
Like most religious practices common to the entire civilized world, the Holy Game (actually a genre of many games, most developed for exactly one occasion) dates back to the Elder Undyarchy of the northwestern Taddols. In its classic form, it was designed to adjudicate disputes in naming rituals between divine entities - which divinity shall (at least for the upcoming 157-day Short Year) be credited as including the Night, or the Duties of Guarding the Undyarch, or even (if you want to get meta) Sports Gambling. However, as the game has diffused over the ecumene, it has taken on different meanings, including settling disputes between different aspects of a god, initiating 157-day long "marriages" between the gods in question, and determining other important questions. Frequently the teams of the mascot-gods of cities have been pitted against each other as a proxy for war or other negative-sum conflicts. (Some actual wars have been fought as the Holy Game, with huge "teams" and appropriate rules. This is extremely rare when it comes to political entities fighting over existential stakes, but not entirely uncommon for societies with intermittent raiding conflicts.)
Several things are common. The game is always a naming ritual and all players must be ritually clean. (So no ghoul players, although ghouls who have eaten previous champions are often highly sought after as coaches and trainers.) It is almost always a team sport (teams most typically ranging from 3 to 6 players) and almost always asymmetric. If two gods' teams have played in the past, the rules shall be modified to make it harder for the god/team that won last time. Developing the rules for a match, especially a new pairing, is considered one of the most prestigious forms of allegorical art, and also a deadly serious religious affair in the maintenance of naming rituals. Gods are fully expected to intervene in proportion to their power and stakes in the conflict, and players are expected to try to enter ecstatic states to facilitate this. The stakes almost always involve the taking of an idol and breaking and/or moving of it (thus letting it serve the role of a "flag" or "ball," and sometimes the idol is in fact a rune-carved rubber ball, although torches, bowls of alcohol (which can't be spilt), and live animals are probably the most common); although the Holy Game can also be a fight to the death, in which case a player or players are consecrated as the idols. (Since most games are asymmetric, it can also be the case that your goal is to steal their flag and their goal is to kill you.)
A republican state is generally understood as one in which the regularly set stakes are which god is to be the civic god - meaning that their temple administration will function as the government for the following Short Year - and the rules of the game imply some kind of input from the populace, either in terms of formally gathered votes or acclaim or gathered donations.
Since many gods are created to contain and negotiate with hostile forces, and their cults serve to propitiate rather than earnestly advance the interests of their god, entire teams regularly serve as heels, working up the ire of the crowd while fully hoping to lose. But since the rules are adjusted each game to be easier for the loser, such staged matches become more and more vulnerable to the hostile god's sincere intervention. When such a god wins, the next match is of course adjusted very rapidly towards the benefit of the less hostile god. But such matches are always ticking time bombs, watched with sincere trepidation, and sincere relief when good triumphs over evil.