If you read 'Characteristics of Games'[1] or watch some talks[2] by Richard Garfield he elaborates quite a bit on this topic. He uses the example of rando-chess, which is very similar to your example.
Quoting #2 below:
"The toy game example of rando chess is an elegant means of constructing a game with customizable levels of chance. Garfield uses it here to illustrate how skill and chance are not opposites. Rando chess is exactly the same as chess, except that, after play has finished, the winner is reversed with probability 1/6. Rando chess, with any probability (<0.5) of reversal, would universally be agreed upon to involve more chance than chess, but would involve the exact same strategic considerations as regular chess and hence the exact same amount of skill. Every skill and every strategic concept in chess applies equally to rando chess, and, perhaps modulo tilt control, the best chess players in the world will also be the best rando chess players in the world... it just might take a longer period of play to determine this ranking. If, somehow, chess could only be played as rando chess, what would society think of it? What probability of reversal would make rando chess a game where neither skill nor chance predominates over the other?"
Quoting #2 below:
"The toy game example of rando chess is an elegant means of constructing a game with customizable levels of chance. Garfield uses it here to illustrate how skill and chance are not opposites. Rando chess is exactly the same as chess, except that, after play has finished, the winner is reversed with probability 1/6. Rando chess, with any probability (<0.5) of reversal, would universally be agreed upon to involve more chance than chess, but would involve the exact same strategic considerations as regular chess and hence the exact same amount of skill. Every skill and every strategic concept in chess applies equally to rando chess, and, perhaps modulo tilt control, the best chess players in the world will also be the best rando chess players in the world... it just might take a longer period of play to determine this ranking. If, somehow, chess could only be played as rando chess, what would society think of it? What probability of reversal would make rando chess a game where neither skill nor chance predominates over the other?"
1: http://www.amazon.com/Characteristics-Games-George-Skaff-Eli...
2: http://www.quantitativepoker.com/2012/09/20-thoughts-on-skil...