Concentration of Armies
It is essential to concentrate your armies in the game. One-army countries can be conquered very easily. The best way to expand is to have strong borders where most of your armies should reside. The countries within your border should contain minimal number of armies. This way your border armies are ready to be used as you need them, rather that been stuck in the belly of your empire.

However, there are also exceptions to this rule. Sometimes, in a continent such as Europe, it may be beneficial to leave armies in non-border countries to reduce the chances of getting invaded. Always attempt to minimise the existence of a single point of failure. Make sure you have a contingency plan so that if something went wrong you can always be in control of the situation.

Spreading too fast and too soon will lead to disaster. Always place yourself in the same position as your enemies and strive to understand their choices against you. It has been observed that time and time again, a Risk player makes a smart move and wins his objective decisively, only to ruin it all by going past the victory mark. He leaves thin borders behind and becomes weaker after a massive campaign. This means others will jump at the opportunity to bring him down there and then. In this regard Machiavelli states:
"Princes and republics should content themselves with victory, for when they aim at more, they generally lose. The use of insulting language towards an enemy arises from the insolence of victory, or from the false hope of victory, which latter misleads men as often in their actions as in their words; for when this false hope takes possession of the mind, it makes men go beyond the mark, and causes them to sacrifice a certain good for an uncertain better.” 
Similarly, Jia Lin states that:
“Even if you prevail over others in battle, if you go on too long there will be no profit.”
Remember, that single army countries are statistically easy to conquer and are therefore tempting. Do not expand too rapidly beyond a sustainable level and do not leave any holes in your borders. All it takes an enemy is a weak point in your defences. Before you know, he will be inside your continent rubbing you off the continent bonus and making chaos. This is in particular more devastating in the beginning of the game since you rely more on continents’ income than any other. Do not forget; a good opponent will never miss a chance to take advantage of your weak borders or your weak status.

Keep the number of your borders to a minimum at all times. Always plan this a few turns in advance so that you know how to expand. This is essential as you can concentrate your armies in each of your border countries which deter potential attackers.

In a similar concept, leaving a buffer country between you and a large army can benefit you since the other player needs to use a fortification move before he can attack you. This is illustrated in the figure below.
Buffer Territory

Suppose you are playing as Red. If you leave North Africa as it is, Blue cannot use his 14 armies in Egypt to start an invasion against you. He is forced to wait at least one turn to move his armies to North Africa before he can attack you. However, if you get North Africa, he can attack you straight away. Use this technique to buy time before someone attacks you.
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