Resolution of a Die Roll, Part 1

So, the previous post on converting ACKS' d20 X+ to a X:12 system as ASSH does got me thinking about pixelization and resolution of an image.

When you reduce an image, the math is done to convey as much of the previous information as possible in a smaller space. Converting those rolls from X+ on a d20 to X:12 on a d12 is somewhat similar - you're looking to convey the same general chance of success in a smaller space.

So let's take this all the way down.

Starting from 20, I go down the steps of the default dice, down to 2.

The last column, after the d2, is extra. It's the difference in percentage chance from the original d20 roll to d2. I had one of those for each number as I worked my way down. I wanted to get as close as possible to the d20's percentage for each choice, whether that be higher or lower - there's more than a few spots on this table where I could have used one or the other number, and the only difference was one was -1.666% and one was 1.666%, for example. I ought to have paid more attention to the delta, and will probably do that in the next iteration of this table.

If I'm looking for a 14+ proficiency throw in ACKS, then, I'll want that to be a 4:12 for a d12, 3 in 8 on a d8, 2 in 6 on a d6, 1 in 4 on a d4, and 1 in 2 on a d2.

Obviously, some things will convert better than others, but that's the nature of pixelization. An 18+ throw in ACKS at 15% goes up to 50% on a d2 - you've got to have *some* chance, and you've only got 2 numbers to convey it in.

I think next I'll start at d100 and work my way down through the DCC dice to d2.

Judged by 12

I was browsing through talk about Astonishing Swordsman and Sorcerors of Hyberborea (here ever after named ASSH) and I was tickled that the thief skills use d12s.

I've never really gotten much chance to use d12s. It's a shame, really. They're like low-resolution d20s, nice and round and chunky to roll.

d10s are dumb. Too pointy. Anyway.

So, what if I wanted to redo all the ACKS skills and proficiencies in d12?

Spreadsheet. (Google! Y U No let me cut+paste from your apps?)

So, there's that to work from. Chance to roll X+ on a d20, or X:12 on a d12. Note I'm looking for best fit, not mathematically best. That statement will make more sense in my next post.

To read this, say you need an 18+ in ACKS. That goes closest with 2:12 - you've got a 1.67% better chance at 2:12 than 18+. Our biggest flux is +/- 3.33% - that's less than a +/- 1 on a d20, in theory.

I expect this to all fall apart on the next table. Let's see what the thief skills look like. We'll start with Open Locks.

OK. So, 'Diff' is the percentage change from X+ to X:12. Some levels fare better than others. 'Delta', however, is the change in change from one level to the next - a level 1 thief in X+ gains 5% more ability when she hits level 2, in X:12, none - she loses 5%, essentially, from her guildmate using the X+ system.

Lucky level 7 is the best it gets.

Worth doing? Probably not. ASSH actually uses the venerable d12, whereas I'd be hard pressed to place the die in anything ACKS does.

It's much better systemically to follow along with ACKS using a d20 than to introduce Yet Another Wrinkle in what to roll for what.

True20/MM Static Toughness, Roll Damage

Dark Earth Games got me thinking here about a very short run I did of an Mutants And Masterminds 3E game, and, before I fell into the OSR, a short fling I had with planning to run True20.

There's an alternative system from 2007 (oh, how time has moved, oh, how old you are now True20!) - Baduin's Alternative Damage System and then some modification to that here that inspired me to putz around with what ended up being a Damage Track on a character sheet I was planning to use.

My main draw to the system was simply missing the change to roll damage! It's ingrained, I guess. Your Toughness becomes a static number, which then has 5 degrees added to it for how badly you're hit, depending on the damage your attacker rolls.

So, here's the whole character sheet, note the damage track:

 Works out simply as such: An attacker just hit our Adept with a sword, Damage 2, plus STR 1, rolls a 20 and adds 3. Let's say he gets a 13.

Our squishy Adept with (static) Toughness 4 compares that on the table. He's already filled in the large upper boxes on the Damage Track with values 9, 14, 19, 24, 29.

The 13 damage rolled is between 9 and 14. Our Adept is Hurt, and fills in a box - we're looking at the Damage Track values as needing to be Equal To Or Greater Than. (essentially, everyone's base Toughness is 5 before CON modifiers or armor)

• The Adept is hit for Damage 4. Less than 9, he is unscathed.
• Damage 12 - second box under Hurt is filled in.
• Damage 15 - first box under Wounded.
• Archers take aim, and he's hit for 7 and 9. He fills in the last box under Hurt from the Damage 9 arrow. The first one winged him, a minor scrape.
• A sword-strike for 11 - his Hurt boxes are full, so he fills in the second Wounded box, the lowest box he can take. He's in trouble.
• Another arrow volley - 15 and 16. The last Wounded box is filled in, and, since he's out of those, he has to fill in the Disabled box. He's in trouble, and limps off to cover.

Note squishy folks are squishy - an Ogre, perhaps, swinging a club, could be rolling d20+7 for damage - if that Ogre pops out a roll of 18 or better, our Adept is dead.

This system doesn't really address the 'spiral of death' that happens with the Toughness save as written - it helps a little in that you're not penalizing a poor Toughness save with further penalties as you get damaged, but there can be a sudden drop-off if you're in a long, low damage fight, and you're just simply running out of boxes. 

In fact, I wrote a little Perl to give me some math on this back when I was working on it.

The Attacker's to-hit is +4, and so is his damage. The defender's Defense is 4, as well as his Toughness. A battle of average men. This was 100,000 simulated battles, I think?

4 Attacker vs 4 Defender, 1d20+4:

Total Hits: 809410

Hurts: 175943 

Wounds: 191688 

Disabled: 97762 

Average Hits: 8.0941

Dying Hits: 40338 4.98363005151901%

Instadeath: 0 0%

It takes about 8 hits, if that defender just stands there and takes it, to get killed. The attacker drops the defender to Dying on 1 hit 5% of the time (he rolled a 20!) That program didn't take into account any further penalties from the damage conditions.

Creeping Death (the Purple Worm)

9 and 30 Kingdoms recently posited on the wonder that is the Purple Worm.

Here's another possible wonderful thing:

Many sages posit that sometimes, ever so rarely, when the stars are right, the sun unflared, the tectonic plates shifted *just so*, an ancient purple worm finds itself a enormous underground geode, curls up, and metamorphoses into a Tarrasque - breaking out from the newly mineral-depleted geode to wreak havoc and lay eggs for it's limited, 6 month lifespan.