It seems I need to consider alternative dice mechanics. The Utrecht group has demonstrated that the endeavors of beginning occultists lack drama due to an absence of mechanical adversity. I can see where they're coming from. And their suggestion that opposition be a dice pool, rather than a target number is a good one. (I'll admit, I went with target numbers primarily because opposed pool are so over-exposed in narrativist games. My Life with Master does them well. Dogs In the Vineyard does them well. Sorcerer, too. Riddle of Steel. Etc. But I'm comfortable with a switch from target numbers to opposed pools if that improves the game.)

So, here's what I think the dice mechanics need to do:

A player rolling a pool of the same size as the GM's pool should be at a disadvantage, rather than at an even 50% chance of success. I'm thinking maybe a 30-40% chance of success if your pool is the same size as the GM's.

A pool of two or three dice extra in the player's favor should tip him up to a 60-70% chance of success.

The player uses larger size dice for Rage, Ambition, and Clarity, depending on the character's level of advancement. A player rolling a pool of the same number of dice as the GM, but with two of his dice being larger because of the character's level, should have a 60-70% chance of success.

Even rolling one die, a player should always have a chance of success, however slim it might be.

Also, I like the mild beginner's luck effect of the high die minus low die mechanic, where if the character only has a one die pool there's no low die to subtract. But I can live without it if necessary.

Recommendations? Mike? Anyone?

Paul

Paul:

A player rolling a pool of the same size as the GM's pool should be at a disadvantage, rather than at an even 50% chance of success. I'm thinking maybe a 30-40% chance of success if your pool is the same size as the GM's.

A pool of two or three dice extra in the player's favor should tip him up to a 60-70% chance of success.

The player uses larger size dice for Rage, Ambition, and Clarity, depending on the character's level of advancement. A player rolling a pool of the same number of dice as the GM, but with two of his dice being larger because of the character's level, should have a 60-70% chance of success.

      Even rolling one die, a player should always have a chance of success, however slim it might be.

Also, I like the mild beginner's luck effect of the high die minus low die mechanic, where if the character only has a one die pool there's no low die to subtract. But I can live without it if necessary.

I did some calculations on a system that doesn't satisfy all your needs, but may point in the right direction. The system is:

* Player and GM roll die pools. The GM always rolls d6s, the player either d6s or d8s or mixed d6s and d8s, depending on stats used and status (Scourge, whatever).
* Alls 5's and higher number are successes.
* If the player rolls more successes than the GM, the character succeeds through his own efforts. Player narrates.
* If the player and the GM both roll (exactly) zero successes, the characters succeeds through luck or outside influences. GM narrates.
* Otherwise, the character fails. GM narrates.

The fourth rule is the 'beginners luck' rule: in the beginning, when the pools are small, the character has a fair chance to win through this rule - but it also shows that he is still subject to fortune and chance. As dice pools grow, the character gets to depend on his own skills alone, and succeeds or fails accordingly.

Numbers I crunched:

1d6 vs 1d6
Player wins through skill: 22%
Beginner's luck: 44%
Total: 66%

2d6 vs 2d6
Player wins through skill: 29%
Beginner's luck: 19%
Total: 48%

3d6 vs 3d6
Player wins through skill: 33%
Beginner's luck: 9%
Total: 42%

4d6 vs 4d6
Player wins through skill: 36%
Beginner's luck: 4%
Total: 40%

5d6 vs 5d6
Player wins through skill: 36%
Beginner's luck: 2%
Total: 38%

5d6 vs 3d6 (player has 5d6)
Player wins through skill: 54%
Beginner's luck: 4%
Total: 58%

2d6 + 3d8 vs 5d6
Player wins through skill: 50%
Beginner's luck: 1%
Total: 51%

The behaviour is basically correct, but:
* Chances of winning (including beginner's luck) with pools of the same size are a bit higher than you were asking for.
* Chances don't increase fast enough when d8s are used instead of d6s.  (One could use d10s instead, which would solve the problem.)

Both of these are excellent proposals. Particularly the idea that the player and GM roll different sized dice. I've been crunching some numbers on an opposed pool system with this feature.

What I'm thinking is a system of counting prime numbers as successes on pools of
d8s and d6s. (What could be more occult than counting primes!) This makes the d6 better than the d8, because the likelihood of rolling a prime number is 66.7%, rather than 62.5% for the d8. And so the GM always rolls d6's. Players will roll mostly d8's, but d6's for Ambition at Misanthrope level, d6's for Rage at Scourge level, and d6's for Clarity at Anathema level. To succeed, the player must roll more primes than the GM. Rolling the same amount of primes as the GM is a failure. The beginner's luck effect is lost, but the probabilities (based on only 4000 randomized throws, so there's definitely some strangeness) seem otherwise very nice:

1d8 vs 1d6: 21%
2d8 vs 1d6: 55%
3d8 vs 1d6: 85%
4d8 vs 1d6: 94%
5d8 vs 1d6: 97%

2d8 vs 2d6: 27%
3d8 vs 3d6: 30%
4d8 vs 4d6: 31%
5d8 vs 5d6: 31%
6d8 vs 6d6: 32%

1d8 vs 1d8: 22%
2d8 vs 2d8: 30%
3d8 vs 3d8: 33%
4d8 vs 4d8: 35%
5d8 vs 5d8: 36%

What do you think?

