COMMANDS & COLORS: ANCIENTS VS KALAH

Commands & Colors: Ancients is a board wargame designed by Richard Borg, Pat Kurivial, and Roy Grider, and published by GMT Games in 2006. It is based on Borg's Commands & Colors system using some elements similar to his other games such as Commands & Colours: Napoleonics, The Great War, Memoir '44 and Battle Cry designed to simulate the "fog of war" and uncertainty encountered on real battlefields. Commands & Colors: Ancients focuses on the historic period of 3000 BC - 400 AD. The core game includes several hundred wood blocks in two colors for the Roman/Syracusan armies and Carthaginian army. Sheets of stickers representing different unit types must be affixed to the blocks prior to initial play. 16 small wooden blocks representing "victory banners" and 7 larger plastic dice must also have stickers applied. Extra stickers are included for use as replacements. The game also contains a full-color rule book, color scenario book, and two color two-page double-sided "cheat sheets" for players to reference during play for dice results and unit statistics. The board is folded card stock laid flat for play. Hexagonal terrain pieces are laid on the board when called for by a scenario. A deck of command cards is included. Units are arranged on the board according to maps and scenario descriptions in the scenario book. Players are dealt a number of command cards equal to their "command value" for the chosen scenario. Often players have different command values and therefore different numbers of cards. Players take turns playing their cards to "order" units, generally allowing the ordered units to move and conduct combat. Cards often refer to a section of the battlefield, either left, center, or right, or some combination of these. There are also many special cards that allow very specific actions. Play continues until one player earns the requisite number of victory banners for the scenario. Victory banners are earned each time a player completely eliminates an enemy unit or leader.

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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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