I haven't once captured a Castle, let alone a Town by starving them to death or surrender,
Like some guys here said, surrender is possible when the enemy is brutally outnumbered, and there is no enemy Lord present.
Only way to carry enough food for a 30 day siege is to disband most of your army, say to less than 20 troops, then the Castle garrison will surely sally out and beat whatever crap you have left. (I'm not dumb enough to try that technique)
Seriously, Sieges are unrealistic and unbalanced.
- As Marshal or Leading Lord, there is no way to send another Lord to find meat or whatever food you need.
- You as Leading Lord or Marshal, cant order another Lord to continue the siege, while You "The Master" go shopping.
- Even though our troops can kill 1000+ men in a jiffy, they can't do hunting.
- Never, since M&B have I seen a single Lord do a "starve to death" siege for 30 days, they usually attack or retreat after some days.
- Siege a town for 100 days is ludicrous, by then the war is will be over, won or lost. And You missed all the fun.