What is the difference between teaching your child to play Chutes and Ladders the regular way, and teaching your child to play Chutes and Ladders where each player has two pieces and they have to choose which one to move each time they roll?
The difference is that the former is the child's first introduction to the great world of gambling, while the second is an introduction to using your brain.
Why do people enjoy dice and luck in games? Because people are addicted to gambling. Really, what is the excitement in that two second period between the time you roll the dice and the time it lands and you discover what will happen to you in the game? Why do you enjoy that?
I think it must be something to do with entering a place where it is not you vs. him anymore, but you vs. the world. The world is more arbitrary than an opponent. Two people are treated equally when they face the world. Either one can win. Two people against each other are not equal. The more skilled one is usually going to win.
Without that die roll, the only way to consistently win is to work at it. Even if your opponent hands you advice and insight into his or her own strategy, you still have to absorb it, make it part of yourself and become a better player. And this takes work and time.
Sure, better players will win Risk more often than worse players. But really: when you play against a better Risk player, and the other player outmaneuvers you, but you win anyway because of lucky dice - did you really "win"? When playing against a worse player and you play better and still lose because of a few dice rolls - did you "lose"? We all know that if you play the game 1000 times, and you are twice as good as your opponent, you will be winning twice as many games. What is the point, then, of a single win or loss? A die roll rolled up good - oh boy, I win. It rolled up bad - oh darn, I lose.
On Luck vs. Randomness.