La Belle Lucie, also known as Midnight Oil, among other names, is a classic game of solitaire. It's a variant of the Fan-type games, in which the deck is dealt in small piles, or fans, of three cards each.
The setup for the game is simple. All 52 cards are dealt into 17 face-up fans of three cards each, plus one extra fan with only one card. The object of the game, like many forms of solitaire, is to move the cards from these piles to four foundations, building by suit from Ace to King. The rules for moving the cards are very simple; in fact, there's only one movement rule. Only one card may be moved from one fan to another at a time, and it may only be placed on top of the card of the same suit whose value is one higher (i.e. the Four of Hearts may be moved to a fan whose top card is the Five of Hearts). A card may only be moved to a foundation pile if it's the top card of a fan. Nothing may be played to an empty fan; once you clear the cards from it, it can't be used anymore. The cards remaining in the fans may be gathered, reshuffled and re-dealt twice, again into piles of three, for a total of three tries to move all cards to the foundations.
The rules of the game are deceptively simple, which quickly becomes obvious after playing a few times. While winning the game does depend somewhat on lucky shuffles and deals, it's largely dependent on the player's skill. After the cards are dealt, it's necessary to stop and figure out which moves are available and which cards will be blocked or made available by each move. To reveal a specific card required to continue building on a foundation, it may be necessary to trace back through several intertwined sequences of moves, only to discover that two mutually exclusive card movements are required to make any progress, and the only option left is to use up a re-deal. This is why the winning rate for this game is around 40% for the average skilled player, albeit with a wide range depending on individual ability.
I personally am a huge fan of La Belle Lucie. It's different enough from any work I might be doing at the time to give me a break, but it requires enough thinking to keep my brain active. It can be extremely frustrating at times to try to keep track of several loops of move sequences at the same time while looking for a way to uncover an important card, and it downright sucks to get a bad deal with all the kings on top, blocking half a dozen useful cards. However, the satisfaction of figuring it all out and putting the last card on top of the last foundation pile is worth it (to me, at least).