Early on in my campaign I ran into a disturbing fact. There were two PC wizards in the same party. One had an intelligence of 17 and another had an intelligence of 18. When we were using only the spells from the original 1st Edition Player's Handbook, we didn't really notice a problem. There are only so many spells around. Some were not interesting to the PC's so it was easy to choose which spells they wanted to roll that fateful percentile to see if they could put that scroll spell into their spell books. As modules began including more and more new spells, and supplements like Unearthed Arcana and a score more that followed over the years brought more and more spells, it became frustrating. By 7th or 8th level the PCs had filled their quota of spells at the lower levels and could not add any of these new spells to their books!

Then along came the straw that broke the camel's back.

The wizards both gained a point of intelligence during an adventure. One wizard could now, after what had seemed an eternity of no new spells, add 4 new spells for each spell level. But the other? He could now add scores of spells to each level! In fact... he could add ALL of them!!!

This made no sense to me at all. As a wizard gains levels he should be able to learn (not to be confused with "memorize") more spells, and not just those of the highest level. It was because of this that I created the charts I present on this webpage. A 20th level wizard should not have the same limit on knowledge of low level spells as a 1st level wizard.

The first modification I made was to eliminate the "Know All Spells" from the 19+ intelligence section of the Max # of Spells/Lvl chart and smooth out the progression at lower intelligences, producing Table 1 below. Fittingly now only Boccob, with an intelligence of 26, can know all spells ever created. Also I ignore the Min # of Spells/Lvl chart because, while it may have been a problem back in the "Good 'Ole Days" of the 1st Edition Player's Handbook, there are now so many spells available for each spell level that it is a statistical impossibility to not meet the minimum number at some point in an adventuring career (the 2nd Edition rule books eliminated the "minimum" anyways).
 

Table 1

Intelligence	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
Max # of Spells/Lvl	0	6	7	7	8	9	10	11	12	14	18	24	32	42	54	68	84	102	All

 

Second, I developed a simple modification to this base number based on a wizard's experience level.
To the base number in Table 1 is applied a modifier calculated by the following simple equations:

(Wizard's Level + 1) minus (3 times spell level)        For spell levels 1 to 5
(Wizard's Level) minus (3 times spell level)              For spell levels 6 to 9

Notes:
1. The two different calculations reflect the fact that one must gain 3 rather than 2 levels before getting your first 6th level spell
2. The +1 to Wizard's Level is necessary to ensure that a wizard with minimum intelligence requirements can still learn at least two spells in their highest spell level possible at the first level they can cast it at.
3. Now a wizard doesn't have the same learning limit for both 1st level spells and 9th level spells!

For example, to calculate the Max # of 3rd Level Spells in the spellbook of Numericus, an 7th level wizard with a 17 intelligence, you would get...
(7+1) - (3x3) = 8 - 9 = -1,  then this -1 modifier is applied to the 14 spells (for a 17 intelligence) from Table 1.

Therefore Numericus can presently know a maximum of 13 3rd level spells, until he either gains a level or gains intelligence.

For those who like an easy-to-look-up chart (and hate doing calculations), the equations above yield the following chart.
Apply (add) the appropriate modifier to the Maximum # of Spells/Level as determined by the wizards intelligence.
 
 

Table 2

                                Spell Level

Wizard Level	1st	2nd	3rd	4th	5th	6th	7th	8th	9th
1	-1	-4	-7	-10	-13	-17	-20	-23	-26
2	0	-3	-6	-9	-12	-16	-19	-22	-25
3	1	-2	-5	-8	-11	-15	-18	-21	-24
4	2	-1	-4	-7	-10	-14	-17	-20	-23
5	3	0	-3	-6	-9	-13	-16	-19	-22
6	4	1	-2	-5	-8	-12	-15	-18	-21
7	5	2	-1	-4	-7	-11	-14	-17	-20
8	6	3	0	-3	-6	-10	-13	-16	-19
9	7	4	1	-2	-5	-9	-12	-15	-18
10	8	5	2	-1	-4	-8	-11	-14	-17
11	9	6	3	0	-3	-7	-10	-13	-16
12	10	7	4	1	-2	-6	-9	-12	-15
13	11	8	5	2	-1	-5	-8	-11	-14
14	12	9	6	3	0	-4	-7	-10	-13
15	13	10	7	4	1	-3	-6	-9	-12
16	14	11	8	5	2	-2	-5	-8	-11
17	15	12	9	6	3	-1	-4	-7	-10
18	16	13	10	7	4	0	-3	-6	-9
19	17	14	11	8	5	1	-2	-5	-8
20	18	15	12	9	6	2	-1	-4	-7
21	19	16	13	10	7	3	0	-3	-6
22	20	17	14	11	8	4	1	-2	-5
23	21	18	15	12	9	5	2	-1	-4
24	22	19	16	13	10	6	3	0	-3
25	23	20	17	14	11	7	4	1	-2
26	24	21	18	15	12	8	5	2	-1

The Red portion of the chart indicates spell levels which a wizard can read from a scroll but cannot memorize, therefore the DM must check for spell failure.

Arising from the chart, there is a point at which the modifier can decrease the maximum number of spells to a negative number. Some DM's may allow a PC to inscribe a spell into his or her spellbook that is higher than they can cast (for use when they are a higher level). This is particular applicable to people who still use the 1st Edition AD&D rules and allow the use of the Write spell, as it is written, for this purpose. From this chart, for example, a character with a 17 intelligence could not write a 6th level spell into their book (or even roll to see if they can know it) until 5th level (when the Max # of 6th lvl spells becomes 1) and would have to save the scroll for a while.

 To complete the example, Numericus (7th Lvl Wizard, 17 intelligence) would be able to enscribe the following numbers of spells for each level within his spellbooks:
 

Spell Level	1	2	3	4
Max # of Spells Known	19	16	13	10

Even if he filled his quota of 10 4th level spells (perhaps his party takes out an evil wizard and they confiscate his spellbooks), each time he gains a level he will be able to add one more new spell to his repertoire.

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