Author Topic: Dierolling Methods to create new Random Number Ranges (Math Involved)  (Read 3118 times)

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I've been giving some thought to this, and I've begun to wonder if we could come up with some better ways to roll dice than d20 and d100?

Now, by better I mean it gives a moderate range without resorting to obscure, expensive dice like d30's.  This stems from my personal feeling that the 1-20 range is too small and the 1-100 range is too large (I want a more gradual effect from bonuses than what a d20 provides, but a d100 is just too much).

For an example, a variant on the way we roll d100's is to go with d6's instead of d10's.  If you subtract 1 from a basic d6 you would have numbers 0-5 on each face.  One number becomes the ones spot and the other becomes the "sixes".  If you translate the result from base 6 to base 10 you get a range of numbers from 0-35.  For simplicity, you could change the faces of the dice to show results like this:

Die 1-
0, 1, 2, 3, 4, 5
Die 2-
0, 6, 12, 18, 24, 30

If you note that a 00 result is a result of 36 similarly to the d100 method, you essentially get a d36.  You can do this with d4's for a d16 or d8's for a d64 as well, if you were so inclined.  I've been thinking about developing my own RPG system for a while now, and I'm liking the d36 range for the "core mechanics" of my own games.

Has anyone else come up with their own dierolling methods for getting new number ranges?  Weighted ranges in particular can make interesting additions to a game.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #1 on: November 16, 2008, 07:31:32 PM »
I've heard of a lot of people using 2d10s or 3d6s instead of 1d20. Those in particular produce more bell curved results, slightly more predictable.

I've never heard of anyone doing what you talk of doing here, that is expanding the RNG from 20 to something higher than 20 (except of course with percentages, which may or may not be rolled at all). It's interesting, and I think might be a fun thing to experiment with in regular old DnD to get the feel for it.

I kinda like it... it expands the RNG making +1 bonuses slightly less relevant, while making +6 a very relevant, but not absurdly high bonus. In a system using this I might not allow bonuses to rolls to go any higher than +12 (a maximum of +6 from ability scores and a maximum of +6 from other sources combined).

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #2 on: November 17, 2008, 04:41:26 AM »
A +4 bonus with the d20 has about the same impact as a +7 bonus with the "d36," so the key here is that you can have a finer control on bonuses and that the total bonuses in opposed checks can stay interesting despite a wider disparity between the two opponents.

Another task that this accomplishes for me is that it helps broaden the power curve compared to the d20 system.  If a challenging encounter requires a d20 roll of about 9 to 12 then a challenging encounter for the d36 comes out to about 15 to 22.  Should challenges be a +1 bonus apart from each other level-to-level then all of a sudden that's 8 levels that are "challenging" instead of only 4 which gives the GMs more tools to throw at the players, which makes the game more interesting for the players because they are less likely to know what's coming next.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #3 on: November 17, 2008, 05:25:40 AM »
This seems overly complicated. Why not just roll 2d20 out of 40?

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #4 on: November 17, 2008, 05:56:05 AM »
This seems overly complicated. Why not just roll 2d20 out of 40?
Because that skews results heavily to the middle, which actually increases the emphasis on bonuses.  Given there's the random fluke chance that you succeed amazingly or fail utterly, they're just a lot rarer with 2d20 than with the d36.

Besides, it can be simplified easily enough by going with the customized dice I mentioned.  With a simple google search I found a set of 12 Blank Dice with labels to label each side for $2.31 online.  If you want to hand-pick your dice colors then there's a second website that does that, albeit the dice cost about 3x as much.  Put 0-5 on one and then 0, 6, 12, 18, 24, 30 on the other and all it takes is some simple addition to come up with the result, no more complicated than rolling a d100.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #5 on: November 18, 2008, 06:36:26 PM »
I think it's a very viable option for die rolling, certainly. The biggest downsides are that you have to make your own dice or suffer brain fatigue as you play, trying to translate the die results. The other downside is that you would certainly have to have a system tailor-made for this die mechanic. d20 would not operate very well if this were tacked on.
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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #6 on: November 19, 2008, 01:48:55 AM »
Honestly, I've read the OP about five times and I still can't figure out how this is supposed to work. More power to ya if you can find a way, but any gaming manual that started with that bizarre description of die rolling would lose me immediately.

So I guess my next question is ,what kind of probability curve are you looking for and is there a less brain-explodey way to achieve it?

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #7 on: November 19, 2008, 03:36:17 AM »
Honestly, I've read the OP about five times and I still can't figure out how this is supposed to work. More power to ya if you can find a way, but any gaming manual that started with that bizarre description of die rolling would lose me immediately.

So I guess my next question is ,what kind of probability curve are you looking for and is there a less brain-explodey way to achieve it?
The two six-sided dice labeled...
0, 1, 2, 3, 4, 5
and
0, 6, 12, 18, 24, 30
add up to all numbers in the range of 0-35, and each number has a 2.78% chance of coming up.

The base numbers was simply to explain how the math works and how you can do this with other dice (for those who have taken more advanced math courses or just play around with base numbers for fun).
For example, the above dice actually represent the digits of a base 6 number.  The die labeled 0-5 is the "ones" digit, and the die labeled 0, 6, 12, 18, 24, and 30 is the "sixes" digit, and if written in base 6 is actually 0, 10, 20, 30, 40, and 50.  If you take that to the next step you'll get the "thirty-sixes" digit and have die values of 0, 36, 72, 108, 144, and 180 representing values of 0, 100, 200, 300, 400, and 500 in our base 6 number.

