Assume two 1st level Rogues, Alice and Beatrice.
Alice gained 3 levels of Rogue and on her 4th level of Rogue, instead of an ability score increase she picked up the Martial Adept feat. She later gained 3 levels in Fighter, and chose the Battle Master archetype.
Beatrice gained 3 levels of Fighter, and chose the Battle Master archetype. She then gained 4 levels of Rogue, and instead of an ability score increase she picked up the Martial Adept feat.
Alice and Beatrice each now total four Rogue levels and three Fighter levels, obtained via different paths. Is the superiority dice gained from the Martial Adept the same dice for both Alice and Beatrice?
(The text above was posted as an example in another question that was closed as too broad. After talking to a moderator, it was decided the best thing would be to post the example as a separate question.)
The Martial Adept feat says:
[...] If you already have superiority dice, you gain one more; otherwise, you have one superiority die, which is a d6. [...]
The already have implies that you need to have superiority dice when you acquire the feat, otherwise it is a d6. Beatrice is safe. RAW, she already has superiority dice when she gets the feat.
Is Alice stuck with a d6 superiority die for the rest of her career?