How do the Wizard's racial bonuses affect the number of spells and cantrips known?

Question

In Dungeon World, the "Spellbook" section of the Wizard's playbook explicitly says:

You start out with three first level spells in your spellbook

However, when creating a Wizard, one of the first steps is choosing the character's race, which we can do by writing our own races & bonuses or by picking from two pre-written options:

Elf: Magic is as natural as breath to you. Detect Magic is a cantrip for you.

Human: Choose one cleric spell. You can cast it as if it was a wizard spell.

In both cases, it seems like we're messing around with how many spells/cantrips the character is supposed to know.

So how should we interpret the racial benefits stated above when it comes to the number of spells & cantrips known? More specifically:

Elf

If I choose "Elf", do I get the "detect magic" spell as a cantrip for free, or do I still need to "spend" one of my three spell selections on detect magic?

More specifically, how many spells and cantrips should a level 1 Elf Wizard have?

1.a) Total of four cantrips and three level 1 spells. The cantrips would be "Detect Magic", "Light", "Unseen Servant" and "Prestidigitation". The 1 level spells would be any three from the Wizard spell list. "Detect Magic" does not need to be chosen as a level 1 spell.

1.b) Total of four cantrips and three level 1 spells. The cantrips would be "Detect Magic", "Light", "Unseen Servant" and "Prestidigitation". The 1 level spells would be "Detect Magic" and any other two spells from the Wizard spell list.

Human

When choosing the Cleric spell, is it supposed to be read as one extra spell from the Cleric spell list? Or is the spell from the Cleric list supposed to substitute one of the three spells I can learn from the Wizard's spell list?

More explicitly, which of these options describe how the character should be built:

2.a) I get to choose three Wizard spells + one Cleric spell (total of four spells)?

2.b) I get to choose two Wizard spells + one Cleric spell (total of three spells)?

Answer 1

The rules do what they say they do.

You start out with three first level spells in your spellbook as well as the cantrips. Whenever you gain a level, you add a new spell of your level or lower to your spellbook.

-- "Wizard", from the DW repo

An elf Wizard has Detect Magic as a cantrip, so they get it along with the rest of the cantrips in their starting spellbook. This does not use up a first-level spell selection because Detect Magic is a cantrip, a spell outside the calculation of spell levels. They can select three other first-level spells for their starting spellbook.

A human Wizard does not change their starting spellbook in any way; they get three first-level Wizard spells and the standard three cantrips. The human racial move lets them treat any Cleric spell as a Wizard spell; if they pick a first-level Cleric spell with this move, they can start with it as one of their three first-level Wizard spells. However, this move is not limited to first-level Cleric spells; you could just as well pick Word of Recall (cleric 7) or Storm of Vengeance (cleric 9). Because they aren't first-level spells you wouldn't be able to start with them, but you could add them to your spellbook later.

Answer 2

I don't know the answer for the Human but I believe it is clear for the Elf.

Elf

The full text reads:

You have mastered several spells and inscribed them in your spellbook. You start out with three first level spells in your spellbook as well as the cantrips. Whenever you gain a level, you add a new spell of your level or lower to your spellbook. Your spellbook is 1 weight.

Emphasis mine.

Since Detect Magic is as a cantrip to you then I see no reason it is not included in "the cantrips". The Elf move doesn't say it acts as a cantrip when casting, or for spell slots. It says it is a cantrip for you. So when something says cantrip, it includes Detect magic. This does mean you get one more spell to start than you would otherwise.

Answer 3

The two rules you quote touch on different subjects.

The first rules specifies you start with three first level spells. Those are your free spells.

The second rule alters the spell level of specific spells. It does not grant those spells for free.

In the rules https://exposit.github.io/dw-srd/dw_wizard_spells.html , Detect Magic is a level 1 spell. For an Elf, it is a cantrip. A human can learn any single Cleric spell as a Wizard spell even if that is not normally a Wizard spell.

So in your case, an Elf and Human Wizards still only have 3 free spells. They just have more choices than any other Wizard.