"10 and 20 Sided Average Dice?" Topic

Question as the title – has anyone come across 10 and 20 sided average dice? I've just been engaged in a wargaming event where such a thing would have been useful. Now I know I can roll 2d10 and take the average but having the "real thing" would be useful.

Not heard of such. Of course they could be ordered or constructed, but the numbers you'd want on the sides aren't obvious to me. Could you expand on this a little?

Never seen or heard of such and I've been gaming a few decades.

Closest thing I have seen is the d10 in Formula De. But it is not an average die.

I'm with Robert on this. What are average dice?

It seems to me any die has the same chance of any given number coming up.

I thought the d6 average die was a pretty well known wargaming "thing"? But maybe it has become part of the arcane greybeard wargamers art that younger whippersnappers have not encountered :)

They are used where you want to reduce the degree of variation in a die throw the dAv has numbers 2,3,3,4,4,5 rather than the usual 1-6

We used 2 ten-sided die, and the #10 would count as 0 unless you rolled 2 – 10's and that would count as 100. you use 2 different colors one would be for 10 through 90 and the other 0 through 9. That's how we always worked it.

I've used that in the past as well, it calmed the nerves of some of my friends playing Fire and Fury when each side rolled opposites of the extremes :) The main reason for asking is that I'm involved in a project where the participants are a bit leery of dice in general and I'd like them not to have to do (even simple) maths when rolling 2 dice and taking the average :)

I've hunted high and low this afternoon and can't find any, I'll probably buy some blank dice and make my own

(Mounting irritation.) Yes, I know what d6 average dice are. And I still have a few. I think we had this conversation before.

But that doesn't tell me what numbers you'd want on a d10 or d20 average die. Do you want, say, 2,3,4,5,5,6,6,7,8,9 for a d10 aaverage or something else? Should a d20 Average be 2,3,4,5,6,7,8,9.9.10,10,11,12,14,15,16,17,18, or concnetrate more on the center of the distribution?

Thats what I'm asking, what would a d10av or a d20av that gave a similar effect as a d6av compared with a standard d6.

It probably wasn't me that you had this conversation with before, as I said it only just came up in a project I'm working on now

You need to specify what you mean by "similar effect".

Roling a 1 on a d6 is a 16 2/3% chance. On a d20, do you want to just eliminate the individual extremes? do you want to clip the 16% outlier (rougly 1, 2, and 3 on a d20)? the averaging d6 moves the average by about .1 of 3.5, or about 5%, so that? or do you want the standard deviation changed (roughly 13% decrease)?

10 and 20 are factorable by 5, 6 is not. 6 is factorable by 3, 10 and 20 are not. "Similar" is going to have some rough edges.

Robert, no need for the mounting irritation, unless there is something in the past between you and David; I take David's explanation of what an average dice is to be in response to Col Durnford's question ("What are average dice?") and not addressed to your, quite reasonable, request for what type of distribution of numbers David was looking for with 10 or 20-sided "average" dice.

David, I've never heard of the term "average dice" applied to anything other than a D6 with the 1s changed to 3s and the 6s changed to 4s, and a quick search (probably the same one you did before posting here) failed to yield any results for D10 or D20 "average" dice. The results I got to my search were mostly tables and formulas for calculating averages for various dice types.

But, I did find sources for blank D10s and D20s, so …you could buy some and write the numbers you want for your "average" distribution on the dice, or even print the numbers on adhesive paper. Of course you would still have to determine what numbers you want for your "average" distribution for a D10 or D20 (this is what, I think, Robert's replies were all about), but once you have determined roughly what you want by way of an "average" there are at least a few posters here who know enough math to help you refine what you generally are looking for.

Anyway, one source for blank D20s (you could use them for D10s also) is wondertrail at:

link

The web page claims the dice are made by chessex.

Amazon also has several sources for blank dice, but they come in complete sets of D4, etc and so you would be paying for dice you might not want.

Hope this helps….

3D print something?

What would the numbering be on such a die?

I could create the STL file. 3D printed dice are not ideal, but it's still a possibility.

Thank you Dennis. Probably just me being cranky. I was "remembering" a previous discussion which appears not to have happened.

David, if you can articulate the effect you want in mathematical terms, someone here--probably eto--can see how close you can get. My first thought is taking off the two highest and two lowest numbers of a D10 and adding them to the middle--so 3,4,4,5,5,6,6,7,7,8--and the four extremes on the D20--so 5,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,16--would be close enough for government work. (Mind you, I've worked with people using artillery-fired nukes, MLRS units and MOPPs, so my notion of "close enough" may be somewhat distorted.)

You can get blank polyhedral dice as well as d6

@Robert – that is exactly the kind of distribution that I am thinking of. I have blank dice on order, I'll give that a go.

