spellbook frequencies

[fizzix]

Estie pointed out some issues with spellbook drop frequency, and there are several options to remedy this. (this is a problem in ironman games).

In this post, I'll look at what wiz-stats currently says about drops. Currently, magic books and priest books are identical as far as drop probabilities so it suffices to look at just one of them.

Let's look at the probabilities of finding each town book if you clear all levels while descending.

level    5     10       15      20     25      30
mb1    0.26   0.85     0.97    0.99   0.99    0.99
mb2    0.0089 0.20     0.71    0.91   0.98    0.99
mb3    0.0039 0.023    0.045   0.17   0.59    0.85
mb4    0.00   0.012    0.02    0.03   0.092   0.24

more succinctly, we can define the average level you would be expected to find a book, and the standard deviation.

book    level     stdev
mb1      8.2      1.2
mb2      13.6     1.3
mb3      24.8     1.8
mb4      33.8     1.6

Immediately something jumps out. the stdevs are pretty small. This implies that a lot can be gained by making the books appear a bit earlier. Right now, books appear at levels 5, 10, 20 and 30. Perhaps something like 2, 5, 10, 20 would be a bit more reasonable. (that will be looked at in the next post.)

We should also note that finding one book is not sufficient. This is the probabilities for the 1st book you encounter, when really you need more than one because books get burned. To examine this we can try to find how many books appear per level. I'll look at a couple levels

level   10   10floor   20   20floor  30   30floor  40  40floor
mb1    0.25   0.16    0.22   0.11   0.28    0.12  0.29  0.10
mb2    0.16   0.15    0.22   0.11   0.23    0.11  0.33  0.10
mb3    0.003  0.02    0.11   0.10   0.19    0.09  0.31  0.08
mb4    0.002  0.002   0.003  0.03   0.12    0.11  0.23  0.09

So it looks like you are likely to get 1 book every 3-4 levels after the point that they fall in depth. (assuming you clear everything of course) Estie's experience was that this was not frequent enough. Changing the depth level will not help with this.

edit: formatting

[fizzix]

Part 2: moving spellbooks earlier

Ok, so what happens if we move spellbooks earlier. Something like:
mb1 1 to 100
mb2 5 to 100
mb3 10 to 100
mb4 20 to 100

then (obviously) you tend to find the books earlier:

book   level   stdev
mb1    2.5     0.8
mb2    9.0     1.3
mb3   15.3     1.5
mb4   25.9     2.3

These levels are more in line with where you will need the book as a mage/priest. Unsurprisingly, the amount of books by level does not change much. So this is a partial solution at best. In the next part we'll look at adding book drops to specific monsters.

[fizzix]

Part 3: Mage special drops

I'll split the mage and priest up separately. (I'm separating the posts by different simulations.)

The idea here is to give spellcasting monsters additional spellbook drops. The goal being to increase the frequency of drops in a thematic way in a manner that does *not* reduce the drops of other items.

I settled on the following for monsters to give spellbook drops.

monster          mb1%   mb2%   mb3%   mb4%
Apprentice       10     x      x      x
Kobold shaman*   15     x      x      x
Scout            10     x      x      x   
Orc shaman**     x      15     x      x
Dark elven mage  20     20     x      x
Gnome mage       10     10     x      x
Master yeek      15     15     x      x
Illusionist      x      20     20     x
Dark elven lord  x      10     10     x
Ranger           x      10     10     x
Ogre mage        x      x      15     15
Mage             x      x      20     15
Demonologist     x      x      15     15
Enchantress      x      x      15     15
Sorcerer         x      x      15     30
Dark elven sor.  x      x      15     30
Ranger Chieftain x      x      15     15 

* also drops priest book 1
** also drops priest book 2

The level at which you find the first book doesn't change at all.

book   level   stdev
mb1    2.5     0.6
mb2    8.0     1.0
mb3   14.6     1.5
mb4   25.5     1.9

However, the amount of books dropped per level is much higher across the board.

level   10   10floor   20   20floor  30   30floor  40  40floor
mb1    0.71   0.12    0.82   0.11   0.87    0.11  0.80  0.10
mb2    0.38   0.15    0.55   0.11   0.60    0.10  0.59  0.11
mb3    0.17   0.16    0.25   0.10   0.41    0.10  0.51  0.10
mb4    0.005  0.005   0.096  0.08   0.27    0.09  0.47  0.10

Total drop numbers increase by about 2 times (higher for mb1). These numbers look reasonable to me. It took several iterations of drop frequencies to get there.

I have not investigated whether spellcaster pits affect the results. I'm guessing that these are an infrequent enough occurrence that they account for less than 5% of total drops. But I have no data to back this up.

Of course the major downside to increased spell book drops is TMJ. Just because your mage wants all the books doesn't mean she wants 20 copies of them! The squelching procedure is available but not straightforward (inscribe inventory books with !k and squelch the rest.) I think the increased playability of ironman mages is worth the tradeoff though.

I'll do priest books in the next post.

