraction. All single digit, producing results in the same range. Exact same conditions for open-ended. Seems very comparable to what you were contemplating.

If you really want to simplify, go with the 2die system. It's not perfectly distributed like you were looking for, but it might still provide a fun range. And it's less work than what you were originally looking at, always being one subtraction.

Mike

[Lee Short]

IME, any method which differentiates between the dice requires a notable amount of extra time to make the differentiation itself.  By the time I have figured out which is the + die and which is the - die, I could have already added together 3 small numbers.  Being colorblind certainly doesn't help here, and YMMV.  

Given that half of the die results on my dice are 0, and that only 1 in 40 rolls are open-ended, the processing really goes very quickly -- even for people who don't use the method regularly.  

I will, however, include your method in my game as an alternative for those without old-style d20's.

[Mike Holmes]

Hmm. Hadn't thought about the colorblind aspect.

Still you can just do like most people do in such situations, and roll them one at a time. So yo drop the plus die, then the minus die, then the neutral die. While you are dropping the neutral die, you locate the smaller of the other two, and if the neutral die comes up higher, you replace. Easy enough, it seems to me.

You seem to be willing to go a long way to eliminate handling time if you are willing to modify normal dice just to get certain circumstances where there are lots of "zero" results on the die.

If you were willing to markup your dice, you could just pen in minuses on the minus die and plusses on the plus die. That way at least you don't have to hunt down the old style d10s.

But, hey, like you say, YMMV.

Mike

[Lee Short]

Well, it helps that I've already got at least 15 of those old style d20's :-).

I'm planning on using paint pens -- gold for +, red for -; those colors are easy for me to see.