Is the computer game correct? Do I check for Poorhouse effect before I build?
No way. How silly would that be? You'd only get a card if you had 0 or 1 cards before building. If you had 0, you couldn't build. If you had 1, you could only build if you had a discount (maybe just using builder privilege for a cost 1 building).
The card reads,
owner takes 1 card from the supply if he has only 0 or 1 hand card after building