Does anyone remember divided dice rolls?

[komradebob]

The thread on Call of Cthulhu firepower reminded me of an old Dragon magazine article about divided dice rolls. This article must have been at least ten or more years ago, but I know several folks here are longtime gamers, so I thought I would ask.

A quick recap for those who have no idea what I'm talking about;

A divided die roll is when you throw one die of a given type ( or perhaps a multiple, like 2d6), then throw a second die with it and divide the result of the first die/dice by the result of the second.

Um, so who cares?

Well, basically, divided die rolls made for a very reasonable critical hit system for AD&D. See, the author of this article I'm talking about sat down and figured out common die division combos. These combos were bell curves, but they generally replicated the results of linear die probabilities.

However...
Unlike normal bell curves, the divided die rolls had a "tail" of very low probability results that stretched out either towards higher or lower results, depending on whether the dividing die was smaller or larger  (in number of sides) than the die it was dividing, respectively.

And this has what to do what the price of tea in China?

Well, this fella's theory was that while say a dagger was generally going to do less damage than a sword, there were times that a dagger was just as deadly, such as in a thrust through a weakpoint. IIRC, In old AD&D, daggers did d4 damage. Swords did d8.

Under this article, however, the author posited giving the dagger a d8 divided by d4 damage. The probablity curve created effectively recreated a d4 result pattern almost every time. However, every once in a while, the dagger could do 8 points of damage.

The relation to Cthulhu:
I mentioned that I thought that guns in CoC weren't deadly enough. Actually, I tend to think that guns in a lot of games that use hit points aren't nearly deadly enough. OTOH, I've known folks that have been shot IRL and lived. One is my granddad. He survived both hmg fire and a grenade attack. The point isn't that grandad is a tough SOB, the point is that things like gunfire are really variable in effect. A big musclebound healthy guy IRL can be killed dead as Julius Caesar by a .22 handgun. On the flip side, people have been known to fall from huge heights and survive.

I truly wish I had access to this article. If anyone remembers it, or it is posted somewhere plaease let me know. Perhaps some mathematically adepts folks here could replicate the other author's  results.

Anyway, something for designers and rules tinkerers to consider.

[Walt Freitag]

I think exploding dice serves the same function in many systems today. Exploding rerolls are arguably easier than dividing, they're mathematically very well behaved (except for the possibility of having specific totals that can't be obtained, which can be avoided by subtracting one from each reroll die), and they have an even longer tail of extraordinary (though extremely unlikely) results.

- Walt

[komradebob]

Sorry, I'm not familiar with exploding dice. can you explain?

[montag]

Sorry, I'm not familiar with exploding dice. can you explain?

AFAIK this is the generic term for all instances of "when you get an extreme result, roll again to possibly get a more extreme result". Like when you roll 3d6 and add them, you roll another d6 if and only if you have a total of 18 from the first roll. The second roll is then added to your original 18 (should your reroll be another 6 you can even get to reroll again ... and again ... and again.)
Also very common in dice pool systems like in Shadowrun or V:tM where the difficulty can be higher than the number of sides on your dice (e.g. 13 in the case of a d10) and you can only succeed if your first roll includes a maximal result (10 with a d10), which allows you to reroll that dice to – hopefully – make it to the required difficulty by adding the second roll to the 10 from the first roll.

[Jeph]

"Exploding dice" refers to any mechanic where if a die rolls a certain value it is rerolled, with the new throw being cumulative with the original (ie, not replacing it). A classic example is Feng Shui in which you throw 2d6, one being positive and one being negative. Both dice can explode, which means that results far outside the range of -5 to +5 are possible.

IE, suppose I have a Guns of 15. I want to shoot a guy, so throw my dice. I roll +3/-6. I reroll the minus die, and throw another -6. I reroll the minus die again, and get a -2. My total is 4 (15+3-6-6-2).

[Christopher Weeks]

I'm familiar with the divided die roll article.  I'm pretty sure it was published around '85.  Does that sound plausible?  It's possible that another article was written long after the first, but if not, my father wrote it.

I emailed the old man this morning when I saw the note, but he's not sure if he even has a copy of the article any more.

I think the handling time is too great for most table-top applications but it's a useful tool for CRPGs.

Chris

[komradebob]

'85? Sounds about right.

Actually, a 20 x 20 chart could be created to cover the combinations resulting from all of your basic polyhedral dice combos and some of your common (2d6,3d6,2d4) rolls. I suspect that is why it worked for AD&D.

I guess Iam familiar wth exlpoding dice in principle, just not the term. I played lots of MERP years ago, and it worked similarly.

[Mike Holmes]

I guess Iam familiar wth exlpoding dice in principle, just not the term. I played lots of MERP years ago, and it worked similarly.

That's what was termed an "open-ended" roll. Exploding dice, isn't too well defined, but more often is used to refer to dice pools, like the d6 System in which the term may have originated.

In any case, terminology isn't really important here, use of terms like tails, etc, like you did above are best when talking about what sorts of curves you're trying to generate.

In any case, I agree with Chris, that even with a table that it's more cumbersome than other equally good exploding or open-ended systems.

Mike

[Christopher Weeks]

Regarding these exploding or open-ended mechanics, do they all boil down to if you roll a six, roll again and add?

If so, the one thing about divided die rolls is that you get more interesting, or at least different, curves.

Which got me to thinking, what math would you have to do to a normally distributed dieroll to make it bimodal?  And can anyone think of a value for such a mechanic?

You could roll a red die and a white die and whichever is higher is used but the white die is negative and ties equal zero.  But that's not mathing a normal die.  You could do something like abs(sin(d6*d6*10)) but the time to process that is really through the roof.  And it would need further complicating adjustment to correct asymmetry.  Am I missing something simple?

Chris

[Mike Holmes]

You mean bimodal in other than adjacent values, right? The fact that 10 and 11 are both the mode for a 3d6 roll isn't all that interesting, is it?

Interestingly, HeroQuest is often bimodal if you consider ties to be in the center of the outcome curve, and, when not bimodal, it has more than one peak to it's curve often. The oddity of this was discussed in a recent thread on the HQ forum here.

http://www.indie-rpgs.com/viewtopic.php?t=10177

What's cool about the HQ curve is how ties are present but rare, making them a special droop in the middle of the curve. Overall, I'm not sure that the bimodal nature is all that important, but as you can see later in that thread, I really do like the results.

Mike

[Walt Freitag]

It's typically if you roll the maximum value on any particular die, roll again and add (possibly subtracting one), and repeat as long as the maximum value keeps being rolled.

Note that if you don't subtract one from the rerolls, you get numbers you can't hit, namely the maximum roll itself, and all its multiples.

If you do subtract one from the rerolls, the math comes out very nicely in that regardless of the number of sides on the die, the chance of rerolls adds exactly .5  to the mean value rolled. The mean for 1d6 is 3.5, so the mean for 1d6x (x for exploding) is 4.

A d2 roll times a constant (or a d2 weighed more heavily, such as a six sider numbered 0, 0, 0, 10, 10, 10) added to another smaller die roll would give you a bimodal distribution. Such as, 10 * d2 + 2d6. But I doubt that has the elegance you're looking form.

- Walt