They might be most easily conceptualized as race games with two main differences: First, when a piece lands on a space or point occupied by an opponent, instead of sending it back to the beginning to start over, the opponent piece is captured, permanently removed from the game.
Running-fight games are found almost exclusively in Islamic-influenced cultures, ranging from West Africa to India, often bearing the names Tâb, Sig, or variations thereof; in fact, the whole running-fight family is sometimes referred to as Tâb games.
However, three European examples exist: Daldøs/Daldøsa (Danish/Norwegian), Sáhkku (Samit), and Að elta stelpur (Icelandic).
Also in this group is the pre-Columbian Mesoamerican game known variously as Bul, Boolik, or Puluc.
Their unusual method of capture is the same as that of Bul, and conceivably they are descended from it, since a description of Puluc was published in German in 1906, and Boolik in English in 1907; Fang den Hut!