KALAH VS LOST CITIES

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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Lost Cities is a 60-card card game, designed in 1999 by game designer Reiner Knizia and published by several publishers. The objective of the game is to mount profitable expeditions to one or more of the five lost cities (the Himalayas, the Brazilian Rain Forest, the Desert Sands, the Ancient Volcanos and Neptune's Realm). The game was originally intended as a 2-player game, but rule variants have been contributed by fans to allow 1 or 2 further players, causing Reiner Knizia himself to later provide semi-official 4-player rules. Lost Cities is a fast-moving game, with players playing or discarding, and then replacing, a single card each turn. Cards represent progress on one of the five color-coded expeditions. Players must decide, during the course of the game, how many of these expeditions to actually embark upon. Card-play rules are quite straightforward, but because players can only move forward on an expedition (by playing cards which are higher-numbered than those already played), making the right choice in a given game situation can be quite difficult. An expedition that has been started will earn points according to how much progress has been made when the game ends, and after three rounds, the player with the highest total score wins the game. Each expedition that is started but not thoroughly charted incurs a negative point penalty (investment costs). Interaction between players is indirect, in that one cannot directly impact another player's expeditions. However, since players can draw from the common discard piles, they are free to make use of opposing discards. Additionally, since the available cards for a given expedition are finite, progress made by an opponent in a given color can lead to difficulty making progress in that same color. The game's board, while designed to supplement the theme, is optional and consists only of simple marked areas where players place discards. If Lost Cities had four expeditions instead of five, it could be played with a standard deck of playing cards. When doing so, the face cards would represent investment cards, with numbered cards two through ten serving as the expedition progress cards.

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