Exactly how often must I log in daily to get bonus gold?

[tehboomer]

Due to your lackluster activity, only checking in on us 4 days in the previous month our people refuse to work harder and send us any additional money! As a result, we have missed out on up to 46,845 gold coins! We must set a good example for our people, with more activity they will work harder for us!

How many times must I log in to acquire that bonus gold?

[cantrips]

6x is the minimum.

[DHaran]

https://utopia-game.com/wol/game/game_bonuses

6 50% of your income
9 100% of your income
12 200% of your income