Risk is even more fun if you add more rules to it, for instance, "territory grab" is where you get to choose where your provinces are. Choosing a Capital province always takes strategy, making sure it is well-guarded by surronding area's. Tatical move is after the attack turn, you transport your troops into other provinces. Throwing some diplomacy is always fun, declaring war, alliances, border agreements, just to name a few.
The way I play it, Risk isn't about luck, it's about cunning diplomacy, making agreements sound good, then using it to your advantage. For instance, one game I was playing a couple friends. It was later in the game, so it was hard to take over a province. I came up with a deal between Kamatchaka and Alaska, so that we would reconquer it back and forth. The object of that was so we would gain risk cars every turn. I would end up keeping both provinces because my turn was last. Eventually I came up with a massive army of 110 men in the Ukraine, I crushed army's leading me to Kamatchaka, since I went last, it was my turn to conquer it, and he had moved his army's else where. I ended up conquering the world in one turn.
Of course, the normal way is good, just not as good.
UPDATE: Only go in Europe if you're ready for full-scale invasions, keep Ukraine heavily guarded.
