Alternative percentile system.

[Ranzear]

d100? 2d10?

Pshaw.

11d10 minus 10 would make a good under-the-hood system (or an awkwardly playable tabletop system) with simulation of odds from 50/50 to one in 100 Billion, yes with a B, for all your coin-flip and acts-of-god simulation needs!

DCs no longer need be placed outside the scope of a dice roll and success dependent on modifiers. Critical Success and Critical Failures need no longer be constrained to 5% chances each.

Unfortunately I can't seem to make a good chart of the percent success or rough odds for any given roll. Does anyone know how to run this gaussian distribution through a wringer to pull these out? Most of my homespun probability work has been on things with no more than a few dozen possible combinations, so 100 billion is kinda daunting.

Could be an interesting MATLAB project once I get further into my current class on it.

[Kurald Galain]

What is your goal for the system?

[akma]

http://www.ogmiosproject.org/articles/stattables.html

[Ranzear]

Absolutely perfect link akma, though it does choke on the 'one in one hundred billion' part and rounds to 0%/100%, which is what they are anyway.

What is your goal for the system?

The ideal I'm searching for is a system where you can always roll higher or lower than a target DC if even just by freak accident.

After rolling a few hundred times with a web app, the system really feels right with DCs falling between 31 and 70. The probability chart agrees with this as both cross the 2% mark, putting rolling above or below into the 'freak accident' category while providing breathing room for modifiers without making anything either 'impossible' or '5% chance to pull it off anyway'.

Skill modifiers in this system become much more interesting against, relative to the system, high DC checks. A +10 from skills or stats turns a 50% success rate (51+) into an 85% success rate, and a 0.5% success rate (75+) into a 7% success rate.

To compare, a +5 modifier on a d20 against a DC of 19 turns a 10% success rate into a 35% success rate, barring critical failures. Though it naturally wouldn't be equivalent, a +5 modifier for 11d10-10 on the rough 10% success rate of 63 or higher improves it to a 23% success rate, or the same 35% (37%) rate with a +8 modifier. The scope is roughly the same, but the capacity for modifiers to really affect rolls instead of simply overpowering the DC is much more appealing to me. It provides more increments for skill modifiers without letting them spiral out of control into obscene numbers beyond the scope of the die being used.

Critical success or failure can then be relative to DC. Probably the simplest version would have critical failure be rolling equal to or below two-thirds of the target, rounded up, and skill modifiers may or may not be applied against it. The 10% odds of 63+ improved to 23% by a +5 modifier still carry a 20% critical failure rate without the +5 modifier or 8.7% with modifier. With the potential for extreme modifiers, not applying the modifier to the critical failure would make the latter too common. As compromise, applying half the modifier rounded down to the critical failure threshold seems to work well, giving a 14.9% critical failure rate for this +5 vs DC63 example.

Approaching the limitation of the system with a +30 modifier brings a DC81 from 0.05% to 50% success rate, while half the modifier applied to the critical failure threshold of 54 or lower gives a 12.5% critical failure rate as opposed to a 66% or 2.5% rate. On the other extreme, a relatively routine 45 DC is passed by a +30 modifier at 15 or higher, but 15 is actually overridden by being a critical failure and any failure is critical with odds of such being around 1 in 58 (1.7%).

A DC99, truly a feat to behold, can be beaten by just a +30 modifier with a 2.9% success rate, but carries a stiff 54% critical failure rate (which at this level would probably destroy the universe). Small modifier increases retain value though, as +32 becomes a 4.6% success rate against a 50% critical failure rate. A systematic limit would be a +50 modifier, which turns a DC100 into a 54% success rate against a 20% critical failure rate. A DC45 is a guaranteed pass at +50 except for the overriding critical failure chance of Just because you have universe-warping powers doesn't mean you can't screw up royally, though the chances could be seemingly impossibly low.

And in the end, a Critical Success (Critical hit, masterwork, etc) is simply a natural roll of the DC or higher. This makes a small tactical advantage (like a prone target) grant great boons, but leaves the creation of universes in the blink of an eye (what I'd call a DC99 or DC100) a feat that is hard to top.