Wednesday, May 12, 2010

Purple Is The Two Black

This post is about the dice in Warhammer Fantasy Role-Play 3rd Edition. Specifically, the Challenge Dice and Misfortune Dice. This will probably be the first in a series of posts looking at various aspects of the often-opaque mechanics of Warhammer 3rd.

Rather than save the big surprise for the end, I'm going to put the most important conclusions of this article right up front where you can't miss them:
  • 1 Challenge Die is about equal to 2 Misfortune dice. For the past month and a half I thought it was nearly as potent as 3 Misfortune dice, but I was grossly mistaken.
  • Improved Active Defenses barely improve your defensive stats over the "non-improved" versions. They are a tiny bit misleading in that regards, because the real benefit isn't what you'd think it is.

The Challenge dice are purple 8-siders, and the Misfortune Dice are black 6-siders. The challenge die is decked out with various penalty symbols, and has only 1 blank side. The misfortune die has half it's sides blank. Clearly the challenge die is much nastier than the misfortune die.

These pie charts show us the distribution of failure symbols and banes on a single die of either type:

On those pie charts (and the ones below), blue represents failure symbols (the little crossed swords that cancel out successes / hammers), and orange represents banes (the little skulls that cancel out boons / eagles and thus cause negative side-effects). The white region is the blank sides, and the black region is the dreaded Chaos Star (which sometimes counts as just another bane, but often presents much nastier side effects of its own). To generate the charts, I just entered in the percentages of each possible outcome into a spreadsheet, and had Open Office generate charts for me. The larger the area, the greater the percentage of rolls it will come up on. A quarter of the circle corresponds to 1/4 of all rolls, etc. As an extra note, the darker I colored the area, the stronger the effect (i.e.: Medium blue is 2 failures, but light blue is just 1 failure).

It's obvious that one challenge die is much worse than 1 misfortune die, but just how much worse is a little harder to figure out. Is it worth 2 misfortune dice? 3 misfortune? Let's look at a few more charts to figure that out. Here's the challenge die pie chart again, but this time we'll set it next to a chart that shows the combined results of 2 misfortune dice:

With charts like this, comparing the dice becomes a relatively simple matter of eye-balling it. I kept the colors the same, but added in purple to represent mixed results of both failures and banes. If you want to know what percentage of the rolls will result in one or more failure symbols, look at the blue and purple blocks. If you want to know what percentage generates bane symbols, look at the purple, orange, and black blocks.

In this case, the blue section of the challenge die chart is smaller than the blue and purple section of the two misfortune dice chart, so we know that you'll be more likely to get at least one failure symbol on the misfortune dice. However, the challenge die generates more banes (and chaos stars) as evidenced by the size of the orange and black sections of that chart being bigger than the orange and purple section of the 2 misfortune chart. Exactly which is worse, 1 Challenge Die or 2 Misfortune Dice, largely depends on the situation. In some Location cards, and for some Action cards, a Chaos Star can be devastating. In those cases, the Challenge die is worse. In all other situations, they're about equal.

(For those who are oriented towards numbers instead of visuals, the challenge die has a 37.5% chance of generating at least one bane. Two misfortune dice rolled together have only a 30.56% chance of generating at least one bane. Failure odds on the dice are 50% for a challenge die, and 55.56% on the pair of misfortune dice.)

The equality of 1 Challenge die and 2 Misfortune was a big shock to me. There's numerous points in the rules (and cards) of the game that imply 1 Challenge is the next step after 2 misfortune. That would suggest it's worth either 2.5 or even 3 misfortune dice, but it's not.

The best example of this implication is the Advanced Defense cards. They all turn your existing Parry or Dodge from 2 misfortune dice into 1 challenge die, and provide some other minor benefit almost as an afterthought. It turns out the minor benefit is actually the lion's share of the bonus provided by upgrading to an Advanced Defense card. Don't take Advanced Parry because you want your parries to do a better job of protecting you from enemy attacks, as the growth in that area is minimal. Instead, if you take Advance Parry, it should be because it will sometimes make one of your attack cards recharge faster. That's the only real benefit over the normal Parry.

