As game designers/educators, we have to deal with the ultimate decision of how to balance luck and skill. Much of what we decide is determined on our own experiences in gaming.
I'll talk about advantages and disadvantages of putting in luck and skill
Probably the epitome of a game, skill is predicated on choice. It's the thing that we, as players, can control; the more we play, the better we get, the more we win. At least that's the theory. The more a designer puts in "skill", that is choices given to the player that directly impacts the game, the more you can establish a barometer on how good you are in a game.
When a game is all about skill, it rewards the experienced. When a new player plays a experienced player, there's no doubt the experienced player will win. In tournament situations, a skilled game really shows who the best of the best is because it favors the most efficient, experienced player.
Unfortunately, many times it can create a runaway situation where a new player may be turned off by an experienced player stomping on them. From the perspective of the new player, it's apparent early in the game that they will not win; when that happens, they're just waiting for the game to end or are looking for excuses to leave.
An established skill game can have incredible longevity. Most hardcore players will play it just to find the nuances of the game. But to establish that level is extremely hard to attain, you'll need a dedicated audience to keep it going and a lot of manpower to show its longevity through tournaments and play sessions.
On the flip side, a game of all skill can have the tendency to get boring as the players can be far too concentrated on the game to be any kind of entertaining. It's great for people that know the game, but the outsider could be bored quickly. The game will need to be simple in order for the outsider to at least be engaged.
Examples of skill mechanics:
-A hand of cards.
-Multiple options to choose during a turn.
-Placing units on a board
-Moving units on a board that's not a specific trail.
-Once-per-turn or Once-per-game abilities
Luck is really the X-Factor in a game. It's the very thing that adds that bit of spice to an otherwise cerebral game.
A completely luck based game like Candy Land is great for beginner gamers (by beginner I mean child that doesn't know any games) because it doesn't force the player to think hard; it's only meant to keep a player engaged when cerebral facilities are still developing.
But luck does something easier that skill based games have a hard time doing...make a game surprising. The randomness of luck, whether it be by dice, lottery, random draw from a deck, or even a flip of a coin can take a game in directions that can't be explored by pure skill. It introduces elements into a game that challenge the skilled player, regardless of how many times they have played the game. Because surprise is more evident, the game can consequently be more "fun".
In some ways, luck takes away from skill. It tends to be swing-y and can frustrate a skilled player because it negates everything they've earned through multiple plays. But luck can favor the player that's behind, it makes the playing field a little more even. But it comes at a cost. It makes runaway victories easier to achieve because luck can also work in the favor of the lead player.
Examples of luck mechanics:
-Dice (that requires a roll for a result)
-Card draw in a deck
-Card flip to determine result
-Lottery (mixing possible results and drawing results from it)
-Event cards that are revealed randomly
Levels - Mixing Skill and Luck:
Most games are a mix of skill and luck. It's how much of each that determines if we like a game or not.
A game that has more luck than skill caters to the beginner player, but can often frustrate or discourage the experienced player. Often, either an experienced player will appreciate the randomness or ditch the game entirely. Critics may deem the game "too random", but the entry point is fairly wide, so initial buys can be solid. These games are great to introduce to new players as the threat of being stomped by a master player are quelled by the fact that luck may swing in their direction.
A game that has more skill than luck may fall in a more competitive category, but a good game that has more skill than luck will introduce just enough luck to make experienced players feel challenged by fairly competent, or even new players. The problem is that experienced players may be able to take advantage of the luck, thereby still creating a runaway situation.
The holy grail is an even balance of skill and luck. It has just enough skill to keep an experienced player going, but just enough luck to make it fun for all.
Regardless of how we set up games, players will have preferences. Some may want more luck, others not. It's hard to see that a person may simply not like your game because they just don't like playing your type of game. In the same way we like watching different types of movies, we also prefer certain games, though it doesn't mean we are restricted to that genre. We can affect how much we put luck and skill in a game by first identifying how much luck and skill there is in our game, then putting in elements that contribute more to skill.
Of course there are exceptions to the rule, but generally, this applies to many games.