We all have regrets in life.
Ideally you should have a table that gently slopes in the shape of an inverted bell curve down to the hole in the middle. The closer the die lands to the center of the distribution, the more likely it is to be bounced in the hole and discarded. :rolleyes:
As The Hamster King showed, that’s not even close to uniform.
Maybe you’re misremembering, and instead of dividing by 3, you should take the result modulo 10 and use 0 for 10. So if your sum was 6, 16, or 26, for example, that would count as a six. Testing this, the probability of each value 1 to 10 only varies by about +/- 8 percent from uniform.
Nitpick - they do have pits taken out of them AND they are painted with a paint with the same specific gravity as the dice themselves.
Otherwise - the paint itself would bias the die - granted to a much, much, much smaller amount than regular pitted pips would.
As far as using ten sided dice - they are almost certainly not of sufficient quality to be random.
This guymade a machine that rolled dice tens of thousands of times and shows the results for both cheap dice and casino dice. You don’t have to be a statistician to see how poor the cheap quality dice performed.
To me the easiest method (and the one used by [at least some] in the crypto community) is to make a 6 x 6 grid and you’d use two visually different die (say blue and red).
You’d roll both at the same time - say using the red die as row and the blue die as column. The columns could be arranged like:
1:3:5
1:3:5
1:3: (and so on)
2:4
2:4
2:4
Or
1:7
2:8
3:9
4:10
5:1
6:and so on
So that the first five columns (30 spaces) were filled with integers 1 thru 10 - three times each- and the sixth column would be roll again. I think others alluded to this method above. You roll both dice at once - and only need to reroll 1/6th of the time.
This is vaguely similar to the method used by rand in their literary classic mentioned above “A Million Random Digits and 100,000 Normal Deviates”*. Their method of getting the number involved obtaining a random five bit binary result - which gave them a decimal number between 1 and 32. They discarded numbers 21 - 32 and used the second digit of numbers 1-20 as the digit.
Depending on what you are using it for - I think the Excel method is much easier. While they aren’t “truly random” - I have never noticed any issues (I have in early versions of excel - as well as the default random number generator in PGP). I certainly wouldn’t use it for picking seed numbers for say something to do with cryptography.
Random.org is cool
- I highly recommend reading the reviews of that book on Amazon - certainly entertaining.
I find it’s easier to fly to Monte Carlo, and pay someone to run a “Them” Simulation.
Or get a Zocchihedron, divide by 10, and round. That would also probably take care of the unevenness, too.
Or Excel, use the =RANDBETWEEN(1,10) 1000x (or even better, 10,000x) in Column A. Then somewhere else use =COUNTIF(A:A, “1”); =COUNTIF(A:A, “2”); and so on (or a reference to the integer in place of the quotes).
I’ve refined this. Make the hole large enough that the number that falls through is about 75, plus or minus a dozen or two. Then just count the dice that fell through (usually between 50-something and 90-something), and use the last digit of that number. No need to even count the spots on the dice.
Murder a bunch of people, select the number you get before the police catch you modulo 10 + 1.
Sorry have to disagree. The d10 appeared some time after the AD&D books came out, I remember being very surprised when I first saw them. Not being a platonic solid it wasn’t obvious how to make one. Also to get a 1-10 result, you could just use the 20 sided die. Especially true since it just went from 0-9 and you had to color half of the faces yourself with a permanent marker that would mean “add 10” to the result.
Sigh, kids these days.
Yeah I think any other dice except 6 sided dice meant for gambling has not gone through the same rigor in balancing, and thus wouldn’t be useful. I just went and looked at 4 different stores selling souvenir dice, and I’d guess about 2/3 hasn’t been balanced looking at the amount of inscription and text they contain.
The version of the D&D Basic Set I had, which looked like this, came with a set of 6 dice, including a d10; but earlier versions only included 5 dice (or none at all). This link lists the contents of the various editions of the Basic Set; and here’s a chart showing the publishing history of the various versions of D&D vis a vis AD&D.
Interesting link. As I recall, the one I had had the dragon in color on the cover of the box and in blue tones on the manual cover. I don’t remember a d10.
It’s quite easy to make any dn dice that is fair (in theory it might take some work to balance same). To do this use an equilateral equiangular n-gon and make an n-sided pyramid from it in both directions. Label the 2n sides 1 to n twice. Or if you prefer for n even you can start with an n/2 sided equilateral equiangular polygon. If n is too small and the die doesn’t roll well, use 2n, etc. sides to start.
Here’s a photo of my first set of poly dice, purchased in summer 1976 along with the white box. No d10.
You don’t actually need a d10 to roll a d10, BTW.
Pick up a book, any book, though one with 200+ pages would be best. Open to a random page. Use the second-to-last digit of the page number as an odds/even binary toggle, telling you to use the page number of either the left or right page. The last digit of that page’s number is your d10 (0 being 10 obviously).
Arrogance Ex Machina is probably referring to the Basic Box Set which came out in 1981, which did include include a 10 sider. AD&D 1ed came out from 1977 to 1979 in three separate books, not in a box set.
From page B4 of the Basic Boxset (the 1981 version, which was revised but not retitled):
The 1ed AD&D Dungeon Master’s guide was printed in 1979 and included the use of the d20 you described on pages 9 and 10.
Missed edit window:
Page 10 of the 1ed DM’s guide from 1979 goes on to say:
So, there you have it. The method you described was used, but 10 sided dice were in existence during AD&D’s first run, and were common enough to be included in the Basic Box Set by 1981.
They say memory is the first thing to go…
You really can’t say that “d10s are too low in quality to give good random numbers”. Like any other product, they vary in quality. Some are garbage, and some are very high quality. There’s no inherent reason that the quality of a die should depend on its number of sides.
I doubt any die matches the quality of those used in casinos, particularly those that come with board games.
In other words, use the solution provided in Post #2.