Elsewhere in these forums a differentiation was made between games and simulations. I do not think Risk has "failed" as a game. Its very longevity disproves that theory. However, as a simulation, at any level, it doesn't rank above the lowest. But, that doesn't matter. Even if the game is driven by the dice, like any game, you need to take that variable into play.
I have posted elsewhere today about a game I am currently in with my two oldest sons, 14 and 11. My 14 year old has had his ears hermetically sealed. I can't get anything through to him about planning and strategy. My 11 year old, is much more competitive and is hungry to learn.
I am working with him to think ahead about how he places his armies. I keep reminding him that he must keep the dice in mind when he begins a campaign. I am teaching him about how to use the dice odds in his favor, either as an attacker or a defender.
What Risk can do, is to get new, and even old gamers to think about the big picture. My oldest spent so much time in the game setup preparing to take a particular continent, he neglected the rest of his territories. And what build ups he made there, he wasted by not concentrating in areas where he had a good chance of winning. My 11 year old, on the other hand, was somewhat reactionary to my oldest's buildup, and somewhat neglected his other strengths as well. However, he didn't throw his eggs in one basket. He had a more balanced approach, and as a result, he is still in the game.
They are learning, and are having fun. I will eventually wean them off Risk and move to more substantial games, er, simulations.
Eventually my plan will work, and I will have manufactured my own opponents. No more solitaire.
Game update, 6/21: It took 5 more turns, but I eventually beat my 11 year old to finish our game. He grasped the concepts of resource management, as well as trying to deny me mine. However, he missed the "global" aspect, and kept fogetting the signifigance of the Alaska-Kamchatka link. As a result, he kep plowing from Asia through Europe to take out Greenland to take full continents away from me. He finally got the point that he only needed to take only one territory per continent to deprive his opponent of extra builds. He also learned that he needed to husbandhis forces, so he could provide a defense in depth, to slow his opponents juggernaut each turn.
It was a real see saw battle. He would attack like a wave, take a lot of my territory, but be just shy of denying me one less army each turn. I would respond, regaining my lost ground, and take a few extra, to whittle down is next turns builds. This worked until he was too thin to defend, and I added about 40 armies to go after his 20+ territories. Got him down to Australia. Then put him out of his misery.
Even in defeat he enjoyed the game, though not happy about losing. But, he liked it.