My original question was really about whether such dice existed, whether there was an "industry standard"

You can get a reasonably approximate bell curve distribution by adding together two dice, with half the number of sides of the maximum number you want. So for an "average" d20, try adding two d10s together for a distribution from 0 to 18 (or 2 to 20). Similarly two d5s (do they exist ? I think they do) for 2 to 10. The 25 possibilities are :-

2 1
3 2
4 3
5 4
6 5
7 4
8 3
9 2
10 1

What are average dice?

for those who don't know, the average die is numbered 2,3,3,4,4,5 – I got some originally for WRG Ancients, where they were used by Regular troops, a normal D6 was used for Irregulars.

Second Herkybird. Ah, for the good old "Golden Days" of youth!

Being a non-yout, I remember using a avg. dice for System 7 musket fire. I have also thought of D8,D10 and D20 avg. dice.

Now two D6's gave an excellent bell curve, with a range of 2 to 12. Not sure if the range will work for you?

General curiosity: What's "average" about it?

The "average" of a d6 is 21/6= 3.5. I can't fathom what the distribution mentioned is supposed to represent, especially as each result on a d6 always has an equal chance of occurring on any given roll.

For a d10 "average" is 187/20=9.35. So same as above.

So what is this distribution supposed to represent? The word "average" doesn't make any sense that I can see.

If you roll 2 dice and take the average of the two numbers, you get a distribution. That's what they are talking about
For six sided dice:
1 1 in 36
1.5 2 in 36
2 3 in 36

and so on

The word "average" doesn't make any sense that I can see.

That's because average (or mean) is tricky when talking about discrete distributions, like dice.

Earlier, when I looked up "averaging d6", I got a differrent distribution than the one people are talking about. "2, 3, 3, 4, 4, 5, 5, 6" has the same average as "1, 2, 3, 4, 5, 6", but a different variance.

But the average only applies when you are looking at aggregates across multiple events. It becomes trickier when you are using the discrete distribution to drive a discrete outcome process, like "hit or miss".

So if you take Dexter Ward's averaging method, but look up the result against something like "hit on a 5 or 6", then a result of 1.5 is the same as 1. Using a "rounding" function first just puts two discrete output functions in the mix, instead of one, which in terms of basic properties doesn't change the nature of the function.

All I know is I am not average because I don't have 2.64 children…

Parz, the objective was to trim the extremes--usually in cases in which only a few dice or a single die was rolled. As noted, in old WRG use of a DAV instead of a D6 meant the range of possible outcomes for professionals was somewhat more predictable than the one for irregulars. We fooled around with it a little in CLS--rolling one volley fire die per battalion instead of one per company, but using a DAV to remove the most extreme possibilities.

Naturally, the DAV loses much of its charm when "roll 12 dice" is a common method of combat resolution.

Oh. Von Blucher. What you describe with two D10's is what I've normally heard referred to as "Percentile Die" or "D100."

I've assumed it's "average" in the sense that the results tend to be closer to the average (which is 3.5 for both average dice and normal d6's).

A more statistically rigorous name might have been "low variance dice", but I somehow don't see that catching on.

Averages makes sense if you specify how many rolls you want to average? The average of die-rolls is a normal distribution (I think) and it will have a decreased variance the more rolls you make? So "average dice" is not well-defined, but we could speak about maybe "N-average dice" for dice that has the same distribution as the average of N rolls?

From a quick experiments with a python script (that I asked a LLM to write for me, as I am much too lazy to spend the evening figuring out how to do it, but the results look good… after a few attempts) there are several average 10-sided or 20-sided possibilities (I did not explore average d10 printed on 20-sided dice; that would also make a lot of sense really).

A bit of an edge-case with fractions. I don't think anyone wants a die that has "3.5" on some sides. So it makes sense to round everything off to integers.

For a d6, a "2-average die" would look just like the common "average dice" (that are the only ones I have seen): 2,3,3,4,4,5. It's the same for the average of 3, 4, 5, or 6 d6. With 7 or more d6 the average die instead has sides 3,3,3,4,4,4. Not particularly interesting.

There are more alternatives, as expected, for 10 sides. With the average of just 2 the average die has sides 2, 3, 4, 5, 5, 6, 6, 7, 8, 9. Pretty much like the old common average d6. With the average of rolling more dice:
3-6: 3, 4, 4, 5, 5, 6, 6, 7, 7, 8
7-8: 4, 4, 5, 5, 5, 6, 6, 6, 7, 7
9-28: 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
29-: 5, 5, 5, 5, 5, 6, 6, 6, 6, 6

The d20 follows the same pattern:
2: 4, 5, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 16, 17
3: 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16
4: 5, 6, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 14, 15, 16
5: 6, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 15

And so on… until eventually reaching a boring version that has half the sides 10 and the other half 11.

May have made some mistakes, doing this manually (other than running the script)… But there are definitely many possible "average" dice to choose from, depending on "how average" you want your dice to be.