Dice Chart Porn

There’s a nifty little site called AnyDice that lets you play with some dice probabilities and makes pretty charts and graphs for you.  You can do some basic stuff pretty easily, and with a little bit of programming, you can model some pretty sophisticated probability curves.

In my last post I offhandedly said something along the lines that FATE’s success and failure on 4 dice was very similar to a d4-d4 system (or, more specifically, a d5-1 – d5-1 system).  Below, you can see three curves that evaluate the validity of that statement.

negative 4 to positive 4

The first curve, output 1, is the black line that represents 1d5-1 – 1d5-1.  This curve ranges from 4 to -4 just like FATE, but has a subdued curve (technically, a pyramid).  Critical success and failure are still somewhat likely, somewhere around 4%.  The next curve is a hypothetical game that acts similarly to FATE except you roll 4d6 and count successes, and then roll 4d6 and count the failures.  This causes a significantly pronounced curve as max success/failure now requires BOTH all of 4 dice to come up as success/failure, and ALL of the other 4 dice to come up as a non-success/failure.  You can see that the odds of a max success or max failure under this method is nearly 0.  In the middle, you have output 3, which is FATE.  Here you can see about 1.25% chance of max success or failure, with a pretty normal distribution curve.

All in all, I think that d4-d4 (a shifted version of d5-1 – d5-1) has a nice curve that still makes average results more common without going so far as to make max success/failure so rare it’s not seen in an average session.  It also has less dice and can easily be expanded to represent larger pools (such as a FATE pool with 6 or 8 dice).

The next chart shows the results of having a 2d10 attack roll where damage for a large weapon is the larger of the two dice, a medium weapon is one of the dice, and a small weapon is the lesser of the two dice.

weapon damage with 2d10

While the medium weapon is linear, the large and small weapon are not, but they have a nice symmetrical distribution.  The numbers average out pretty well too.  The mean results here end up being 3.85 damage for small weapons, 5 damage for medium weapons, and 7.15  damage for large weapons.

The other idea I tossed out in the prior post was to roll a d10 and subtract the other d10.  In this case, the combined results will center on 0.  Then, the idea would be that if you had a positive number, you would do damage equal to the negative die.  This means that you can only do major damage if you can hit with a significant negative.  Your power offsets your accuracy.  Here is a chart of the damage % chances for a character with a +3 total bonus to attack using d10-d10 against a target of 1.

chart damage using negative die

As you can see, with a +3 bonus using d10-d10, this character is 72% likely to hit for at least 1 damage.  Low amounts of damage (not coincidently, 1 through 3 damage) are equally likely – but then the damage chart begins to curve so that very high amounts of damage are progressively less likely.

Here is another visualization of the damage chart, this time showing your % odds of doing AT LEAST the amount of damage shown on the x axis (100% chance of at least 0).  This looks like a reasonable damage curve to me.

damage using negative die

I’ll play a bit more with this using different bonuses and target numbers to see how things play out.  If you want to play with the mechanic, the code for it at AnyDice is below.

function: target is A with X:n and Y:n {
if X+Y >= A {
result:[absolute Y]
}
else {
result: 0
}
}
output [target is 1 with d10+3 and d{-10,-9,-8,-7,-6,-5,-4,-3,-2,-1}] named “damage from negative d10”

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4 thoughts on “Dice Chart Porn

  1. connorbros

    Do you ever have any trouble with accessibility at your table, or do you find it’s safe to assume that any rule you construct (within reason) people will absorb and (given a few sessions or so) remember and feel confident manipulating?

    -Dustin

    Reply
    1. JackOfHearts Post author

      Even if the math turns out to be a little complex, the mechanic is going to have to be simple. My group is split between people that are going to invest and learn the mechanics and those that aren’t going to do so quite as much.

      I’m fascinated by game engines, which is really where these series of posts is coming from, and why I’ve been wringing my hands about a system for Lost Worlds rather than slapping something in like FATE, Cortex, or D20. I may end up doing that anyway, but I enjoy exploring the options.

      Still, I think something like d10-d10 isn’t too much for anyone to grasp easily as a core mechanic. Roll a white and black d10, subtract the black d10 from the white, add the modifiers and the result is your to-hit number (or simply your damage if positive and if to-hit goes away). Otherwise, you figure that to-hit with 1 extra math step from regular d20, but with the additional benefit of non-linear attack and damage, and some nice thematic die-based triggers off the white and black dice.

      Of course, I’m always on the lookout for more elegant solutions!

      Reply

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