Risk Strategy
Now you know how to play the game, but the real question is, how to win? Like all good strategy, the plan that leads to victory in RISK is relatively simple. You just need to understand a few important principles.* Concentrate your force to attack. The best way to attack is to stack as many pieces as possible into a single space and then roll, roll, roll onward. Take a territory, move into it with everything you can, and start a new invasion from that space. Keep doing that until you've achieved your objective or run out of steam. That's the basic idea behind everything you do, and all the other strategic principles exist to support that type of attack.
* Hold continents. That's a pretty obvious bit of advice, and it's easier said than done. The bonus armies you gain for holding a continent are well worth the trouble. The thing to remember is that if you take control of a continent, other players are going to try breaking up your control to prevent you from getting the bonus armies (and you're going to do the same thing to them!). Because of that, it's not worth taking a continent if you can't hold it. You'll only invite vicious counterattacks. It's better to build up for a while and then grab the last few territories with enough strength to hold them.
There are many things to consider when deciding which continent to aim for. The actual size of the continent is less important than the number of territories it contains with connections outside the continent. Both Australia and South America have four territories, for example, and both pay a bonus of two armies. Only one of Australia's territories, however, can be attacked from outside the continent, while two of South America's can. That means that to earn South America's two bonus armies, you need to defend twice as much territory -- you need strong armies in both Venezuela and Brazil to keep out the enemy. To defend Australia, you need a strong army only in Indonesia.
Now you're thinking, "Then I'll forget about South America and try to control Australia." In fact, Australia is a popular stronghold, especially early in the game when things are precarious. It's not always the best choice, however, because the length of its borders isn't the only consideration.
The problem with Australia is that the only place you can go from there is into Asia, which is far and away the most difficult continent to control with 12 territories, five (5!) of which are connected to other continents. Asia is so notoriously hard to control that few players ever attempt it, and then only late in the game.
In other words, if you hole up in Australia, you may get trapped in Australia.
* Shorten your borders. This principle is closely related to holding continents. We'll explain why in a moment. The basic idea here is that it takes fewer armies to defend one territory than two, or to defend two territories instead of three, and so on. This kind of efficiency is important during other players' turns, when your frontiers are under attack.
Just what does it really mean?
Mainly, it means that it's better to defend yourself by holding the enemy's ground than by fighting over your own. Let's look at South America as an example. The obvious way to defend South America with 20 armies is to put one army in Peru and one in Argentina, then split the remainder and put nine in each of Venezuela and Brazil. (If the enemy in North America is much stronger than the enemy in Africa you might shift some of those armies from Brazil to Venezuela -- splitting them 10/8, for example, or even 12/6 -- you get the idea.)
Why is this a poor strategy? Because the enemy -- let's say Africa -- can concentrate his armies on North Africa and smash them into Brazil over and over until it finally crumbles. Even if the invasion fails, the Africans can fortify North Africa at the end of the turn and be secure behind their own bulwark of armies.
Now consider what happens if South America puts its main defensive force in North Africa. Defensively, Africa is forced to put strong armies in Egypt, East Africa, and Congo. At least one of those territories is going to be weak, inviting attack. When it comes time for Africa to attack, its forces are split, which prevents the African player from concentrating his attacking force into one super-stack (remember principle #1?). If the invasion fails to capture North Africa, Africa can fortify only one of its defensive territories, leaving the door open for a devastating counterattack by the South American armies.
If you look at the map carefully, you'll see that this principle holds true for every continent. If you want to hold North America, the best territories to defend are Kamchatka, Venezuela, and Iceland; if you want to hold South America, the best perimeter is Central America and North Africa. Things get a bit more complicated in Europe, Africa, and Asia because those continents have so many interconnections. Still, if you were defending Europe, you'd rather fortify North Africa than Western Europe and Greenland rather than Iceland. If you're struggling for control of Asia, holding just Ukraine is easier than holding Ural and Afghanistan.
Some continents form natural bodies that can be combined without lengthening their borders at all. If you already control North America, for example, you have three border territories to defend. If you take control of South America, you'll gain two more bonus armies per turn and still have only three border territories to defend (your big southern defense force shifts from Central America to Brazil, or better yet, from Venezuela to North Africa). Likewise, if you control Europe, you can add Africa and the Middle East to your empire without increasing your border defense burden. If you control Asia (lucky you), you can take Australia and actually shorten your border!
* Use your cards wisely. First and foremost, try to earn a card every turn.
If everyone else gets a card every turn and you don't, you will fall behind and each turn it gets harder to catch up. If you don't do anything else, look for a weak spot where you can capture one territory and get your card.
Early in the game, it's best to hang onto your cards as long as possible. Let someone else cash in three hard-earned cards for a measly four or six armies. You're not so desperate. With 15 or 20 bonus armies, you can really do something.
Later in the game, the difference between 35 and 40 armies isn't so huge. It's best to trade in your cards when you have a chance to go on the offensive and seize lots of territory, but never, ever, find yourself in a position of being wiped out while holding a complete set of cards. If the situation looks grim, trade in your cards and shore up your position. Maybe your enemies will think twice about attacking if you've just reinforced strongly.
* Understand the odds. Whether you're attacking or defending, always roll as many dice as you're allowed. If you're the attacker and you can't roll more dice than the defender, then attacking is probably a bad idea -- probability says you're going to lose the battle.
If you roll fewer dice than you're allowed to -- defending with only one army when the territory contains three, for example -- you will lose more armies than you should, and the enemy will lose less. If it's not obvious, that's the opposite of what you want.
In the typical case -- attacker rolling three dice, defender rolling two -- the defender is likely to lose six armies for every five lost by the attacker. Keep that in mind.
* When you're trying to figure out how much territory your army can conquer (or how many armies you need to take a chunk of territories), you can figure it out simply by using this formula:
Enemy armies to be defeated
+ Number of territories to be occupied
= Armies needed
This formula isn't mathematically precise. What it tells you is how many armies you need in order to have a slightly better than 50% chance to succeed. If you follow this formula, you will conquer more than you fail.
Let's look at an example. Assume that the Africans want to capture South America. The South American player has 12 armies in Brazil, three in Venezuela, and one in each of Peru and Argentina, for a total of 17 defending armies in four territories. According to the formula, the African player has a better-than-50/50 chance of taking the whole continent if he attacks with 21 armies. If he's feeling especially lucky he might try with only 20, or even 18, but that doesn't leave much room for error. A careful player would attack with 24 or 25, just to be prepared for setbacks. The formula tells you how many armies you need to get the odds in your favor -- it doesn't guarantee success. The dice decide that. You've been warned.
Finish off weak players. That sounds cruel, but if you don't do it, someone else will. Few things are worse than hammering down a player from 12 territories to two, then running out of steam. The next player will pick off the two territories you left behind and capture the eliminated player's cards. You did all the hard work; someone else reaps the reward. That isn't fair, either. Plan your offensives to wipe out a player and cash in his cards to replace your losses or continue the conquest.
( This text was copied from here.)