Hare games are two-player abstract strategy board games that were popular in medieval northern Europe up until the 19th century. In this game, a hare...
Hare games are two-player abstract strategy board games that were popular in medieval northern Europe up until the 19th century. In this game, a hare is trying to get past three dogs who are trying to surround it and trap it. The three dogs are represented by three pieces which normally start on one end of the board, and the hare is represented by one piece that usually starts in the middle of the board or is dropped on any vacant point in the beginning of the game.
Hare games are similar to Bear games and hunt games. One side has more pieces than the other with the larger side attempting to hem in the smaller side. The smaller side though is usually compensated with more powers. Where Hare games differ is that the hounds can only move forward or sideways, and not backwards. The hunters in the Bear games can move in all directions. Furthermore, the dog in the Hare games cannot capture any of the hares, unlike the tigers, leopards, jaguars, and foxes in the hunt games which can capture their respective prey counterparts.
There are several different Hare game boards depending upon the country of origin. Many preferred the narrow double-ended spearhead-like boards with orthogonal and diagonal lines running through them. There were several variations on this design. However, one in Denmark used a round board, and another design is found in Latvia.
Hare games are referred to by different names. In 19th century France, a hare game that was popular among the military was called The Soldiers' Game. The dog is sometimes referred to as a hound, and hence the alternative title to this game as Hare and hounds. Other names are French Military Game, Game of Dwarfs, The Devil among tailors, and Trevolpa or Volpalejden .
As the rules of the game are simple to program, there are many electronic implementations of the game. The second link below allows you to play this game. In this computer game, the hares and hounds are reversed. Instead, it is the hounds attempting to surround and immobilize the hare.
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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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