Conquer Club

How can I kill neutral troops if when I start killing them and my dice rolls are bigger the computer says that I annihilated them but nothing happens and if I roll a smaller number than the computer then the computer kills one of my men. Why is that??

The problem you are having is that some maps, Feudal Epic, have 2 different sort of attacks that can be made; Assaults and Bombardment. Assaults are the regular sort of attacks where once all the enemy troops in the territory you are assaulting are dead you advance your troops into it. Bombardments are different, when all of the troops on the territory you are bombarding are dead they are replaced with a single neutral troop. (As such bombarding territories that are already neutral isn't very useful.)

2013-11-02 09:15:22 - Mihkelp bombarded Feudal Empire 2 from Feudal Empire Castle and annihilated neutral player's troops

You are succesfully killing the neutral troops, but since you are bombarding instead of assaulting they are being replaced. Different territories can either bombard or assault different places. Your problem is that you are trying to attack territories from a territory that can only bombard them. You need to deploy your troops on a territory that actual borders the places you are trying to attack if you want conquer. Check the legend of the map. In this case it says "Castles can conquer adjacent regions and bombard non-adjacent regions within the same kingdom." Note, that in this map some of your troops will automatically be deployed on your castle. You need to place the rest somewhere that can actually attack something if you want to continue to advance, and then you can reinforce the troops from your castle to somewhere useful at the end of your turn.
I recommend that you get the add-on know as BOB, it can make it easier to figure what can assault or bombard what.

Thanks that was very useful