Klondike (solitaire)


Klondike is a solitaire card game. In the U.S. and Canada, Klondike is the best-known solitaire card game, to the point that the term "solitaire", in the absence of additional qualifiers, typically refers to Klondike. Equally in the UK, it is often just known as "patience". Elsewhere the game is known as American Patience, as well as Fascination, Triangle or Demon Patience.
Klondike solitaire is also traditionally known as Canfield, though in the US "Canfield" refers to a particular solitaire card game devised by Richard Canfield.
The game rose to fame in the late 19th century, being named "Klondike" after the Canadian region where a gold rush happened. It is rumored that the game was either created or popularized by the prospectors in Klondike. Its inclusion in Microsoft Windows in the 1990s has contributed significantly to its popularity in modern times.

Rules

Klondike is played with a standard 52-card deck, without Jokers. After shuffling, a tableau of seven fanned piles of cards are laid from left to right. From left to right, each pile contains one more card than the last. The first and left-most pile contains a single upturned card, the second pile contains two cards, the third contains three, and so on, until the seventh pile which contains seven cards. The topmost card of each pile is turned face up. The remaining cards form the stock and are placed facedown at the upper left of the layout.
The four foundations are built up by suit from Ace to King, and the tableau piles can be built down by alternate colors. Every face-up card in a partial pile, or a complete pile, can be moved, as a unit, to another tableau pile on the basis of their highest card. Any empty piles can be filled with a King, or a pile of cards with a King. The aim of the game is to build up four stacks of cards starting with Ace and ending with King, all of the same suit, on one of the four foundations, at which time the player would have won.
There are different ways of dealing the remainder of the deck from the stock to the waste, including the following:
If the player can no longer make any meaningful moves, the game is considered lost. At this point, winning is impossible.

Probability of winning

The probability of being able to win a game of Klondike with best-possible play is not known. The inability of theoreticians to precisely calculate these odds has been referred to by mathematician Persi Diaconis as "one of the embarrassments of applied probability".
The best information about the winnability of Klondike concerns a modified version of the game called "Thoughtful Solitaire" or "Thoughtful Klondike", in which the location of all 52 cards is known.
The probability of winning Thoughtful Klondike has been calculated as being approximately 82%, more precisely as having a confidence interval of 81.956% ± 0.096%. Thoughtful Klondike is not quite the same as simply playing with all cards face up, as this would allow an impossible movement of a pile if the top downturned card happened to be in sequence with the upturned card underneath it. Using physical cards, Thoughtful Klondike can be played by peeking at the face-down cards, while with electronic programs Thoughtful Klondike can be played by allowing unlimited use of undos to return to the start if a choice turns out to be unfavourable.
Because the only difference between the two games is the knowledge of card location, all thoughtful games with solutions will also have solutions in Klondike. Since any winnable Klondike game must necessarily be winnable when played thoughtfully, the results on Thoughtful Klondike tells us that 82% is an upper bound on the winnability of regular Klondike when we don't know the location of all cards. The true probability with best play might be much smaller, because the difference between a right and wrong move cannot be known in advance whenever more than one move is possible and some cards are still hidden. Ultimately, very little is known about the winnability of regular Klondike. The number of games a skilled player can probabilistically expect to win has been estimated as at least 43%, but this gives a massive gap of almost 40% between that number and 82%.

Scoring

Standard scoring in the Windows Solitaire game is determined as follows:
MovePoints
Waste to Tableau5
Waste to Foundation10
Tableau to Foundation10
Turn over Tableau card5
Foundation to Tableau−15
Recycle waste when playing by ones−100

Moving cards directly from the Waste stack to a Foundation awards 10 points. However, if the card is first moved to a Tableau, and then to a Foundation, then an extra 5 points are received for a total of 15. Thus in order to receive a maximum score, no cards should be moved directly from the Waste to Foundation.
Time can also play a factor in Windows Solitaire, if the Timed game option is selected. For every 10 seconds of play, 2 points are taken away. Bonus points are calculated with the formula of * 35, if the game takes at least 30 seconds. If the game takes less than 30 seconds, no bonus points are awarded.

Variations

Single 52-card deck

Below are some variations of the game of Klondike:
The game can be played with a Tarot-style 78-card deck. There are two ways of doing this. Each has nine increasing tableau stacks.