[fizzix]

Part 4: priest drops

Here's the monsters that can drop priest books

monster          pb1%   pb2%   pb3%   pb4%
Acolyte          10     x      x      x 
Gallant          10     x      x      x
Kobold shaman*   15     x      x      x
Orc shaman**     x      15     x      x
Priest           20     20     x      x
Dark elven pri.  20     20     x      x 
Druid            15     15     x      x
Paladin          x      15     15     x
Dark elven druid x      15     15     x
Troll priest     15     15     x      x
Black knight     x      15     15     x
Ogre shaman      x      15     20     x
Spirit naga      x      x      20     10
Mystic           x      x      15     15
Death knight     x      x      15     15
Necromancer      x      x      15     15
Patriarch        x      x      15     30
Knight templar   x      x      15     30
Master mystic    x      x      15     15
Grand master mys.x      x      10     30

* Can also drop MB1
** Can also drop MB2

The levels where you are likely to get a priest book look very similar as for mage books and are probably within the margin of error

book   level   stdev
pb1     2.5     0.9
pb2     7.8     1.0
pb3    14.3     1.5
pb4    24.1     1.7

Total drops are roughly inline with magic books.

level   10   10floor   20   20floor  30   30floor  40  40floor
pb1    0.64   0.13    0.75   0.11   0.77    0.10  0.78  0.11
pb2    0.35   0.15    0.36   0.10   0.61    0.11  0.58  0.11
pb3    0.15   0.14    0.27   0.11   0.44    0.12  0.54  0.09
pb4    0.004  0.005   0.13   0.12   0.21    0.10  0.44  0.11

Next post: conclusions.

[fizzix]

Here are the conclusions:

1: I love statistics, no, really I do
2: Lowering the dungeon-levels for random book drops makes the first appearance more in-line with when a mage/priest is likely to want them.
3: Giving monsters thematic drops is a cool mechanic and a nice way to boost overall drop count to ensure book-dependent characters find enough in the dungeon
4: TMJ with too many books will be a problem and might elicit complaints from people who have not mastered the intricacies of squelch and inscribing.
5: pull-request into 3.5 dev is incoming.

[Philip]

Question #1: These drops replace the standard drops, correct?
Question #2: Shouldn't priests magic book drops be more in line with the illusionist? A priest is at least as threatening as an illusionist, with summoning, damage spells and not unthreatening melee. An illusionist is dangerous if there are other monsters around, but a priest creates monsters.
Question #3: While we must think about shamans dropping enough spellbooks to get spare copies and perhaps your first copy of book 2, maybe making the chance for spellbooks to drop 10% each? If fixed drops from them do not in fact replace normal drops, issue is void.

As for the conclusion, I suggest the readme, help files, shopkeepers, and perhaps download pages have a warning about how to deal with TMJ.

I support the plan to make spellcasting monsters drop books, but I would also like to warn in advance that ironman is a challenge option, and that changing the game to suit ironman tends not to be a good idea. There is already a well-balanced variant designed for ironman, Ironband. Perhaps Sil can be counted too.

[buzzkill]

I support the plan to make spellcasting monsters drop books, but I would also like to warn in advance that ironman is a challenge option, and that changing the game to suit ironman tends not to be a good idea.

This will make both Ironman and standard V easier. I thought is was long ago settled that changes wouldn't be made specifically to accommodate Ironman.

[Timo Pietilä]

This will make both Ironman and standard V easier. I thought is was long ago settled that changes wouldn't be made specifically to accommodate Ironman.

Ironman I agree, but artifactless should be considered with changes. Game should be winnable without artifacts. Harder maybe, but winnable.

[Magnate]

Ironman I agree, but artifactless should be considered with changes. Game should be winnable without artifacts. Harder maybe, but winnable.

Are you talking about artifact spellbooks? These aren't in V yet. Fizzix's changes shouldn't have any impact on other artifacts, because these thematic drops are *in addition* to normal drops, not instead.

[fizzix]

This will make both Ironman and standard V easier.

The change in difficulty to standard V is extremely minor. Basically you might save about 2k gold that you would otherwise be spending on town books. Beyond that, I don't see any huge difference. In standard V if your books get burned you just hop back to town and get new ones. If the book isn't stocked, you have very boring gameplay options to get a new one. (This is akin to the scumming for stat-restore potions that's since been removed.) Please outline what significant increase in ease of gameplay you envision.

I thought is was long ago settled that changes wouldn't be made specifically to accommodate Ironman.

I'm not sure about this being settled. In fact, there's long been a policy to make sure that stuff you need should be found in the dungeon at roughly the same rates as you consume them. This is why !CCW and ?phase have had drops increased. And it looks like the increase to phase needs to be more.

When you're talking about game balance (and really this is nothing but a balance issue) angband is tough, because you have all different kinds of players to consider, from divers to people who replay each level 3 times. Balancing everything for the player who clears each level exactly once seems a reasonable compromise and also something we're actually capable of gaining statistics on. The fact that this overlaps with ironman is almost coincidental. Because of all these reasons, adjusting game balance for ironman has been the standard approach, not for ironman per se, but for all players.

[fizzix]

Question #1: These drops replace the standard drops, correct?
Question #2: Shouldn't priests magic book drops be more in line with the illusionist? A priest is at least as threatening as an illusionist, with summoning, damage spells and not unthreatening melee. An illusionist is dangerous if there are other monsters around, but a priest creates monsters.
Question #3: While we must think about shamans dropping enough spellbooks to get spare copies and perhaps your first copy of book 2, maybe making the chance for spellbooks to drop 10% each? If fixed drops from them do not in fact replace normal drops, issue is void.

As for the conclusion, I suggest the readme, help files, shopkeepers, and perhaps download pages have a warning about how to deal with TMJ.

I support the plan to make spellcasting monsters drop books, but I would also like to warn in advance that ironman is a challenge option, and that changing the game to suit ironman tends not to be a good idea. There is already a well-balanced variant designed for ironman, Ironband. Perhaps Sil can be counted too.

1: no, these are in addition to standard drops.
2: I tried to keep the total priest and mage books about equal. This involved increasing the frequency of the priest books slightly, because there are slightly fewer of them. A player can't distinguish between 20 and 25%, but the stats gathering can.
Conc: see the answer to buzzkill about using ironman-like stats for general game balance. If you have a preferred approach for how to approach game balance, please let me know.