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PostPosted: Sun Feb 27, 2011 5:10 pm 
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Okay, so generally speaking we're in agreement that Chargen and Post-Chargen should be interchangeable in terms of what kinds of characters can be built. This presents us with a problem: chargen cash. Now, currently under all chargen systems: BeCKS, Build Points, even Priority, the more Karma you invest in Resources, the more Resources you get per point of Karma/BP/Priority. It is roughly an exponential progression: as seen particularly in BeCKS, you get 500 Nuyen per Karma point at 0 Resources, but you get 20,000 Nuyen per point at 101+ Resources, forty times as much.

In fact, it's even worse than that. The progression is such:

500/pt
1,500/pt
4,000/pt
9,000/pt
15,000/pt
20,000/pt

which follows no real pattern at all, and therefore sucks. There's nothing that can be extrapolated to a reasonable cash-for-karma conversion factor for higher-Karma starting characters, for example: even if we kept a running total of how much Karma had been spent on Resources in the past, and used the BeCKS conversion for all future cash expenditures (meaning that characters would essentially only earn Karma post-chargen and use cash-for-Karma for Resources), you still have the problem that there is no formula for what happens once a character has already traded in his 120 Karma for his million nuyen, and wants to trade in his 121st point.

So, what do do? Well, Kage has already expressed his desire to keep the million nuyen sacred cow, as well as the ability to have 5,000 nuyen at chargen (btw, note how BeCKS in fact starts everyone with ZERO nuyen... even worse!) so let's try to accommodate that. Now, obviously an exponentially-increasing series for Resources is fundamentally unsustainable post-chargen, and linear is, well it's possible, but at 5,000 nuyen per Karma point you have to invest 200 Karma to get to a million nuyen.

So let's instead go for a quadratic progression instead. In other words, we need to define a(n), b, c such that:

a(0) = X -- Some whole number: in BeCKS this is 0; under BPs this is 5,000
a(n) = a(n-1) + b(n)
...
a(120) = 1,000,000

b(0) = b(0)
b(n) = b(0) + c * [FLOOR (n/d)]

n = Total Karma spent on Resources
a(n) = Total Resources available at (n) Karma
b = Amount of cash granted for exchanging the nth Karma point for cash
c = Stepwise increase in b
d = Step interval; amount of Karma at which (20 in BeCKS)

So, commencing math. Be back in a bit.


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PostPosted: Sun Feb 27, 2011 5:56 pm 
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Okay, let's try a(0) = 0, b(0) = 3,000, c = 1,000, d = 10

a(0) = 0
a(20) = 70,000
a(40) = 180,000
a(60) = 330,000
a(80) = 520,000
a(100) = 750,000
a(120) = 1,020,000

That's pretty close. You end up with 3,000 nuyen per Karma point at 0 karma, 14,000 nuyen per Karma point at 111-120 Karma, 15,000 nuyen at 121-130 Karma, and a progression that goes quadratically in-between and beyond.

In fact, a(120) is going to be 120 * b(0) + c *120 * (120-d) / 2d = 120 [ b(0) + c*(120-d)/2d)], which unfortunately means we can never, for non-fractional values of b(0), c, or d, have both a(0) = 0 and a(120) = 1,000,000; you need a(n)-a(0) to be divisible by 120. Hmm...


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PostPosted: Sun Feb 27, 2011 6:44 pm 
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a(0) = 4000, b(0) = 2,800, c = 1,000, d = 10

a(0) = 4,000
a(20) = 70,000
a(40) = 176,000
a(60) = 322,000
a(80) = 508,000
a(100) = 734,000
a(120) = 1,000,000

Weeeell... at least the million comes out even, but just about nothing else does. You're adding 2,800 nuyen per Karma point at 0, and 13,800 nuyen per Karma point at 111-120.

Here's a better one: a(0) = 10,000 b(0) = 6000 c = 1500 d = 30

a(0) = 10,000
a(30) = 190,000
a(60) = 415,000
a(90) = 685,000
a(120) = 1,000,000

That's far better. You're adding 6,000 nuyen per Karma point at 0-30, 10,500 nuyen per Karma point at 91-120, and 12,000 nuyen per Karma point at 121-150 Karma.

(Edit): Oh, wait:
(Further on:)
a(180) = 1,765,000
a(240) = 2,710,000

You'd need to invest nearly 100 karma to get your next million? Maybe this progression isn't fast enough...


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PostPosted: Sun Feb 27, 2011 6:56 pm 
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Carrying a(0) = 4000, b(0) = 2,800, c = 1,000, d = 10 further:

a(180) = 2,038,000
a(240) = 3,436,000

Okay, that seems better. Investing 60 Karma past the 120 gets you another million, and a further 60 gets you alomst another 1.5 million. That progression looks good, but the per-Karma addition is so ugly. Ugh, more numbers to follow.


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PostPosted: Sun Feb 27, 2011 7:20 pm 
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Here's an interesting one:

a(0) = 40,000, b(0) = 2,500, c = 1,000, d = 10

a(0) = 40,000
a(20) = 100,000
a(40) = 200,000
a(60) = 340,000
a(80) = 520,000
a(100) = 740,000
a(120) = 1,000,000

2,500 nuyen per Karma point at 0; 13,500 nuyen per Karma point at 111-120.

Further:
a(180) = 2,020,000
a(240) = 3,400,000

Which is good, IMO. Also:

a(-10) = 15,000
a(-15) = 2,500
a(-16) = 0

Meaning you can gain bonus Karma for giving up starting Resources at a 2,500 Y-to-1 Karma ratio, though you'll have to re-invest the Karma to get back up to more favorable cash-to-Karma rates post-chargen.

I think I like this one, even if we don't go for universal cash-for-karma. It's more consistent than the pick-random numbers approach that BeCKS has


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