D&D General Why is the multi-classing spell slot math so weird?

[tetrasodium]

If you have 2 levels as a Rogue or Fighter, the rule doesn't apply, since you add "One third of your Fighter or Rogue levels (round down) if you have the Eldritch Knight or Arcane Trickster subclass" (emphasis mine). You don't have the subclass at level 2, so rounding up from level 2 never comes into play.

If you pivot to Wizard after becoming a 4th- or 5th-level Eldritch Knight or Arcane Trickster, look at the outcome as described in the opening post. Under the existing rule, no slots are gained from the new Wizard level, which seems a little bizaare (to me, at least). Why shouldn't you go from the equivalent of a 2nd-level full caster to 3rd when you gain a level as a full caster?

The spell slots for Eldritch Knights and Arcane Tricksters are already based on 1/3 level rounded up; it would be more mathematically consistent, and I would argue thematically appropriate, to do the same when multiclassing.

You shouldn't because your spells known EK with 5 spells known &2 cantrip ps known just went from only being able to cast abjuration and evocation spells to spells from all school gained ritual casting three cantrips and six first level spells they are able to scribe spells into a spellbook they can prepare spells from in addition to ritual casting and arcane recovery all applicable to their EK slot progression.

If you must find a problem, that problem is the fact that the resulting multiclass is not preparing spells as a level 7 EK plus a level 1 wizard with the two pools of spells/slots kept entirely separate