The play-by-mail wargaming community in the 60’s used publicly available random numbers like the rightmost digit of certain stock prices on a particular day. That way two people who were physically separated could be assured that the “rolls” during the game were fair.
This meant that play-by-mail systems tended to be designed around 1-10 random numbers instead of the normal 1-6 used by tabletop systems. This caused problems if you wanted to adapt a play-by-mail for tabletop play. Much effort was expended to come up with a good way to generate 1-10 random numbers with 6-sided dice buy no one ever figured out a good solution.
The advent of the 20-sided dice changed all that. Early d20s were numbered from 1-10 twice so they could be used just for this purpose. This is why owning d20s became common among gamers in the 60’s and 70’s and why Gary Gygax could assume that his audience would own them when he created D&D.
The d10 was a later invention. It didn’t appear on the scene until the 80’s. When I started playing D&D in the late 70’s there were no d10’s.
Yes that works very nicely. I don’t any way to improve on your efficiency there. But then again, I only have a master’s degree in mathematics, not mathemagics.
That won’t work. These are six-sided dice, so you can’t get 1,7 (for example). There are only 36 possible outcomes, not 56. You would need to divide them up this way:
11,12,13 mean 1
14,15,16 mean 2
21,22,23 mean 3
and so on, until…
54,55,56 mean 10
and if the first number is a six, discard the result and roll again.
This is pretty much equivalent to the first method listed above. One caveat here: if you roll two dice simultaneously and they are the same color, it’s important that you don’t fall into the trap of sorting them by putting the lowest on the left and highest on the right, for example. You can read them from right to left or top to bottom or whatever you want, but be consistent about it and don’t let the numbers influence you.
Having a 10-sided die is a great solution if you’re doing this at home but 6-sided dice are more ubiquitous. Having a method that works with 6-sided dice means you can use the method anywhere without having to carry your own die with you at all times.
Heck, if we’re going for ubiquity, just flip four coins or a coin for times, heads = 1, tails = 0, and get a binary number. Discard any result that is not 1 through 10. Is it efficient? Not really, given that roughly a third of the time you will get a discarded result, but it is near-ubiquitous. I couldn’t even tell you if I have a die in my house right now, or where it would be. But I got plenty of coins.
If you only have six sided dice, here is the simplest method of non-curved results I can figure:
Roll 2 six sided dice:
Take the result of the first die from 1-5; 6 means re-roll the dice.
If the second die shows 4-6, add 5 to the result of the first die, otherwise just take the result of the first die.
This method gives a 1 in 6 chance of re-roll, otherwise it keeps results curve free.
More people probably have Excel available to them than dice. Just use =RAND() to get a uniformly distributed number between 0.000 and 1.000. Then use the first digit after the decimal point.
One roll - 5 six-sided dice, (or roll your 2 dice 2.5 times!) add them together, divide by 3 and round up to the nearest whole number.
1-3 = 1
4-6 = 2
7-9 = 3
…
Assuming balanced dice, you will get an even distribution of answers.
Or buy thee a 10 sided (percentile) or 12 sided (ignore 11 and 12) or 20 sided die.
How balanced are the d10 and d20 dice? They don’t seem manufactured to the highest standards. I would guess that slight errors in manufacturing would cause the dice to land on certain numbers more than others.
And I’ve wondered about normal dice in the casino. Are they truly random? How do they balance them to account for the different weights of the different faces? The side with the 1 must be heavier than the side with the 6, since the 6 has 6 pits taken out of it.
I do that all the time when I need a 2- or 3-digit random number (7 or 10 flips, respectively).
When using the coin to determine a 1-digit random number this way, sure, you’ve got a 37.5% chance of having to re-do it, but it only takes a few seconds to flip a coin 4 times.
Roll 1,000 dice and add them up. Use only the last digit of the sum. Not perfect, but close enough for practical random number generation. Disappointingly slow method, though. Zero wil be slightly more prevalent, at the peak of a bell curve that favors 3,500. Put a small hole in the center of the table, so a few dice fall through, which can be disregarded. That will bring it a lot closer to random by flattening out the curve.
The rightmost DIGIT. You ignored the fractional parts.
It didn’t have to be stocks. It could be any publicly published number that varied randomly, like racing results. It’s the same technique as used by the numbers game.
Split every atom in the dice, and read the energy output with some instrument. Take samples of the random noise in any unit that will commonly have values > 10 and then use them modulo 9, then add one and round.
So there are 1 + 5 + 15 = 21 rolls that translate to 10. However there are 6^5 = 7776 possible rolls total. So the odds of getting a 10 with your system are about 0.27%. In a linear system the odds of getting 10 should be 10%.