Solitaire card games/La Belle Lucie

Other names: The Fan, Clover Leaves, Three Shuffles and a Draw, Alexander the Great, Trefoil or Midnight Oil

All cards are visible from the start, but this does not imply that this game is solvable with strategy. The default rule is very hard to win. The majority of games cannot be solved. For example, moving a single card onto another blocks that stack until both cards can be removed to the foundations. Any setup that has a lower card of a specific suit below a higher of the same suit, or all kings not on the bottom of each cascade cannot be solved without cheating. The shuffle and redeal is of little help. For each king left in the second redeal, there is a 66% chance that the cascade cannot be solved (if the king is not lowest). Moving aces out (Trefoil rule) has cosmetic character.

Rules

 * The tableau consists of seventeen fans of three cards each with a single card counting as an eighteenth fan.
 * Only the top card of each fan could be played.
 * Any aces are moved to the foundations and are built from there.
 * Cards are moved to the foundations by suit in ascending order (e.g. 2♦ over A♦ ).
 * Cards are moved to other fans by suit in descending order (e.g. 7♣ over 8♣).
 * When a fan becomes empty, it cannot be filled again, even with a King.
 * Once all possible moves have been exhausted, the entire tableau is reshuffled and redealt, again in fans of three with the remainder counting as a separate fan. There are only two reshuffles allowed in the game.
 * The game is considered won when all cards are transferred into the foundations.

Variations

 * Trefoil:
 * The aces are immediately transferred to the foundations and the remaining 48 cards are shuffled and dealt in sixteen fans of three to begin the game.
 * The tableau consists of sixteen fans of three cards each and the four remaining cards formed into two fans of two.
 * Cards are moved to other fans by alternating colours in descending order (e.g. 7♦ over 8♣). [The alternating colours rule for moves between fans.]
 * The Fan:
 * When a fan becomes empty, it can be filled with a king. This rule is recommended as it makes things easier and increases odds of solving the game. [The king rule.]
 * No redeals of cards. [The no redeal rule.]
 * Three Shuffles and a Draw:
 * When all possible moves have been exhausted after the two reshuffles without finishing, the player can still make one last possible move wherein one can pick out (or draw) a buried card, i.e. any card that is not the top card of any fan, and use it to continue the game and finish it. This special move and three shuffles involved (including the original shuffling of the cards before the start of any new game) give the variation its name.
 * Shamrocks
 * Before the game begins, each King which is on top or middle of its respective pile is placed underneath. A King that is on top of a lower-ranked card of the same suit should be placed under that lower-ranked card, no matter what else in its pile. To play on the tableau, a card can be placed over a card that is one rank higher or lower, regardless of suit (a 6♠ can be placed on a 7♣ or a 5♦). However, each pile can hold no more than three cards at a time; thus no card can be placed on a pile with three cards.

The "no redeal rule" and the "king rule" are often used together since redeals are needed to get to cards under a king unless it’s allowed to move kings to empty fans.

Strategies
Since all cards are visible after the deal, the basic strategy is to think before doing moves. A redeal is not always of much help, since it will give fewer fans than the initial deal.

Cards under a king are blocked until the redeal or until the king is moved to the foundations (if the "king rule" is not in effect).

For standard rules

 * Since cards only can be moved once (because 7♣ only can be moved to 8♣), the cards under moved cards will be blocked until the redeal or until the cards above are moved to the foundations.
 * It is always safe to build on a fan that contains only one card.
 * It is likewise always safe to build on a king, since the cards under it is blocked anyway (as long as the "king rule" is not in effect).
 * It is also safe to build on a sequence of two or more cards in suite (like 7♣ on 8♣), since the cards under it is blocked anyway.
 * It is always safe to move cards to the foundations.
 * Before moving a card consider if the destination card can be moved first (e.g. before moving 7♣ over 8♣, consider if it is possible to move 8♣ over 9♣).

For the "alternating colours rule for moves between fans"
The "alternating colours rule for moves between fans" will significantly change the strategy used in the game:


 * Even if cards can be moved multiple times, and thus cards under moved cards are not always blocked, it will often be the case, especially when the fan becomes larger.
 * Even if it is not always safe; if a fan contains only one card it is safer to build on it than on other fans.
 * It is likewise safer to build on a king than on other cards, since the cards under it is blocked anyway (as long as the "king rule" is not in effect).
 * Build evenly on the foundations; i.e. try to move all four Aces up to the foundations first, then move all the 2's, etc. Not following this strategy will limit the moves possible between the fans, even after a redeal.
 * Before moving a card consider if the destination card can be moved first (e.g. before moving 7♣ over 8♦, consider if it is possible to move 8♦ over 9♣).
 * All cards can be moved over two other cards. Therefore before moving a card, say 7♦ over 8♣, consider the need to instead move 7♥ over the destination 8♣, or the possibility to instead move the source card 7♦ over 8♠.