The functional form of the entropy $S = - \sum p \ln p$ can be understood if one requires that entropy is extensive, and depends on the microscopic state probabilities $p$.

Consider a system $S_{AB}$ composed of two independent subsystems A and B. Then $S_{AB} = S_A +S_B$ and $p_{AB} = p_A p_B$ since A and B are decoupled.

$$
S_{AB} = - \sum p_{AB} \ln p_{AB} = -\sum p_{A} \sum p_B \ln p_A  -\sum p_{A} \sum p_B \ln p_B
$$

$$
 = -\sum p_{A}  \ln p_A  - \sum p_B \ln p_B = S_A + S_B
$$
This argument is valid up to a factor, which turns out to be the Boltzmann constant $k_B$ in statistical mechanics: $S = - k_B \sum p \ln p$ which is due to Gibbs, long before Shannon. 

How do you prove $S=-\sum p\ln p$?
I am a bit behind the curve, and just started playing BF3. I played BFBC2, and liked it, and enjoy what I see so far in BF3.

The new server setup confuses me though. Since it appears that there are no more 'standard' servers (think BC2 or even most other games on the xbox like Halo or CoD), you can see a list of all of these 'public' shared servers, with odd descriptions. 

One thing I noticed a lot through them was people saying '500% on [map name]'. I was very unsure of what this meant. 

I was in an awesome match last night, and after dying once, I was kicked. I had no clue what for. Because I had just selected 'quick match' I was unsure of any server rules. I would like to understand what hosts are meaning by their description. 
