The key to Risk is Australia. The Greeks knew it; the Carthaginians knew it; now you know it. Australia only has four territories to conquer and more importantly, it only has one entrance point, and thus only one territory to defend. Conquering Australia early in the game guarantees an extra two armies a turn, which is huge at that point in the game. Later in the game, that advantage lessens, but after securing Australia, you should be off to a very good start. If you're not in a position to take over Australia, South America will do. It also only has four territories, but it has two entrances and thus two territories to defend. On the bright side, it's also adjacent to Africa and North America, which are good continents to expand to (though they're both considerably more difficult to hold than Australia). This being the internet, there are, of course, some people who have thought about the subject a lot more than I and developed many detailed strategies.
Like many of the classic games, the original has become dwarfed by variants - games set in another universe (LotR Risk) or in a futaristic setting (Risk: 2042) - but I've never played those. However, I recent ran across a little internet game called Dice Wars. It's got the general Risk-like gameplay and concept of world domination via dice, but there are many key differences:
- The Map and Extra Armies: A different map is generated for each game. One of the other differences is that the number of extra armies (or Dice, in this game) you get per turn is based solely on the number of territories you control (and there's no equivalent to turning in Risk cards for more armies). This nullifies the Australia strategy of conquering an easily-defensible continent, but the general strategy remains: you need to maneuver your forces so as to minimize the number of exposed territories, slowly and carefully expanding your empire.
- Army Placement and Size: Unlike Risk, you can't choose where to place your armies (nor can you do "free moves" at the end of your turn, which are normally used to consolidate defenses or prepare a forward thrust). If you mount a successful attack, you must move all of your armies except one that you leave behind. This makes extended thrusts difficult, as you'll leave a trail of easily conquered territories behind you. This is one of the more annoying differences. Another difference is that any one territory can only have a certain number of armies (i.e. there is a maximum). This changes the dynamic, adding another element of entropy. Again, it's somewhat annoying, but it's easy enough to work around.
- Attacking and Defending: In Risk, the attacker has a maximum of 3 dice, while the defender has a maximum of 2 dice. Ties go to the defender, but attackers still have the statistical advantage, no matter how many armies are facing off. If both territories have an equal amount of armies, the attacker has the statistical advantage. In Dice Wars, the number of dice used are equal to the number of armies, and instead of matching up single dice against each other, they just total up the dice. If the attacker's total is greater than the defender's, they win. Again, ties go to the defender. So in this case, if two territories have the same number of armies, the statistical advantage goes to the defender. Of course, you generally try to avoid such a situation in both games, but again, the dynamic is quite different here.
Of course, I'd already played a bit to get to this point, and you can probably spot my strategy here. I started with a concentration of territories towards the middle of the map, and thus focused on consolidating my forces in that area. By the time I got to the screenshot above, I'd narrowed down my exposure to four territories. I began expanding a to the right, and eventually conquered all of the green territories, thus limiting my exposure to only two territories. From there it was just a matter of slowly expanding that wall of two (at one point I needed to expand back to an exposure of three) until I won. Another nice feature of this game is the "History" button that appears at the end. Click it, and you watch the game progress really quickly through every battle, showing you the entire war in a matter of seconds. Neat. It's a fun game, but in the end, I think I still prefer Risk. [hat tip to Hypercubed for the game]