I found all the chess pieces, but I do not remember where they are on the map.
The only thing I remember is that they are always inside the houses and in view of the player, so you will never find them in a chest or anything like that. They are all in the city, so do not try to go to the dwemer city to find them. Why do not you try to go back to the Council and interact with the chessboard? You may already have them all and you don't noticed, as happened to me xD. Also you can try to search them in the guards barrack inside the Council building. I hope I helped you in your search of the chess pieces. Bye!

Good to know they aren't secreted away in a chest then! I'll just have to keep my eyes peeled, they're probably obvious and I missed em somehow hah

i did complete it ... now what ?

It gives you a permanent effect in the Effects section of your magic menu, it's called Strategist, I think or something similar.

ma man ty <3

i have all but three pieces. ive been inside every home, even the farm house, ive triple checked, but i cannot seem to find just three of the pawn (warrior) pieces. if anyone makes a guide for this it would be awesome.

using this medium to keep track of what i have, and where i found them.
3 in selthris house: 1 red sphere, 1 red spider, on table near alchemy table, 1 yellow warrior in slave room, next to lamp on table.

3 in shaglaks house: 1 yellow ballista on the shop counter. 1 yellow and 1 red warrior on the table next to the door.

1 in taminas house: 1 red ballista on the enchanting table.

2 in council hall: 1 yellow sphere on desk to the left of the thrones. 1 red warrior in small room off small downward hall, in the shelf (non locked room).
4 in morag tong baraks: 1 yollow sphere, in main office on a back shelf. 1 red ballista and 2 yellow warriors on main office desk.

was tryihng to keep track, but my system crashed one day and i lost all progress. im sorry i didnt keep going. i will try again when i get the game re installed.