The game is complex from a game-theoretic perspective, involves randomized strategies, and can be approached by reasoning about the opponent's reasoning. We have also found it to be fun, engaging, and slightly addictive. It is thus a great test case for studying actual strategic behaviour of people on Facebook.
I’m wondering whether it’s meant to be straightforward to devise an optimal strategy... it’s a zero-sum game, the catch is, there’s a large number of pure strategies — but do you have to mix over a large number of pure strategies (to guarantee to break even over time)? Maybe there’s a set of 5 good numbers (e.g. 34,26,21,15,4) that work if you allocate them at random to the hills; those suggested numbers look like a good bet against opponents who split their troops about equally amongst 3,4 or 5 hills.
Next I start thinking up ideas for improvement, usually after losing a round... how about a multi-round variant, in which the surviving troops get to defend the hills they captured? In a subsequent round, a defender would cancel out (say) three attackers, and you are allowed to send additional troops to a hill you already captured, in which case, you have to cancel them out with opponent’s attackers, and if any survive, they add to the defenders of that hill. It looks like eventually, all hills will end up with so many defenders that further attacks should be futile, but there is no guarantee of how long it will take to reach that state.
1“Hill” comes from the Gross and Wagner paper linked-to in the Wikipedia page. More abstractly they are sometimes called battlefields or sites.