Chop-sticks

Chop-sticks is a two-player abstract strategy game of pure mathematics and logic, with no random elements. The game is believed to have originated in East Asia, though its exact historical provenance is undocumented. It is played using only the players' hands, requiring no physical equipment. The objective is to force the opponent into a position where they cannot make a legal move, which occurs when both of a player's hands are reduced to zero fingers extended. The game state is defined by the number of fingers extended on each player's two hands, typically starting with one finger extended on each hand for both players. A turn consists of a player using one of their own hands to "attack" one of the opponent's hands. The attacking player adds the number of fingers on their chosen hand to the number of fingers on the opponent's chosen hand. The sum determines the new finger count on the opponent's attacked hand. If the sum is five or greater, the attacked hand is reduced to the sum minus five. For example, attacking a hand showing three fingers with a hand showing four fingers results in a sum of seven, which becomes two fingers (seven minus five). The game continues with players alternating turns. A hand showing zero fingers is considered "dead" and cannot be used to attack, but can still be attacked by the opponent. A common variant allows a player with a single non-zero hand to "split" the fingers, redistributing the total number of fingers between both hands, provided the split results in both hands having a non-zero count. This variant increases strategic depth. The game is deterministic; with perfect play, the outcome is predetermined from the starting position.

Gameplay and controls are entirely physical and gestural, requiring no interface or digital input. Two players face each other. Each player begins by extending one finger on each hand, holding both hands in front of them. A turn proceeds as follows: the active player selects one of their own hands (left or right) and one of the opponent's hands. The player then taps the opponent's chosen hand with their chosen hand. This physical tap represents the attack. The number of fingers on the attacking hand is added to the number of fingers on the opponent's hand. The opponent then adjusts the fingers on the attacked hand to reflect the new total, applying the modulo-five rule (any sum of five or more subtracts five). For example, if the attacking hand has two fingers and the opponent's hand has three, the opponent must extend five fingers, which then becomes zero (dead hand). If the attacking hand has one finger and the opponent's hand has four, the sum is five, resulting in zero. If the sum is four or less, the opponent simply extends that number of fingers. A player may not attack with a hand showing zero fingers. In the variant allowing splits, a player whose turn it is and who has exactly one hand with a non-zero finger count may, instead of attacking, redistribute that total number of fingers between both hands, provided each hand receives at least one finger. The game ends when a player has zero fingers on both hands, resulting in a loss for that player. No other controls or rules exist.