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A seige is about surrounding the city with ZOC.
Example A, barb without obstruction.
A) Barb has 3 movement points, is able to walk in a straight line for three tiles.
>OOO > (Barbarian entering and exiting)
-OOOO
--OOO
Example B, barb walking past an archer/ranged unit.
B) Barb has 3 movement points, is able to walk in a straight line for three tiles. Ranged units don't exercise ZOC (unless promoted!)
>OOO > (Barbarian entering and exiting)
-OROO (R being ranged unit)
--OOO
Example C, barb walking past a melee unit.
C) Barb has 3 movement points, has to stop in the first tile adjacent to enemy melee unit (your warrior for example). Next round barb wants to continue, again moving past you, again only one tile possible to move.
>BOO (Barbarian stopping first tile adjacent to M unit)
-OMOO (M being melee unit)
--OOO
>OBO (Round 2: Barbarian stopping again at first tile adjacent to M unit)
-OMOO (M being melee unit)
--OOO
>OOOOOB > (Round 3: Barbarian has free movement again because exiting ZOC)
-OMOO (M being melee unit)
--OOO
The ZOC for said melee unit would be, where M is the unit, O is a tile and X is a tile with ZOC.
OOOOOOOO
-OOXXOOO
OOXMXOOO
-OOXXOOO
If you get the hang of ZOC's it's much easier to hunt barbarians and enemy units.
Hope this helps.
Edit: had to put in hyphens otherwise layout was screwed.