What is the default Hungarian Migration game rule in CK3?

Immediate: The Hungarian Migration will already be active on game start. (patch 1.20.1.2)

Does changing the Hungarian Migration rule disable achievements?

Yes for “Player-Only”: the file gives it the flag blocks_achievements. The other settings keep achievements on.

Game rule · Historicity · Flavor

Hungarian Migration

Historical
Immediate · default
Random
Player-Only ✕

Hungarian Migration is a game rule in Crusader Kings III (Historicity and Flavor) with 4 settings: Historical, Immediate (the default), Random and Player-Only. “Player-Only” 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 Hungarian Migration game rule in CK3?: Immediate: The Hungarian Migration will already be active on game start. (patch 1.20.1.2)
Does changing the Hungarian Migration rule disable achievements?: Yes for “Player-Only”: the file gives it the flag blocks_achievements. The other settings keep achievements on.

4 settings

Historical
The AI will attempt to start the Hungarian Migration between 890 and 910.
The script checks it once, in 1 place
Events 1
- game_rule.1011
Every has_game_rule = launch_historical in game/common and game/events, by the top-level object it sits in.
launch_historical
Immediate
Default
The Hungarian Migration will already be active on game start.
The script checks it once, in 1 place
Events 1
- game_rule.1011
Every has_game_rule = launch_immediate in game/common and game/events, by the top-level object it sits in.
launch_immediate
Random
The AI will attempt to start the Hungarian Migration any time between 5 years after game start and 910.
The script checks it once, in 1 place
Events 1
- game_rule.1011
Every has_game_rule = launch_random in game/common and game/events, by the top-level object it sits in.
launch_random
Player-Only
Disables achievements
The AI will not attempt to start the Hungarian Migration.
launch_off

Source: game/common/game_rules/00_game_rules.txt line 1169 (key hungarian_migration), modifiers from game/common/modifiers, names from the English localisation; Crusader Kings III 1.20.1.2.