The chart to the left illustrates my point about the Improved Parry. This graph takes a typical attack roll (4 Characteristics Dice, 1 Expertise Die, and 1 Fortune Die) and charts the odds of scoring 0, 1+, 2+, or 3+ successes. The different colored lines correspond to various levels of defense.

In particular, pay attention to the brown and yellow lines, which overlap significantly. The yellow line is vs 1 challenge and 2 misfortune, essentially an attack against a target in leather armor who uses Parry and has Weapon Skill Trained. The brown line is vs 2 challenge, essentially an attack against a target in leather armor who uses Improved Parry (and thus also has Weapon Skill Trained, since it's one of the prerequisites). The target with Improved Parry will be hit 70.37% of the time, and the target with the normal Parry will be hit 72.78% of the time.

A similar relationship exists between the light-green and light-blue lines on that chart. They're against a target with 1 point of Defense, so he's got slightly better armor. Again, having an "improved" active defense only shaves a tiny bit off the odds of being hit (down from 65.42% to 63.25%), and the two lines are practically on top of each other. The challenge die is just a hair's breadth more potent than 2 misfortune dice. Adding one more misfortune die has a lot more impact than converting two misfortune into a challenge (about 7% improvement, instead of about 2.5%, in the specific dice pools shown on the chart).

For the sake of completeness, I'll provide one more pie chart, this time a picture of the results of rolling 3 misfortune dice. I'll again set it side-by-side with the familiar 1 challenge die graph for comparison:

Interestingly enough, three misfortune dice have exactly the same odds of all coming up blank as does a single challenge die. That, coupled with the challenge die's strong chance of rolling 2 failures, were both factors in my over-estimating the power of a challenge die when I first started playing with the game.

Another non-obvious "advantage" to the 3 misfortune dice comes in the form of "mixed" or "overlapping" results, represented by the purple regions of the above pie charts. Rolls that fail because of a challenge die are likely to have a "silver lining" in that they'll score boons, but rolls against a handful of misfortune dice are likely to negatively impact both your successes and your boons.


Anonymous said...

Interesting stuff Rolfe, and given my twisted sense of humor I really like the title.
One question I have is that the graph compares successes between attacks with black dice and purple dice. We can see from your first two pie charts that the chance of 2 black dice giving failures at all is higher than that of 1 purple, but the purple has a higher chance of 2 failures. However, the purple die has the chaos star. The banes and the chaos star can certainly stink to role on the player end of things, but I have no idea of what they do to NPCs. This may shift things a bit more towards the purple die, though I'd definitely prefer to defend with 3 black dice :)

rbbergstrom said...

The chaos stars, and the whole boon/bane axis, does tend to complicate things. I'm working on some additional charts, but there's enough interesting math behind these dice to make for a dozen articles.

Anonymous said...

Seems to me that the challenge die is worth about 2.25-2.5 misfortune dice depending on how heavily you weight the chaos star.

To start, a challenge die is worth 2.25 misfortune dice if you assume the chaos star is as bad as either a bane or a failure. If you consider the chaos star worse than either, than the value of the challenge die rises as a proportion of that value.

Explanation of the math:
On average
1 challenge die will give you:
0.75 failures
0.375 banes
0.125 chaos stars

2 misfortune dice will give you:
.67 failures
.33 banes

You'll notice that the challenge die causes 12% more failures and 13% more banes. If there were no chaos star, this would imply that a single challenge die is about 1/8 (or between 12-13%) worse than the two misfortune dice. Add in the shaos star, and it becomes 25% worse.

Because the chaos star can be devastating, this number can easily be adjusted (even on the fly if you've got a calculator)—for every percent you think the chaos star is worse than a bane or failure, raise the number of misfortune dice that a challenge die is worth by 1/8 of a percent. So, for example, if you consider the chaos star to be the equivalent of two banes or two failures (a 100% increase in value over just one), our number of (one challenge die equalling) 2.25 misfortune dice suddenly becomes 2.38 misfortune dice. If you believe it's 3x as bad, we're now at 1 challenge die being worth 2.5.

Hope that's helpful somehow.

Anonymous said...

Correction on my previous post:
It's not 2.25 misfortune dice, but rather 1.25x as bad as two misfortune dice.

So when I said "2.25 dice", that should actually be "2.5 dice", and when I said "2.5 dice", that should actually be "3 dice".