It seems to me to be an unfortunate fact that very often new mechanics are developed around the polyhedrons that are available, rather than what numbers would really be sensible or interesting. There are, of course, all sorts of non-standard dice available nowadays, like d30s or whatnot, and that is expanding the mechanics, but these dice remain esoteric (and in some cases, not statistically fair), so for those of us who are stuck with-- or choose to remain with-- the standard dice, I have come up with some methods for rolling some rather strangely shaped dice on the standard models.
A d2 can be rolled by simply rolling any die, and taking a value of 1 for odd, and 2 for even.
A d3 can be rolled by rolling d6, and dividing by 2.
Some other odd numbers are possible by a "roll and drop" method-- roll the next larger die, and reroll in the case of a maximum (and in this case unwanted) value. This can work for rolling a d5 (use a d6, and reroll if you get a 6)-- the same method works for a d7, a d9, a d11, and a d19. Provided you don't mind having more values that require a reroll, a d20 will also work for a d17 or d18.
I should also point out here for those less familiar with the actual probabilities involved that rolling 3d6 is NOT the same as rolling a d18, any more than 2d6 is the same as d12.
What about a d16? You could do it on a d20, but the amount of values that prompt a reroll is getting a bit high-- there are better ways. Roll a d8 and a d2, and if the result is even, add 8 to the d8. This can, of course, be used for higher multiples, too: emulate a d24 with a d8 and a d3, or a d36 with 2d6. This also means that if you don't own a d30, but use a game that requires one, you can simulate it quite well by rolling a d10 and a d3. (or, in terms of actual shapes thrown, a d10 and a d6)
Generating a d36 with d6's is actually a sort of base-6 version of a d100. The square of any die can be rolled in this manner, so we also now have a d36, d64, d144, and d400. Indeed, a d16 can be emulated with 2d4 in this manner, as well, if you prefer it.
A d15 is doable, as well, by rolling a d30-- a real one, or a fake one-- and dividing by two. This will probably be faster than rolling a d20 and having the possibility of several rerolls. You can probably stretch it into a d14, too...
... maybe even a d13. But, let's face, no matter what method you try to use so far, you might be rerolling a few times. I don't know if anyone would ever need a d13, but, it too can be simulated with much fewer rerolls. The trick is in simulating a larger die, and then dividing to get the right value. This was actually already done above, in simulating a d15 if you don't have an actual d30. In the case of a d13, you'll want to roll a d40-- that is, a d20 and a d2. You'll need to reroll a 40, but otherwise, divide anything else by 3. This gives you a range 1-13-- with only one bad value out of 40, instead of 7/20 bad ones trying to do this on a d20.
Hopefully these methods have not only shown how to simulate some weirder values, but the mathematical methods involved can be applied more generally, just in case someone needs a d288 or something.
(That one's actually easy, do it with 2d12 and any other die acting as a d2 ;) )
There's an interesting system in Spirit of the Century that uses what it calls "fudge dice", which are technically d3s marked with one plus sign, one minus sign, and one blank side. (In practice, we use normal d6s, counting the 1 and 2 as minuses and the 5 and 6 as pluses.)
Your stats span a narrow range from -1 to 5, and each roll adds one stat to the result of four fudge dice. So, depending on the whims of the fudge dice, a player using a rather average score (zero) might get a miserable failure (-4), a solid success (4), or anywhere in between, while an expert in a field (5) would range between merely adequate (1) and legendary (9).
It's not a fancy method for achieving unusual die values, but it is a novel use of simple dice, which interests me.
Interesting... however, I got one question: I couldn't quite get how you'd emulate a d36 with 2d6. Would you mind explaining that, please?
