Abalone is a two-player abstract strategy board game designed by Michel Lalet and Laurent Lévi in 1987. Players are represented by opposing black and...
Abalone is a two-player abstract strategy board game designed by Michel Lalet and Laurent Lévi in 1987. Players are represented by opposing black and white marbles on a hexagonal board with the objective of pushing six of the opponent's marbles off the edge of the board.
Abalone was published in 1990 and has sold more than 4.5 million units. The year it was published it received one of the first Mensa Select awards. It is currently sold in more than thirty countries.
The board consists of 61 circular spaces arranged in a hexagon, five on a side. Each player has 14 marbles that rest in the spaces and are initially arranged as shown below, on the left image. The players take turns with the black marbles moving first. For each move, a player moves a straight line of one, two or three marbles of one color one space in one of six directions. The move can be either broadside / arrow-like (parallel to the line of marbles) or in-line / in a line (serial in respect to the line of marbles), as illustrated below.
A player can push their opponent's marbles (a "sumito") that are in a line to their own with an in-line move only. They can only push if the pushing line has more marbles than the pushed line (three can push one or two; two can push one). Marbles must be pushed to an empty space (i.e. not blocked by a marble) or off the board. The winner is the first player to push six of the opponent's marbles off of the edge of the board.
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KALAH
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...
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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