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The Player’s Handbook includes the Intelligence “Chance to Know” for Magic User and Illusionist spells. In short, Mages can’t learn some spells, determined based on their intelligence. Which doesn’t quite integrate with the DMG, UA or OA. Of course.

 

“Each and every magic-user character must employ the Table [for minimum and maximum number of spells /level] in order to determine which and how many of each group of spells (by level) he or she can learn.”, PHB, p. 10.

A “level group” includes all of the spells of a particular level. During character creation, the mage rolls the Chance to Know for the Level 1 level group. When the mage can cast Level 2 spells (i.e., a Level 3 mage), the mage rolls for the Level 2 level group, etc. The mage makes “a complete check of each spell in the level group” for Chance to Know, in the order of their choosing (see Maximum Number below however). Any spell that passes the Chance to Know roll will be able to be comprehended, learned, and memorized once acquired. Any spell that fails the Chance to Know roll likely cannot ever be understood by the mage (see Write and Change of Intelligence however).

The Minimum Number is a safety net for the rare case where too few spells could be understood. After all, what’s the fun of playing a mage who can only understand a single spell! If the minimum number isn’t reached after rolling Chance to Know for the entire level group, the player works through the list of spells that failed on the first pass (again, in any order they wish), checking one spell at a time until they reach the Minimum Number.

Some groups delay rolling Chance to Know until each individual spell discovery, but that’s flawed. The Minimum is the reason “one complete check” (PHB, p. 10) of a new level group is done, since if the minimum is not reached  any mage rolling below the minimum wouldn’t be able to recheck the level group until encountering all of the spells of the level group—an unlikely event!

 

The Maximum Number defines the spells that could be learned. As written, while rolling Chance to Know for a level group, If the maximum is reached, the character may not ever check any further in the level group (see Change of Intelligence). However, applying the Maximum to the Chance to Know roll for the level group creates significant issues, given that for the low-level spells the mage will mathematically almost certainly reach their maximum (even if you don’t roll for the UA spells) long before reaching the end of the spell group:

• The mage won’t be able to create new spells (as they will have already reached their maximum on the initial Chance to Know roll).
• If the mage discovers a “heretofore unknown” spell , they will already have reached their maximum, so be unable to even roll Chance to Know.
• For a mage with a low intelligence, they will start with only 2-3 additional 1st level spells they can cast, and they have to find those specific spells. Even a mage with an 18 Intelligence will only have 14 Level 1 spells they can cast, so never even roll Chance to Know for the majority of spells they find.

The text itself is contradictory, as Maximum is also defined as the maximum a mage can have in their spell books. For me, I apply the Maximum only to those spells that have actually been learned (in their spell book, memorizable and castable). Check the entire level group; the mage can choose to learn on discovery what spells to learn, up to the maximum.

That also means that for all practical purposes, if the Minimum Number of Spells/Level is reached, the mage can stop checking, and check any remaining spells at time of discovery. It also prevents consigning mages with a lower Intelligence to a fate of seeking those missing spells—they can just decide, with each spell the find, whether to add it to their list of learned spells (after checking Chance to Know).

The 1st Level Mage

The intelligence of the mage dictates which spells can be known (DMG, p. 39). The 1st Level mage first rolls Chance to Know for the entire level group of 1st level spells. They then add to their spell book Read Magic and three additional spells randomly selected by the DM (although on a roll of “0” the player may choose). Obviously, an apprentice must know Read Magic to be of use to his master—they cannot fail this roll. At the same time, Read Magic is one of the minimum number of spells that can be comprehended, as well as counting towards one of the maximum number of spells learned.

The three additional spells is defined with flexibility, as:

“If your campaign is particularly difficult, you may wish to allow choice automatically. You can furthermore allow an extra defensive or miscellaneous spell, so that the character begins with 5 spells.” DMG, p. 39.

As the mage defaults to four spells to seek their fortune, if a roll to determine those three additional spells specifies a spell that can’t be comprehended (due to a failed Chance to Know roll), the spell category (offense, defense, misc.) should be rolled again. That aligns with “While the intelligence of the player character will dictate how many and which spells can be and are known, this knowledge is not automatic” (DMG, p. 39) and incorporates the illusionist “ignoring any rolls that result in duplication”; rolling again is the simplest solution. Certainly the intent is not to have a mage without usable spells in their starting spell book!