I personally would rather use a d10 and a d4 for a d36. Because although it is simply to implement, it's hard to describe with words, so please forgive me for using code instead (yes, I know I'm a geek :-/ :P ):
//<
switch (d4.value()) {
case (1): // returns [1..10]
result = d10.value();
break;
case (2): // returns [11..20]
result = d10.value() + 10;
break;
case (3): // returns [21..30]
result = d10.value() + 20;
break;
case (4): // returns [31..36]
if (d10.value() <= 6) { result = d10.value() + 30; }
else { result = d10.value() - 4 + 30; }
break;
}
//>
PS: the code tag has some very strange behaviour. :huh: Like inserting a ";" after each "<", and highlighting only working after a "<". Just that you know. ;)
--------- Edit ---------
Yes, I know it slightly messes the statistics for the [31..36] range. However, I think that it wouldn't be that bad, as common dice are not equal anyways, so I wonder if the slight skewing would be noticable at all.
My personal preference for creating any unusual dice, however, would be an electronic device. Either a computer program, or a calculator with a (pseudo) random number generator. You just enter the desired interval and hit "return" - no multiple dice rollings and stuff. Of course, you'd have to live with the consequences of your result returning every few billion times you call that random number generator. ;)
Sure. :)
Emulating a d36 with 2d6 is much the same as emulating a d100 with 2d10, only the counting system used is base-6, instead of base-10.
This means that one die represents the "sixes" place, and one represents the units. I'll call one die the "upper" die, and the other the "lower" die. If the upper die is a 1, then just take the lower die as written. If the upper die is a 2, then add 6 to the lower die-- giving a range of 7-12. If the upper die is a 3, add 12, and so on... all the way up to a 6 on both the upper and lower die being "add 30 to the lower die," which is 6, giving 36.
To put it in code:
result = (upper - 1) * 6 + lower;
QuoteEmulating a d36 with 2d6 is much the same as emulating a d100 with 2d10, only the counting system used is base-6, instead of base-10.
I'd just like to say that that's pretty much awesome.
While on the topic of fudge dice, there's a similar technique where you roll 2d4 of different colors, adding one and subtracting the other. Like fudge dice, it centers on +0, but it goes from -3 to +3 and has a bit of a bell curve (I think).
My favorite idea in terms of odd dice is using six sided dice numbered from zero to five. I'm not sure why, but they strike me as a cool idea.
QuoteLike fudge dice, it centers on +0, but it goes from -3 to +3 and has a bit of a bell curve (I think).
Yeah, it's a bell curve, just like 2d6
16 possible rolls:
1 & -1, 1 & -2, 1 & -3, 1 & -4 = +0, -1, -2, -3
2 & -1, 2 & -2, 2 & -3, 2 & -4 = +1, +0, -1, -2
3 & -1, 3 & -2, 3 & -3, 3 & -4 = +2, +1, +0, -1
4 & -1, 4 & -2, 4 & -3, 4 & -4 = +3, +2, +1, +0
-3 : 1/16 (6.25%)
-2 : 2/16 (12.5%)
-1 : 3/16 (18.75%)
+0 : 4/16 (25%)
+1 : 3/16 (18.75%)
+2 : 2/16 (12.5%)
+3 : 1/16 (6.25%)
What's wrong with pennies for d2's?
If you don't mind an ever-so-slight bell curve, d3's can be done with 2d2, much in the same way a d11 can be done with 2d6. Obviously, the bell curve for the d11 is noticable, but I doubt the d3 bell curve would be signifigant.
"bell curve dice" could be repesented more or less like this:
1dX (bell curve die) = YdZ, where:
X = YZ-(Y-1)
It's a weird system that obviously affect probability, but the number range is certainly accurate.
Eidt- Seperated that first sentence from the rest, to avoid it getting confused together :)
Quote from: sdragon1984If you don't mind an ever-so-slight bell curve, d3's can be done with 2d2
If I understand what you've said correctly, it doesn't seem that the curve would be slight at all-- rolling 2d2 means there are four possibilities: AA, AB, BA, or BB. A d3 has three possible outcomes, so however you map it, one of the possibilities is going to be twice as likely as the two others. If you want a curve, this is ideal, but it is not a very good emulation of a d3.
Speaking of bell curves, what is the curve like on 3d6?
The curve for 3d6.
3: 1
4: 3
5: 6
6: 10
7: 15
8: 21
9: 25
10:27
11:27
12:25
13:21
14:15
15:10
16:6
17:3
18:1