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I recently lost my gaming rig due to catastrophic failure (everything went, mb/ram/cpu/gpu/hdd/ugh).
So here I'm sitting on my old old old single core AMD 3300+ with 1GB ram and a Radeon X800 GPU. Go me, woo!
Anyhow, I have consequently been exerimenting with Browser based games, and found some to be quite fun. One little gem that I have found is called World of Ants:
You need to build up an ant colony, which includes buildings (chambers), resource gathering (mines), and armies to conquer your neighbours. It has a tech tree for researching new units and other upgrades (such as raising your units' offensive or defensive power, hitpoints, etc), and doesn't require any kind of financial outlay to "play-to-win".
Since it seems to be relatively unknown I thought I'd post it on the boards here for anyone who wants to take a look at it. Typical of these style of games, it will take some days for you to make progress (after your initial developements) and as such, falls under the "extremely casual play" catagory, since you can touch the game for 30 minutes once or twice a day during the week, building up your resources, and then spend 3 or 4 hours on weekends running your hordes of warrior ants around attacking and pillaging the neighbouring "Wells" (ant-holes/villages).
It's heaps fun and would be family friendly to boot. It does, however, suffer from a small population, but that's all the more reason to try it out imo.
Give it a shot! There's nothing to lose...