![]() Because the only difference between the two games (Klondike and Thoughtful) is the knowledge of card location, all Thoughtful games with solutions will also have solutions in Klondike. There is a modified version of the game called "Thoughtful Solitaire", in which the identity of all 52 cards is known. There are four types of hands: winnable games, theoretically winnable lost games (the player made a selection that resulted in a lost game, but could not know what the correct selection was because the relevant cards were hidden), unwinnable games (there is no selection that leads to a winning result), and unplayable games. In addition, some games are "unplayable" in which no cards can be moved to the foundations even at the start of the game these occur in only 0.025% of hands dealt. ![]() The number of games a player can probabilistically expect to win is at least 43%. ![]() The issue is that a wrong move cannot be known in advance whenever more than one move is possible. Another recent study has found the Draw 3, Re-Deal Infinite to have a 83.6% win rate after 1000 random games were solved by a computer solver. Note that these results depend on complete knowledge of the positions of all 52 cards, which a player does not possess. If one allows cards from the foundation to be moved back to the tableau, then between 82 and 91.5% are theoretically winnable. About 79% of the games are theoretically winnable, but people do not win 79% of the games they start because they make a wrong move somewhere and lose the game prematurely. Turning three cards at once to the waste with no limit on passes through the deck, but allowing the player to switch once to a single pass through the deck one card at a time after that single pass, however, the player cannot go back to turning three cards at a time and can turn over no more cards from the waste.įor a standard game of Klondike of the forms Draw 3, Re-Deal Infinite, and Win 52, the number of possible hands is over 7,000 trillion.Turning only one card at a time, but placing no limit on passes through the deck.There are different ways of dealing the remainder of the deck: Once the player has done this, they will have "finished" that suit, the goal being, of course, to finish all suits, at which time the player would have won. Once this is accomplished, the goal is to move this to a foundation, where the player has previously placed the Ace of that suit. The aim of the game is to build up a stack of cards starting with two and ending with King, all of the same suit. Any empty piles can be filled with a King or a pile of cards with a King. The four foundations (light rectangles in the upper right of the figure) are built up by suit from Ace (low in this game) to King, and the tableau piles can be built down by alternate colors, and partial or complete piles can be moved if they are built down by alternate colors also. The piles should look like the figure to the right at the beginning of every game. The first and left-most pile contains a single upturned card, the second pile contains two cards (one downturned, one upturned), the third contains three (two downturned, one upturned), and so on, until the seventh pile which contains seven cards (six downturned, one upturned). From left to right, each pile contains one more card than the last. After shuffling a standard 52-card deck (without Jokers), seven piles of cards are laid from left to right.
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