The answer to this question is simply both. Both of these elements come into play when you are playing blackjack or any card game for that matter. Blackjack however cannot simple be thought of as a game of luck as there is proven strategies that increase a players win ratio. Yes, it is possible to win on a regular basis by luck alone but over the long term the opposite will occur. Those players who apply skill and strategy into how they play blackjack win more overall than those who play by the seat of their pants. A real blackjack player will always use skill to achieve the best possible results.
There are players, some famous, if have used card counting to have an edge over the casino. This is a skill very few have the ability or intelligence to master. If one argued that blackjack was a game of chance only then you would not see land based casinos refusing entry into their casinos by known card counters. If the casino were to asset its claims that it was only a game of chance then they would have no fear of those who apply such strategic skills in order to win at blackjack. Recent reports suggest that casinos suffer below a 2% loss as a result of those who count cards. This defies and refutes any claim of the game being luck versus a game of skill. Any real player who understands the game in detail and employs a strategy understands blackjack is anything but a game of chance.
The reality is that blackjack can be beat by using blackjack strategy. This is the real draw to the game as most people who play card games tend to be attracted to them for the increased amount of thought that must be used to gain positive results. Those same people will not be seen playing at a slot machine for the same reason. A Slot machine is 100% a game of chance. You invest your money, spin the reels and hope for a positive outcome. The majority of time slot players lose and in fact slots account for the largest percentage of profit with all casinos, both land based and online. So if blackjack was a game of chance then would it not be likely more blackjack players would also be slot players?
Those new to blackjack will hear the term counting cards often. They generally envision some computing device in their heads that has the ability to remember what cards have been dealt. In fact those devices have been created in a crude sense and used famously by a group from Boston. However what they fail to recognise if they are considering such an undertaking is the incredible skill in mathematics that is involved in counting cards. To do this simply in your mind is near impossible and without the aid of expensive miniature computing devices few will be successful at it.
Skilled card counters tend to keep it to the basics and use smaller numbers in order to understand or count the cards that have been dealt and are remaining in the deck. Depending on the number of decks used at the blackjack table it is not hard to see how this is near impossible for the average person and best to go with a proven blackjack strategy.