Too often I see people mistakenly confuse the two concepts of luck and randomness. Here are my definitions:
Luck: an event that occurs beyond any player control that has direct effect on victory. A series of lucky or unlucky events will decide the game, regardless of your skill.
Randomness: an event that occurs beyond player control that can be planned for, or whose effect requires an adaptation of strategic or tactical play.
An example of luck: roll a die. whoever rolls highest wins. A series of lucky events will even out over time, in therory. In practice however ...
An example of randomness: a series of random math problems, all numbers between 1 and 10, problems involve multiplication and/or division. No matter what numbers you actually get, you can be assured that the higher the skill of the person solving these problems, the more he will get correct. There is no preparation that can help you here.
Now, there is luck in randomness. In the above example, if a person is better at multiplication than division, than more division problems will be unlucky for him. In this case, the luck is praying on his lack of skill. Better preparation for the exam will diminish the effect of this luck.
Next case: let's say that in the luck example, a person can prepare events such that he will win the die rolls on 1-4, instead of 1-3, giving him a 66% chance of victory, instead of 50% chance. The net result is that he will win 2/3 of the time, or perhaps 2/3 of the games. Does this really matter? Is there any glory to winning, or losing, because you have increase your odds of an event entirely dependent on luck? If you win an event with 1/6 chance of winning, is that exciting? If you lose with a 1/6 chance, is that fun? If you win on a 5/6 chance, is that fun?
I'm sure a lot of people will answer the above questions differently than I do. Yes, they say, if the theme is intense, and the story arc exciting. Yes, since a player can decide to withdraw from bad odds and try again at a different area where he has a better chance. Such is the excitement of the war-gamer. More power to you.
Next case: Puerto Rico plantation tiles get flipped up. A player, depending on player order, may decide to take the Settler for first choice of these plantations, if there is on he wants. Or he may encourage his RHO to do this. Or he may calculate the odds of getting what he needs in the next Settler phase after these plantations are gone. It could be, that his RHO keeps taking all the coffees before he can get them, and he loses the game to a solid coffee monopoly. OK, that's a bi of a strech, but even with that kind of strech, the luck element in the plantation draw does not determine your success in the game unless you have planned so badly that it is the only thing that can help.
Now, when you lose a game of PR, or win a game of PR, the finger is pointed at the players. The randomness is there, and even a smidgen of luck, perhaps. The games always unfold differently because of it. IMHO, winning or losing in this situation is a more rich experience.
Games without either luck or randomness, such as Go, Chess, etc... are very good games. The beauty of randomness is that the games can never be analyzed with perfection for several levels. The beauty of luck is the inherent gambling nature in many of us. I just prefer to keep gambling out of my multiplayer gaming