My opponent has a Vi Hothead attached with a BF Sword, they chose to double its might. The Vi then pushed into my battlefield and I used Acceptable Losses when priority was passed. Does the Vi might stay at the doubled total from before the BF Sword was killed?

Ruling

Yes, Vi’s Might will stay at the doubled total. When the B.F. Sword is removed by Acceptable Losses, the amount added by the doubling effect remains static as it was calculated at the time the doubling effect was applied.

Reasoning

1. Doubling Mechanics: Per Rule 432.1.a, doubling creates an effect that adds a static value (+X) equal to the unit’s Might at the moment the doubling effect is applied. This added value is fixed and does not change even if the unit’s base Might or other equipment bonuses are modified or removed after the effect is already in place.
2. Removal of Might Bonus: According to Rule 137.3.a, an Equipment's Might bonus applies only while it is attached. While the B.F. Sword’s +3 bonus is removed when the card is destroyed by Acceptable Losses, this only affects the unit’s base Might. It does not retroactively change the static value added by the previously resolved doubling effect.
3. Layers of Might Calculation: Under Rules 471.1 and 471.2, while the game re-evaluates characteristics as layers change, the doubling effect has already locked in its bonus amount based on the snapshot of the unit's Might at the time of resolution.
4. Acceptable Losses: Per FAQs #4344, #9829, and #9207, Acceptable Losses simply destroys the gear. The destruction removes the static +3 bonus, but does not trigger a recalculation of a doubling effect that has already resolved and locked in its numerical value.

Sequence of Events

1. Doubling Applied: Vi’s Might is calculated (Base + B.F. Sword bonus), and the "Double" effect adds a fixed value equal to that total.
2. Acceptable Losses Played: Acceptable Losses resolves, and the B.F. Sword is destroyed.
3. Effect Cessation: The B.F. Sword's static Might bonus is removed.
4. Result: Vi loses the +3 bonus from the B.F. Sword, but retains the fixed value added by the doubling effect.

Note: I could not verify the exact base Might values of "Vi, Hotheaded" or the specific +3 Might bonus of "B.F. Sword" because these cards were not returned in my database lookup. Additionally, the specific Rule 422.4.b you referenced is not in the provided rules text; I have based this ruling on the general mechanics of continuous effects and equipment found in the Core Rules (Section 137 and Section 471).