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Yes, you usually get something.

On p. 101, it explains what happens when you get a new Hate by GM action:

GMs can add a 3-point Hate Relationship as a consequence of a throwdown or other major event. Unless the Sleuth went out of her way to earn the Hate, the player gains 3 Relationship build points to put into other Relationships.

But if a Love turns into a Hate, that's a Major Shift (p.98) and instead you are offered a Cool refresh to transform the Relationship:

...giving the Sleuth a Cool refresh of 5 points. If the Player accepts, the change happens.

On p.88 it is explained that the results of player actions do not earn the build points:

Hates are a trade-off. They are a liability, and will make your life hellish. But at character creation, the GM awards you extra Relationship points if you have a Hate. Your friends may be more protective, bond more tightly since you've fought off this aggression together. You don't get that bonus if a Like or Love turns into a Hate, or if a new Hate appears during play thanks to the character's actions.

It depends on where the Hate came from:

On p. 101, it explains what happens when you get a new Hate by GM action:

GMs can add a 3-point Hate Relationship as a consequence of a throwdown or other major event. Unless the Sleuth went out of her way to earn the Hate, the player gains 3 Relationship build points to put into other Relationships.

But if a Love turns into a Hate, that's a Major Shift (p.98) and instead you are offered a Cool refresh to transform the Relationship:

...giving the Sleuth a Cool refresh of 5 points. If the Player accepts, the change happens.

On p.88 it is explained that the results of player actions do not earn the build points:

Hates are a trade-off. They are a liability, and will make your life hellish. But at character creation, the GM awards you extra Relationship points if you have a Hate. Your friends may be more protective, bond more tightly since you've fought off this aggression together. You don't get that bonus if a Like or Love turns into a Hate, or if a new Hate appears during play thanks to the character's actions.

Yes, you usually get something.

On p. 101, it explains what happens when you get a new Hate:

...Unless the Sleuth went out of her way to earn the Hate, the player gains 3 Relationship build points to put into other Relationships.

But if a Love turns into a Hate, that's a Major Shift (p.98) and instead you are offered a Cool refresh to transform the Relationship:

...giving the Sleuth a Cool refresh of 5 points. If the Player accepts, the change happens.

Yes, you usually get something.

On p. 101, it explains what happens when you get a new Hate by GM action:

GMs can add a 3-point Hate Relationship as a consequence of a throwdown or other major event. Unless the Sleuth went out of her way to earn the Hate, the player gains 3 Relationship build points to put into other Relationships.

But if a Love turns into a Hate, that's a Major Shift (p.98) and instead you are offered a Cool refresh to transform the Relationship:

...giving the Sleuth a Cool refresh of 5 points. If the Player accepts, the change happens.

On p.88 it is explained that the results of player actions do not earn the build points:

Hates are a trade-off. They are a liability, and will make your life hellish. But at character creation, the GM awards you extra Relationship points if you have a Hate. Your friends may be more protective, bond more tightly since you've fought off this aggression together. You don't get that bonus if a Like or Love turns into a Hate, or if a new Hate appears during play thanks to the character's actions.

Yes, you usually get something.

On p. 101, it explains what happens when you get a new Hate:

...Unless the Sleuth went out of her way to earn the Hate, the player gains 3 Relationship build points to put into other Relationships.

But if a Love turns into a Hate, that's a Major Shift (p.98)

...giving the Sleuth a Cool refresh of 5 points. If the Player accepts, the change happens.

Yes, you usually get something.

On p. 101, it explains what happens when you get a new Hate:

...Unless the Sleuth went out of her way to earn the Hate, the player gains 3 Relationship build points to put into other Relationships.

But if a Love turns into a Hate, that's a Major Shift (p.98) and instead you are offered a Cool refresh to transform the Relationship:

...giving the Sleuth a Cool refresh of 5 points. If the Player accepts, the change happens.