Mathematics applied to D&D

@leo Becaue I would have done that if you weren't here now. I'll do that later, maybe, now let's focus on talking since you already know (the relevant part of) the problem

and yes, indeed the game is D&D, in its 3.5th iteration

also known as D&D 3.5e

editions in this game are a weird thing, they're more like different games with some common points. Anyway

leo

8:28 PM

where can I get the game?

Zachiel

You really want to see the whole game? It's like several dozens of books. Most of what we need to understand the problem, luckily, is published online on d20srd.org

here is where ability scores are introduced

Unfortunately, the free reference document lacks the rules for leveling up

It goes like this. At first level and whenever you level up, you look at Intelligenge, one of your ability scores. You specifically look at the Intelligence bonus, which is in the table of the last page I linked you

leo

Silly question maybe, but, is not a video game then?

Zachiel

No, it's a tabletop roleplaying game.

Some Videogames have been made based on it, such as Neverwinter Night or Baldur's Gate (also, Knights of the Old Republic)

Just to name the most famous ones

you'll notice that I took whatever the intelligence score was and I called it 0, for convenience.

or 1, if it was odd to begin with

leo

yes

Zachiel

So those skill points we were looking at before are only a part of the total, but since the part I didn't talk about is just the same every level, they don't really change the solution of our problem

my problem, sorry ;)

leo

8:40 PM

the matter is, we first have to isolate the things that are pertinent and then state the problem properly, so we can ask a question on main math.se

Zachiel

Let's suppose an even starting Int score

I have some doubts about how the problem might or might not change according to this starting point but let's see this later

leo

I think we are clear in one thing. We want to get as much spts as possible spending as least as we can

and to do so is enough to optimize the way we get Int points

Zachiel

mhhh

I think the money is more of a constraint than some sort of thing to optimize

leo

yes

but you said...

Zachiel

I mean, of course I daon't want to spend more money than I could otherwise do to get the same results, but at the same time I'm aware maximizing spts will probably cost me more than just buying the +5 tome

And I don't want to get some middle point between least expense and most points. Most points is my final target.

@leo express your doubts

leo

8:48 PM

@Zachiel I see.

Zachiel

So, there's a table in the books that's not on the site where it says "a character this level should have gained this money from level one to now"

It's called the Wealth By Level table (WBL for short)

So a level one character starts with so few gold pieces (gp) he can't buy much, let alone a Tome (which is one of the best magic items he can put his hands on). Not even a +1 one.

leo

If money is not a concern I'll go like this: start with 1 Int point. Then buy 5 Int points so you have Int = 6. Then buy 5 and 5 again, that is buy 10. Keep buying 10 as long as your money allows you

Zachiel

Oh, no, 5 is the max you can get ever.

Those bonuses are not cumulative

leo

5 max per level?

Zachiel

no, 5 max per character

leo

8:52 PM

hmm

Zachiel

let's have the example this room has been created for

leo

ok

I don't have clear the rules then.

Zachiel

mmmh let's see if I can clear those for you then

leo

please :-)

Zachiel

Int is a score that can be raised in different ways during the game

Of the several ways, only some count towards the spts gain

leo

8:55 PM

ok

Zachiel

and those are:
-one ability point gained every 4th level (which I'm supposing to be spending in a different ability, so I'm not counting it)
-up to 5 points (insight bonus) gained through spells or Tomes
-up to 3 points for hitting age category checkpoints. (this will came into play later, and while it increases Int it decreases physical scores way faster so I'm gonna consider doing it only once.)

So basically we're looking at the second way only, now.

Bonuses in this game are not cumulative. Let's say I have a ring that gives +2 deflection to my armor class and a spell that gives a +3 deflection to my armor class, only the greater would count. In the same way, every time i get a +A inherent and a +B inherent bonus to intelligence, only max[A,B] counts.

(deflection is a bonus type. Bonuses of different types stack as you would expect)

(inherent is the bonus type tied to Tomes. Which I always call insight, which is a different type of bonus that's not relevant here, because I'm an idiot.)

leo

hmm

Zachiel

(I know you don't really care about this difference between insight and inherent but if you follow my link to the tomes I gave you earlier you will find the inherent word.)

leo

ok, so let me see If I understood

say I start at level 1 with 1 Int point. Then I can buy up to 5 Int points?

Zachiel

you can buy 5 more, up to 6 total

leo

9:06 PM

Then I'll end up with 6 int points?

