I love Dice Wars. It's a simple strategy game in which you march across a generated regional map by directing stacks of dice to roll against their neighbours.
I don't know where the best place to play it anymore is, now that the Flash version won't work in browsers, but you could do worse than giving KDice a try. It's Dice Wars but with online multiplayer.
I've played dozens and dozens of hours of Dice Wars against the AI, and only a couple of hours of KDice against real people. It does change things a lot.
Not the underlying rules, which remain the same. You start with a single territory on a largely unclaimed map. You direct your stacks of dice to capture neighbouring territories, and your failure or victory in battles is determined by all your dice being rolled against all their dice. At the end of each round, your dice are replenished by an amount equal to the territory you hold.
These rolls encourage a to-and-fro, as you weigh up the risks of stretching yourself thin across several territories with the reward of being mightily replenished if you hold those territories at the end of a round.
The main thing that's changed by playing it with other people is that other people are smarter than the AI. KDice's community is small, and seems to include several players who have been playing it for years. I found them friendly, but they know your strategies, and given the game's tactical simplicity, success comes down to second-, third-, and fourth-guessing your opponent. Or the luck of the dice roll.
Or - perhaps - the luck of your randomly assigned starting position. I haven't played it enough to make a definitive judgement, but if you're looking for a pleasant bin to throw your time into this weekend, KDice deserves more players. It's free to sign up.