The illusionist originally followed a different process than the magic-user for starting spells, rolling d12 against the entire 1st level illusionist level group (rerolling duplicates), with the DM allowing an additional one to two spells for a difficult campaign (DMG, p. 39). UA aligned that process to the magic user, rolling on a table of offensive, defensive, and misc. spells, expanded to include UA spells (UA, p. 80).

Acquiring New Spells

Mages acquire new spells from three sources: one spell upon gaining a level, discovery of scrolls and spell books, and spell creation. The Maximum Number of Spells/Level comes into play whenever acquiring new spells.

“…it is possible to acquire knowledge of additional spells previously unknown as long as this does not violate the maximum number of spells which can be known.” (PHB, p. 10).

Any future spells discovered that have not yet had Chance to Know determined are considered unknown (see Spell Discovery), and are checked at time of discovery if the mage has not reached their Maximum Number of Spells / Level.

 

There’s no exception defined for a mage that has reached their Maximum: “As soon as this maximum is reached, the character may not check any further in the level group” (PHB, p. 10). That said, it’s easy enough to house rule the mage can drop a spell. We play that to learn a spell —in the rare case that Maximum Knowable has been reached—the mage loses one spell at random. A more lenient style would permit the player to choose the spell to be lost.

Gaining a Level

When a mage gains a new level beyond the first, two things happen. If they’ve gained access to a new level group, they check Chance to Know for all of the spells of that level group to confirm minimum (and likely maximum) spells. They also gain a new spell (DMG, p. 39).

Polyhedron #30 (JUL 1986) article DISPEL CONFUSION wrote:

“It is up to the individual DM to determine whether new spells are assigned or given by choice in a particular campaign. In either case, the “chance to know” roll still applies, and the character may or may not be given a chance to choose another spell if the first offering call not be learned. Also, the DM may choose to make only certain spells available through the training process, so the choice may be limited.”

Where does that spell come from when they gain a level? The DM can certainly allow a player to select any spell upon leveling (effectively, creating it). However, the rules for spell creation, which involve money, time, a library, and a chance of failure don’t align with the timeframe and costs for training. Gygax (Dragon, January, 1980) also states:
“even if a spell-caster is capable of knowing/memorizing many and high-level spells, he or she must find them (in the case of Magic-Users and Illusionists) or have the aid of deities or minions thereof (in the situation faced by Clerics and Druids)” and “The ramifications of spell scarcity are bound to aid your campaign.” Spells should be hard to acquire, and don’t just appear ready-to-use.

The trainer providing a scroll, or a spell from their own spell book, is more consistent with those philosophies than the player just choosing what they want. The trainer could, of course, offer his student a choice of the spells within his spell book. Or not. That leaves open where the mage acquires the spell when leveling without a trainer/tutor—a scroll acquired as part of the increased training cost is one explanation.

Spell Discovery

As long as the mage hasn’t learned their Maximum Knowable spells for the spell group, they can learn additional spells.

When a mage discovers a spell they can comprehend (determined by the earlier Chance to Know) in a spell book or scroll, they can add it to their spell book (after casting Read Magic to know that they know it!). Transcribing a scroll into a spell book requires one day for each spell level (e.g., a 3rd level spell takes three days) before the spell can be memorized.

When the mage discovers a heretofore unknown spell that has never had the Chance to Know rolled, and has not reached their Maximum, they roll the Chance to Know. Success means they can comprehend and learn the spell. How could they encounter a spell without a previous Chance to Know roll? That spell could be a unique spell created by a module or campaign, or was otherwise previously unavailable. As an example, my campaigns don’t check the UA spells at character creation; when a UA spell is discovered, the mage determines Chance to Know.

Creating New Spells

The mage can also research new spells by creating them (DMG, p. 115). Whether the spell is new, or a listed spell the character has been unable to locate during the course of adventuring, the mage can attempt to create the spell as long as they have not reached the Maximum for that spell group.