It's all really just the same as rolling 2d10 and putting one number in the ones digit and the other in the tens, except we're doing it on a base 6 number with d6's and then translating that back to base 10 by changing the die values.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #8 on: November 19, 2008, 11:41:26 AM »
Why not use a d4 and a d10 to make a d40 ? Less work that way.

Personally I'm fine with the d20 - if anything I like to reduce the number of dice I'm rolling (except for a once-in-a-while big blast spell because rolling 12d6 is fun ;)).
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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #9 on: November 19, 2008, 12:05:12 PM »
Why not just, I dunno, buy a couple of d30s if you want an expanded uniformly distributed RNG?

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #10 on: November 20, 2008, 05:07:31 AM »
Why not just, I dunno, buy a couple of d30s if you want an expanded uniformly distributed RNG?
Because d30's are expensive and huge, and they have to be because if they're not somewhat larger than a d20 then each side doesn't have enough surface area to reliably stop the die and it just keeps rolling off the table.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #11 on: November 20, 2008, 11:27:50 AM »
« Last Edit: February 27, 2009, 02:51:00 AM by Wordman »
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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #12 on: November 21, 2008, 08:56:51 AM »
It wouldn't be 2% or 3%, it would be more like 4% or 5% in most cases.  There's no point to handling small bonuses in this system because you'd need several to have a significant impact on your dice and there's no point in having all big bonuses when there aren't any small ones.

As for the d40, there are some people who do not favor D&D because of the d4.  Not only can a given d4 be very confusing to read, but you have to learn it twice because they're marked in two different ways.

Lastly, when it comes to the d24's I just tell you to look at the price tag.  A d24 is no less specialized than the 2 d6's I'd make for the games and at the same time it could be almost 5x as much to purchase.  While I by no means expect the game I'm making to be a stupendous success that actually becomes something I could sell for cash money, I'm not going to shoot myself in the foot in the case that it does.  While granted it's only about $1 per "book" I'd save to provide the custom dice, if I sell 1000 books then that's $1000 I'd be saving.  Conversely, if the game is so horrible that only me and my friends wind up playing it then I'd prefer we buy the 2 d6's and each also bring a 2-liter of soda to the first game.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #13 on: November 21, 2008, 04:18:48 PM »
« Last Edit: February 27, 2009, 02:51:33 AM by Wordman »
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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #14 on: November 21, 2008, 04:59:38 PM »
I'd think that the main reason to use an alternate die rolling method would be to get more consistent results than a d20 gives, and anything involving standard d6s is probably good, since they're a lot more available than special gaming dices(I've lost count of how many of those I have from old board games, ruined monopoly sets, etc), you could do things involving large number of dices.
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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #15 on: November 21, 2008, 11:17:55 PM »
I'd think that the main reason to use an alternate die rolling method would be to get more consistent results than a d20 gives, and anything involving standard d6s is probably good, since they're a lot more available than special gaming dices(I've lost count of how many of those I have from old board games, ruined monopoly sets, etc), you could do things involving large number of dices.
That's one.  The other is that I want scaling bonuses to be more gradual and more uniform.  The target range of +3-5 for a primary ability score in 4e is a 10% while a similarly expected +3-5 in d36 yields a tighter 5.5ish%, reducing the importance of having spectacular ability scores at the start and, at the same time, slightly decreasing the negative impact of MAD.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #16 on: November 23, 2008, 06:21:18 PM »
So, counting in base 6 up to 2 digits...

Without modifying dice, just multiplying one of the two dice by 6, you get a 7 minimum and 42 maximum. It's a shift upward by 6, but it removes most of the need to make custom dice. Plus it has the added benefit of being a 'd42' ;)



I see what you're saying about the d100 being too large, but you can increment it smaller, say at 3% intervals, and it mimics fairly closely what you're apparently going for with the d36 method.

As a commentary to what seems to me be your intent in the OP, what I see with a broader variance in rolling possibilities is that skill and ability of the character have less to do with the outcome of a contest. A bell-curved die system is the opposite of this; you can have high numbers, but average is more likely. So skill and ability make more of a difference in difficult situations where average just won't cut it.

Character ability is something that I like to have. When the dice tend to take that away or make it unimportant, I get frustrated. So, your method is a good one in simulation of making non-regular polygons into regular polygons. I just feel that going too high in the dice reduces the ability of a character to change the random fate of the dice. Maybe I'm looking at it from the wrong perspective.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #17 on: November 23, 2008, 10:50:49 PM »
Stuff
The reason video games are so popular is because all the math and dierolling happen behind the scenes, they don't have to be done manually by the player.  It's better to use modified dice than it is to have someone multiply by 6 every time someone rolled dice.  It's also adding more math to have people multiply bonuses for a d100 by 3.  Further, I'm not making the d36 to compensate for a small penis size, so the false sense of satisfaction from throwing around bigger numbers is of absolutely no interest to me.

In all seriousness, I didn't make this thread so that I could defend my position about whether the d36 is cool or not, I made it so people could come up with other cool probability tricks you could do with the usual allotment of dice.

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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #18 on: November 24, 2008, 02:54:23 AM »
« Last Edit: February 27, 2009, 02:52:19 AM by Wordman »
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Re: Dierolling Methods to create new Random Number Ranges (Math Involved)
« Reply #19 on: November 25, 2008, 05:11:34 PM »
There's certainly the old "bell curve trick" with dice. Roll d12 + d8 instead of d20, and you end up with your scores grouped towards the middle and far less likely at the extremes. This creates a game where abilities are much more reliable in general. You're just that much more likely to keep rolling numbers in a particular "zone." You can do the same thing with d4 + d6 (for d10), or d8 + d4 (for d12). Etcetera.

I think The 20' By 20' Room had some cool-ass break downs of dice and probability maths a couple of years ago.