Zachiel

yes

leo

ok

Zachiel

if you start with 0 going to 5 is pointless, you'd better stop at 4

leo

then at the end of level 1, I'll have 3 skillpoints and 6 Int points

Then at level 2, I can buy another 5 Int points?

@Zachiel ?

Zachiel

No. If you manage to get all your five points by the end of level one you're done with. You'll have 6 Int point forever, that will get you 3 spts every level from now on, end of the optimization.
The point is you need money to buy those Tomes and you don't have enough at level 1. Maybe by level 6 you'll get enough money to buy a single +1 Tome. And by level 7 you would have had the money to buy a +2 Tome but you really don't, because you were hasty and you got the +1 Tome at level 6.

leo

9:13 PM

ok I think I now understand

Zachiel

so the tricky part is understanding when it is convenient to spend part of my budget early to get some skill points at the plower levels, despite knowing this is going to shift your bigger investment to a later level

leo

yes

Zachiel

I guess that age thing is easy to optimize. If you would get any Tome at any point, increase your age and buy the cheaper Tome.

So I should really start from an odd number (since I'm aiming for an even one) and never consider the age increase, as if I had already done it to begin with

then actually increase my age only when I'm ready to buy my first tome

(or at any point before, it's not relevant)

but I'm digressing

leo

ok

so the Int points are just like a modifier to increase the skillpoints

Zachiel

the point is, since we want to maximise spts, let's do this in a way that makes that +5 Tome useful, which is starting from an odd Int value

@leo exactly. They have other uses in the game, but they don't matter in my problem

leo

9:18 PM

but once it gets to 5 it can't be bigger in the future

Zachiel

@leo that's true about the bonuses I can shop through tomes

there's not a cap on the total, just on the inherent bonus

leo

ok so say I start at level 1 with 1 Int point. Then I buy the 1 Int point Tome. Then later in the game I can buy the 5 Int point Tome, but once I buy that one, I can't buy any others?

Zachiel

exactly. Once you buy the +5 (which you should buy sooner or later) you can stop thinking about it

also, once you buy the Nth tome, all tomes labeled N or less are useless

leo

ok

I'm understanding :-)

Zachiel

and basically the only reason I have for getting N<5 tomes is because I need to wait for some future level to bring me some more money

leo

9:23 PM

yes

Zachiel

Unfortunately, the amount of money coming in with every new level is not following any formula. I can pass you the numbers, I think, but not in a place that's accessible to the public, because it's one of the biggest parts of the game that has people buy the manuals instead of just using the free site I linked several times in this very chat.

leo

hmmm. I see.

Zachiel

or just google "d&d wealth by level 3.5"

leo

I think I almost can formalize the problem so it can be posted in math.se

but money then would be a corncern

Oh, well I really know don't

and I don't know if I can solve it in my own

Zachiel

oh, keep in mind that table has the aggregated data, so for instance at level 3 you don't get 2700 gold pieces, you get 1800 that, added to the 900 you had from level 2...

leo

9:29 PM

yes yes

let me give another example

Zachiel

@leo help in formalizing it is very appreciated. Also, if you want to see my original question it's here rpg.stackexchange.com/questions/46744/…

@leo sure

leo

I start at level 1 with 1 Int point. Then I buy say the 2 Int Tome. Then, until I buy some better Tome, my skill points at the end of each level would be calculated by spts = spts + 1

Zachiel

yes, but.

You'd better buy the 1 Int tome, which is enough to bring your int to an even value

therefore saving more money for later

that's also why I don't usually like to start with odd values, because the extra resources spent to gain that useless (for now) int point could have been spent elsewhere. But then this gets into a plethora of different considerations which would only make the problem more complex and would probably dissolve into smoke if I tought about them long enough.

leo

but then this can be split in cases

and they are not that much

@Zachiel yes you'd better buy the 1 Int tome, or wait a bit and buy the 3 Int tome

Zachiel

9:48 PM

@leo Unless buying the 1 int or the 3 int makes the 5 int tome shift too many levels forward

which I don't think will happen, because of the almost exponential rate at which gold is gained, but you never know

until you've done the math, I mean

leo

10:03 PM

@Zachiel I see. I have to go now. I'll write a draft of a possible question later. See you :-)

Zachiel

@leo thank you and see you. It's been nice to discuss togheter. Please let me know when you've got something. ;)

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Mathematics applied to D&D