The player presents to the GM the specifics of the desired spell, after which the GM determines the spell level (DMG, p. 115). If the GM determines the spell level is above the level the mage can cast, research is possible, but useless. If the spell caster doesn’t spend enough money on research, there will never be success. In either case, there will be no indication that their attempt is fruitless. The DMG instructs that the player will be unaware of the specifics of the calculation. Even if the spell creation is impossible, the DM should still permit them to keep throwing their gold away week after week until they give up. For a game 40+ years old, that’s unlikely and impractical—the GM and player should be in accord for the spell level. At the very least the GM should permit the mage to consult a sage to determine spell level.

With access to a library within one day’s travels (or a shrine, in the case of a cleric), researching a new spell requires a minimum number of weeks equal to the determined spell level. Any day of interruption will set progress back one week. The research cost for each week will be:  a base cost of 200 gp / spell level per week + a variable 100-400 gp / spell level each week for materials. If no library is at hand, the base cost increases by a factor of 10 (from 200 gp to 2000 gp)!  After the minimum research period, the base chance of creating the spell that week (and each week thereafter) is 10%, modified by intelligence, mage level, and spell level:  ((10 + Intelligence + mage level) – (2 × spell level)))%.

For each additional 2,000 gp spent per spell level, the base chance can be further increased by 10%, (i.e., for a first level spell an additional 2,000 gp/spell level for a 20% base, and additional 4,000 gp for a 30% base, an additional 6,000 gp for a 40% base, and an additional 8,000 gp for a 50% base (the maximum)).

Unearthed Arcana

Unearthed Arcana defines a heretofore undefined capacity for spell books. A standard spell book, with an encumbrance of 450 gp) is composed of 72 pages of thick vellum, and can contain only a limited number of spells—spells of levels 1-3 use three pages each, spells of levels 4-6 use six pages each, and spells of the levels 7-9 require nine full pages each.

UA also adds the spell and requirement of the 1st level Read Magic to the Illusionist, and a table for the initial illusionist spells, making the illusionist spell process virtually identical to the magic user.

Write

The Write spell will: “inscribe a spell he or she cannot understand at the time (due to level or lack of sufficient intelligence) into the tome or other compilation he or she employs to maintain a library of spells.”

Write conveys no additional abilities. Mages can’t automatically comprehend spells inscribed in a spell book; that’s superseded by the Chance to Know roll.

Combining Write with UA, Write could inscribe a spell into a spell book, to later be cast, in extremis, just as if the spell book were a scroll. But that still doesn’t negate the Chance to Know—UA requires the spell to be knowable in such a circumstance (differing from casting an unknowable spell from scroll, which is permitted (DMG, p. 128)).

Change in Intelligence

“If intelligence goes down or up for any reason, and such change is relatively permanent, the magic-user must check again as explained above for known spells by level group.”

On first glance, a change in mage intelligence completely randomizes their spell selection. However, a closer read shows “for known spells”. If the Intelligence decreases, OA states that Chance to Know is checked for known spells until enough spells are forgotten to comply with a new Maximum. The wise mage will first check those spells that passed Chance to Know buy have yet to be discovered!

On increase, the mage begins their check anew, re-checking each level group in the order of their choosing for additional spells until they have reached their new Maximum.

Oriental Adventures

OA includes a number of statements in the context of the wu jen, all more definitively stated than the original text in the PHB:

• Chance to Know is checked for every spell at the time the mage gains access to a new spell group.
  • If the Minimum is not reached, start checking again, one spell at a time, until the Minimum is reached.
  • If the Maximum is reached while checking Chance to Know, stop.
• If a spell that has not failed Chance to Know is encountered “in the field”, the mage can check Chance to Know if not at Maximum.

References

 

TSR 2010, Players Handbook [1e], 1978.
TSR 2011, Dungeon Masters Guide [1e], 1979.
Dragon Magazine, Issue 33, “Sorceror’s Scroll: AD&D’s Magic System: How and Why it Works,” January, 1980.
TSR 2017, Unearthed Arcana [1e], 1985.
TSR 2018, Oriental Adventures [1e], 1985. p. 25. [Not quite identical to PHB]
Dragon Magazine, Issue 139, “Sage Advice,” November 1988.
Dragon Magazine, Issue 147, “Spelling it Out,” July, 1989. [Not consistent with RAW]