Paul

The figures show pretty much the progression you were hoping for, so, why not. Basically, the mechanism itself isn't important, it's important that it brings you the probabilities you wished for.

What I'm thinking is a system of counting prime numbers as successes on pools of
d8s and d6s. (What could be more occult than counting primes!)

Just a quick comment now, although I hate to make it. (Because I like the idea of counting primes.)

This makes the d6 better than the d8, because the likelihood of rolling a prime number is 66.7%,

Victor wrote:
To the best of my mathematical knowledge, the chance of rolling a prime on a d6 is only 50%. There are three primes on a d6: 2, 3 and 5. The number 1 is not a prime number. Wikipedia on 'prime number'.

Ah, poop.

There must be some way to save this idea.

You could do 'prime', and have d6s and d10s, with probabilities of 50% and 40% respectively. You'll need to do some new calculations.

You could do 'odd or square' with the d's you used to, that would generate the same probabilities; but its more contrived.

Interesting but complex would be 'primes and doubles', where each prime grants one success, but in addition each number showing twice grants 2 successes, each number showing thrice 3 successes - this privileges smaller d's over larger ones, and more so for larger pools.

An interesting quote from the Wikipedia article 1:

"One is currently considered neither a prime number, nor a composite number - although it used to be considered prime. Defining a prime as a number that is only divisible by one and itself, one is a prime. However, for purposes of factorization and especially the fundamental theorem of arithmetic, it is more convenient to not think of one as a prime factor, or to think of it as an implicit factor that's always there but need not be written down. To exclude the number one from the list of prime numbers, primality is defined as a number having exactly two distinct divisors, one and itself. The last professional mathematician to publicly label 1 a prime number was Henri Lebesgue in 1899, although Carl Sagan included one in a list of prime numbers in his book Contact in 1985."

So, perhaps Acts of Evil uses Lebesgue Primes, or pre-Euclidian Primes...

Paul

That would be interesting, to find out whether Euclid or Pyhtagoras (a veritable numerologist) called one a prime. "Euclidian primes", "Pyhagorean primes", that would sound great. Let's do some research...

Hm:

Prime numbers form a very important class of numbers, and much of number theory is devoted to their analysis. The only proper divisor of a prime number is 1. The first few prime numbers are, of course, 2, 3, 5, 7, 11. Those numbers that aren't prime are composite, for instance, 4, 6, 8, 9, 10. The number 1 holds a special position. For Euclid, it was the unit rather than a number.

A prime number is rectilinear, meaning that it can only be set out in one dimension. The number 2 was not originally regarded as a prime number, or even as a number at all.

Let's do some research...

The Department of Mathematics and Applied Mathematics - University of Cape Town Prime FAQs and Facts says, that if "you define a prime number as a positive integer which has no divisors other than 1 and itself, then 1 must be regarded as a prime number." But that there is now "general agreement that it is more convenient to use a definition which excludes 1 from the set of prime numbers." This is because the Fundamental Theorem of Arithmetic is problematized if you consider 1 to be a prime number:

"Thus, if you allow 1 to be a prime number, you must immediately exclude it from your first major theorem about prime numbers. That is enough justification for agreeing not to consider 1 to be a prime. Note that it is not wrong, in any moral, legal or mathematical respect, to regard 1 as a prime number. But if you use your own personal definition for a concept which is not how others view that concept, you are liable to be misunderstood."

Wikipedia says that The Fundamental Theorem of Arithmetic was "essentially first proved by Euclid." Hence my invention of "pre-Euclidian primes". Which is so nicely evocative of Lovecraft's "non-Euclidian geometry" that it sure makes me happy. But I have no idea how historically accurate it might be.

Paul

Paul wrote:
But I have no idea how historically accurate it might be.

But hey, you can always coin 'pre-Euclidian prime' as a term of art, and make it the basis of your game. Who's going to stop you?

Well, my first quote seems to indicate that the Greeks, including Euclid, didn't hink of 1 as a number.

Yeah, my further reading suggests the same. "Pre-Euclidian primes" is actually seeming more wrong than just calling them primes. Right now I'm thinking of writing it like this:

To resolve a conflict, the player will roll a pool of dice, count how many of them show a prime (1, 2, 3, 5, or 7), and compare that count against a similar roll by the GM. The sizes of these opposed pools of dice are determined by simple formulae that correspond to the various types of NPCs with whom the characters will conflict. Rolling more primes than the GM is a success. Rolling an equivalent count, or fewer, is failure.

And then maybe I'll thank Lebesgue in the Acknowledgements :)

Paul

I still think you should just use TNs...I'm not for adding color to mechanics unless it actually adds to the game in some other way. How about d4 and d6 and anything but a 1 is a success? That's quick, and not far from what you have now.

Mike

I still think you should just use TNs...

So, no opposed pools?

Paul

No, sorry, should have been more clear. If you want 5 out of 8 on a d8, then you should just count 1-5s as successes. TN 5. TN 4 for d6. It's not as colorful, but I think it's easier. Even better, the system I proposed (and it'll give players a chance to roll all of those D4s they got for MLWM, too).

Or did I miss the system moving on again? :-)

Mike