GURPS Dungeon Fantasy 8: Treasure Tables

[pst]

Originally Posted by Peter Knutsen

One thing that would have been nice is a set of tables for low-value, medium-value and high-value loot.

I think that would be really hard to achieve. But I think it will work nice to just generate a bunch of random stuff, and then insert suitable things from that list when needed. That something is too valuable for the circumstances is only one thing that would make an object unsuitable for a particular situation.


Fun with DF8!

* What is the cheapest thing possible to generate?

I think it's <2,1,1-3> <1-2,1,6> <1-2,3>, that is a cup with a dull-colored string, for $0.625! :-)

The chance of that appearing randomly is 1/139968.

(Or maybe a pixie cup would be even cheaper because of using less material?)

* What is the most expensive thing possible to generate?

There is no limit how valuable gems can be, since you can throw "bigger" all day long.

* What is the average cost of a generated object?

I don't know. I immediately created 45 items for fun. They have an average value of $24811.647 and a median value of $9633.60.

[Greg 1]

Originally Posted by pst

I think that would be really hard to achieve. But I think it will work nice to just generate a bunch of random stuff, and then insert suitable things from that list when needed. That something is too valuable for the circumstances is only one thing that would make an object unsuitable for a particular situation.

This seems like the best way to handle it. If you want the haul to be worth about $4,000, just keep rolling until you have about $4,000 worth of stuff, rejecting anything too valuable.

* What is the cheapest thing possible to generate?

I think it's <2,1,1-3> <1-2,1,6> <1-2,3>, that is a cup with a dull-colored string, for $0.625! :-)

Well, killing that dragon was worth the effort. ;)

[Steven Marsh]

Originally Posted by pst

Cup with a Dull-Colored String

Awesome; I think I've got my new band name! :-)

[Bruno]

Originally Posted by pst

* What is the most expensive thing possible to generate?

There is no limit how valuable gems can be, since you can throw "bigger" all day long.

* What is the average cost of a generated object?

I don't know. I immediately created 45 items for fun. They have an average value of $24811.647 and a median value of $9633.60.

The question about the most expensive thing also contains the answer regarding average cost. While there may be a floor on value (0$, valueless) the ceiling is infinite. Therefore on a practical level there is no average value, the same way there is no most expensive item.

It does inspire the interesting theoretical question, though, as to what the average of an infinite series containing a number of finite-valued terms and an infinite number of infinite terms is. I'm rusty, but I think that makes the mathematical average "infinite" as well. Don't ask me about median or standard deviation. :P

[pst]

Originally Posted by Bruno

The question about the most expensive thing also contains the answer regarding average cost. While there may be a floor on value (0$, valueless) the ceiling is infinite. Therefore on a practical level there is no average value, the same way there is no most expensive item.

Well, actually you can have an finite average value regardless of there being no upper limit. Here is My Simplied Random Value Generator™:

Roll 1d. If you throw 1-5 that's the value. If you throw 6, use My Simplified Random Value Generator™, and then double that value.

Example <6,6,6,5> would generate double double double five = 40.

Set v equal to the mean value of this. Since the six possibilities have the same probability

      1+2+3+4+5 + 2v     15 + 2v
v =  ---------------- = ---------
            6               6

So 4v = 15, so v = 15/4. Very finite, even though I'm doubling it every time. The DF8 "Bigger" rules for Jewelry and Gems just add same-size values each iteration.

To infinity, and beyond!

[SCAR]

Originally Posted by pst

Well, actually you can have an finite average value regardless of there being no upper limit. Here is My Simplied Random Value Generator™:

Roll 1d. If you throw 1-5 that's the value. If you throw 6, use My Simplified Random Value Generator™, and then double that value.

Example <6,6,6,5> would generate double double double five = 40.

Set v equal to the mean value of this. Since the six possibilities have the same probability

      1+2+3+4+5 + 2v     15 + 2v
v =  ---------------- = ---------
            6               6

So 4v = 15, so v = 15/4. Very finite, even though I'm doubling it every time. The DF8 "Bigger" rules for Jewelry and Gems just add same-size values each iteration.

To infinity, and beyond!

I love maths, you can prove almost anything if you don't know what you're doing!

Bruno is correct, if you have N items, one of which is Infinity, the sum of all the values is Infinity, and the Average, Infinity/N = Infinity

ps. "cup with a dull-colored string" as a treasure item - I think I need to see the look on any players face when they find that!

[martinl]

Originally Posted by SCAR

I love maths, you can prove almost anything if you don't know what you're doing!

Bruno is correct, if you have N items, one of which is Infinity, the sum of all the values is Infinity, and the Average, Infinity/N = Infinity

Only if N is finite. If N is not finite, and it is not in this case, you have infinity/infinity, and you must use other methods to find the answer.

Isn't there an old bit of HHGTTG quippage with the same error? ...

It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this it follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination. -HHGTTG

Edit: That said, I'm not sure about pst's method, and a quick sim of the series seems to have it converge at around 2.779

Edit 2: My bad. He's right, it's 3.75.

Edit 3: And on further thought, his method is both sound and elegant.

[Turhan's Bey Company]

Originally Posted by SCAR

ps. "cup with a dull-colored string" as a treasure item - I think I need to see the look on any players face when they find that!

They'll be thrilled to have found an album by Steven Marsh's band.

[SCAR]

Originally Posted by martinl

Only if N is finite. If N is not finite, and it is not in this case, you have infinity/infinity, and you must use other methods to find the answer.

Isn't there an old bit of HHGTTG quippage with the same error? ...

Do you mean countably infinite or uncountably infinite? - not that it really helps
I though DF8 had a finite number of possible treasures.

[SCAR]

Originally Posted by Turhan's Bey Company

They'll be thrilled to have found an album by Steven Marsh's band.

Touche - I can see this one running for a long time!