What is the default Branched Rite Amount game rule in CK3?

Default: A Faith supports one extra Rite per 70 Counties, founding its first at 140. (patch 1.20.1.2)

Does changing the Branched Rite Amount rule disable achievements?

No: none of its 5 settings carries the flag blocks_achievements in patch 1.20.1.2.

Game rule · Tweaks · Faith

Branched Rite Amount

Default
Fewer
Far Fewer
Many More
More

Branched Rite Amount is a game rule in Crusader Kings III (Tweaks and Faith) with 5 settings: Default (the default), Fewer, Far Fewer, Many More and More. None of its settings disables achievements. Patch 1.20.1.2, from game/common/game_rules/00_game_rules.txt.

This section as JSON: /raw/game-rules.json

Quick answers (2)

What is the default Branched Rite Amount game rule in CK3?: Default: A Faith supports one extra Rite per 70 Counties, founding its first at 140. (patch 1.20.1.2)
Does changing the Branched Rite Amount rule disable achievements?: No: none of its 5 settings carries the flag blocks_achievements in patch 1.20.1.2.

5 settings

Default
Default
A Faith supports one extra Rite per 70 Counties, founding its first at 140.
default_branched_rite_amount
Fewer
One per 100 Counties, the first at 200.
The script checks it 3 times, in 3 places
Script values 3
- rite_growth_counties_per_rite
- rite_growth_fallback_min_counties
- rite_growth_rites_soft_max_cap
Every has_game_rule = fewer_branched_rite_amount in game/common and game/events, by the top-level object it sits in.
fewer_branched_rite_amount
Far Fewer
One per 140 Counties, the first at 280.
The script checks it 3 times, in 3 places
Script values 3
- rite_growth_counties_per_rite
- rite_growth_fallback_min_counties
- rite_growth_rites_soft_max_cap
Every has_game_rule = much_fewer_branched_rite_amount in game/common and game/events, by the top-level object it sits in.
much_fewer_branched_rite_amount
Many More
One per 35 Counties, the first at 70.
The script checks it 3 times, in 3 places
Script values 3
- rite_growth_counties_per_rite
- rite_growth_fallback_min_counties
- rite_growth_rites_soft_max_cap
Every has_game_rule = much_more_branched_rite_amount in game/common and game/events, by the top-level object it sits in.
much_more_branched_rite_amount
More
One per 50 Counties, the first at 100.
The script checks it 3 times, in 3 places
Script values 3
- rite_growth_counties_per_rite
- rite_growth_fallback_min_counties
- rite_growth_rites_soft_max_cap
Every has_game_rule = more_branched_rite_amount in game/common and game/events, by the top-level object it sits in.
more_branched_rite_amount

Source: game/common/game_rules/00_game_rules.txt line 726 (key branched_rite_amount), modifiers from game/common/modifiers, names from the English localisation; Crusader Kings III 1.20.1.2.