DVONN VS KALAH

DVONN is a two-player strategy board game in which the objective is to accumulate pieces in stacks. It was released in 2001 by Kris Burm as the fourth game of the GIPF Project. DVONN won the 2002 International Gamers Award and the Games magazine Game of the Year Award in 2003. DVONN is played on a board with 49 spaces. The board has a hexagonal layout 5 hexes wide. One player has 23 black pieces to play, the other player has 23 white pieces. There are also 3 neutral red pieces, called DVONN pieces. The object of the game is to control more pieces than your opponent at the end of the game. The game starts with an empty board and proceeds in two phases. During the first phase, the players place their pieces on the board, starting with the three red DVONN pieces. Pieces can be placed on any unoccupied space. White starts, and the players alternate. So Black is the first to place a piece of his own color. The first phase ends when all pieces are placed on the board, filling it completely. The second phase involves the building of stacks of pieces (a single piece is also considered a stack) by moving stacks onto other stacks. A stack is controlled by a player if his color is on top. A stack is immobile if it is surrounded by 6 neighboring stacks. The white player has the first move in this phase. Any mobile stack of height n (with n > 0) can be moved (in a straight line) in any one of the 6 directions by exactly n spaces by the player controlling it, if it lands on another stack. Jumping over empty spaces is allowed, as long as the tower does not land on an empty space. Single DVONN pieces cannot be moved, but they can be once they are part of a stack. After each move, all stacks that are not connected via a chain of neighboring stacks to any stack containing a DVONN piece are removed from the board.

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Kalah, also called Kalaha or Mancala, is a game in the mancala family invented in the United States by William Julius Champion, Jr. in 1940. This game is sometimes also called "Kalahari", possibly by false etymology from the Kalahari desert in Namibia. As the most popular and commercially available variant of mancala in the West, Kalah is also sometimes referred to as Warri or Awari, although those names more properly refer to the game Oware. For most of its variations, Kalah is a solved game with a first-player win if both players play perfect games. The Pie rule can be used to balance the first-player's advantage. Mark Rawlings has written a computer program to extensively analyze both the "standard" version of Kalah and the "empty capture" version, which is the primary variant. The analysis was made possible by the creation of the largest endgame databases ever made for Kalah. They include the perfect play result of all 38,902,940,896 positions with 34 or fewer seeds. In 2015, for the first time ever, each of the initial moves for the standard version of Kalah(6,4) and Kalah(6,5) have been quantified: Kalah(6,4) is a proven win by 8 for the first player and Kalah(6,5) is a proven win by 10 for the first player. In addition, Kalah(6,6) with the standard rules has been proven to be at least a win by 4. Further analysis of Kalah(6,6) with the standard rules is ongoing. For the "empty capture" version, Geoffrey Irving and Jeroen Donkers (2000) proved that Kalah(6,4) is a win by 10 for the first player with perfect play, and Kalah(6,5) is a win by 12 for the first player with perfect play. Anders Carstensen (2011) proved that Kalah(6,6) was a win for the first player. Mark Rawlings (2015) has extended these "empty capture" results by fully quantifying the initial moves for Kalah(6,4), Kalah(6,5), and Kalah(6,6). With searches totaling 106 days and over 55 trillion nodes, he has proven that Kalah(6,6) is a win by 2 for the first player with perfect play. This was a surprising result, given that the "4-seed" and "5-seed" variations are wins by 10 and 12, respectively. Kalah(6,6) is extremely deep and complex when compared to the 4-seed and 5-seed variations, which can now be solved in a fraction of a second and less than a minute, respectively.

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