DOWNFALL VS KALAH

Downfall is a two-player game for players aged 7 and older, first marketed by the Milton Bradley Company in 1970. The game consists of a vertical board with five slotted dials on each side. Each player starts with ten numbered tokens or discs at the top of the board. The object of the game is to move the discs to the bottom of the board by turning the dials. Players alternate turns moving the dials and cannot move a dial that their opponent has just moved. The winner is the first player to move all of their discs into the tray at the bottom. An advanced version of the rules dictates that the discs arrive in the tray in numerical order. Since neither player can see the other's board, it is common to inadvertently advance - or hinder - the opponent's gameplay. The game rewards forward thinking and planning; players may try to "trap" their opponent into turning a dial that will advance their own disc, while trying to ensure that their own discs are not caught and dropped out of order. The game is currently available in the UK under the name New Downfall, manufactured and marketed by Hasbro. The new version follows the same rules but has a more futuristic design in red and yellow. The game's box art is parodied on the cover of Expert Knob Twiddlers, an album by Mike & Rich (Mike Paradinas & Richard D. James).

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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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