Friday, June 8, 2012

dice and math

Because I've been going through so many role-playing rules lately, I've been looking at dice mechanics and probability and sizing up which systems are simplest. Not which systems are best, because best is subjective. The basic differences in systems can always just be boiled down to percentages. The average to hit roll for an average human against another average human varies from system to system, but each variance can be expressed as a percentage which illustrates how each system is different.

In d20 (and most versions of D&D) the base roll is a d20 against a 10. Each number on a d20 can be expressed as 5% of a whole. Needing to roll a 10 or higher translates to 55% chance of success.

In World of Darkness the base roll might be a dice pool of four d10s against an average Defense of 2, which lowers the pool to 2d10. To get one success then would translate to 51% chance of success.

There is no average in GURPS since it's a point-buy system. Assuming a character with a DX of 10 and no combat skills, you can brawl without a skill but the character doesn't do as much damage, and the percentage chance to hit is 50%. But in GURPS your opponent can dodge the attack, and assuming a similarly unskilled character with a Dodge of 8, they have a 26% chance of evading that attack. Which means that an average character only has a 38% chance of successfully hitting another average character.

In Deadlands... forget it. It's too chaotic.

I've been tinkering a lot with 2d6 and 3d6 lately so just for fun, if you assume you need to roll 8 or higher on 2d6 the chance of success is 41%.

Extreme results have differing percentages as well. Assume you need to roll the highest number possible, and on a d20 it's a 5% chance, on 2d10 it's 1%, and on 3d6 it's less than 1%. On 2d6 it's 2.78%

Which then begs the question: Why don't people judge their games by the percentages? The more I crunch the numbers the more attractive 2d6 becomes to me. Yet most games, and probably most gamers too, shy away from using 2d6 because it's too plain or generic. There's a combat system waiting to be born out of 2d6 that nobody has adequately explored yet, or maybe they have and I've just never seen it.

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