Chopsticks (hand game)
Chopsticks is a hand game for two players, in which players extend a number of fingers from each hand and transfer those scores by taking turns to tap one hand against another. The basic version is an example of a solved game in that so long as both players play optimally, the game's victor can be predicted at any point.
Each player uses both hands to play the game, the number of digits extended on a hand showing the number of points that the hand has. Both players start with each hand having one point — one finger extended on each hand. The goal of the game is for a player to force their opponent to extend all of their fingers and thumbs on both hands. A hand with all fingers and its thumb extended is called a "dead hand". Players take turns to tap one of their hands against another hand that is not dead (either their own other hand, or one of their opponent's). The number of points on the tapping hand is added to the number on the tapped hand, and the player with the tapped hand extends their digits to show the new score. The tapping hand remains unchanged.
A player may tap their own hand to transfer points from one hand to the other. For example, if a player had three points on his or her right hand and one on his or her left, the player could rearrange them to have two on each hand. A "dead hand" is treated as having no points, for this purpose, which allows a player to bring a dead hand back into play by transferring points to it. You cannot prolong the game by not taking your turn. 
Transferring or splitting points between the two hands is not allowed when the values of both hands merely switch places, as it could be used as in tactic to unnecessarily prolong the game. For example, if a player's left hand has three points and their right hand has two points, they are allowed to transfer points such that one hand has four points and the other hand has one point, but it would be an illegal move to transfer three to the right hand and two the left hand. It would also be illegal, if a player has one point on one hand and one dead hand, to transfer the one point to the dead hand.
Variations of play
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One variant, also known as "Overlap" or "Remainders", changes the rules so that if one hand gets more than five points the leftover points are left on the hand. This means that five is subtracted from the number of points that one hand gets, and the only way a hand can get knocked out is if it accumulates another five or more points. For example, if a player has four on a hand and the other transfers three points to that hand, the hand gets two points (since 3 + 4 = 7 and 7 Mod 5 = 2 ).
This way of playing is generally for more advanced players and requires more strategy.
Similar to Leftovers/Overlap, Exact Play is where for a hand to be knocked out, it must equal exactly five points. It therefore becomes an illegal move for a player to give points to an opposition hand if it will result in its total exceeding five. This variation adds a stalemate end-game (e.g. If both players have two hands of four points — neither can transfer points between hands or give points to an opposition hand) where the game is often restarted. This adds a new dimension of strategy, as poor choices by a player who may appear to be in a strong position can lead to a stalemate.
Players are allowed to evenly divide an even number of points in one hand to an empty hand or combine two hands, an action known as "split". For example, a player with a dead hand and four fingers on the other can use their turn to "split" the points 2:2. This variation is quite commonly played in India. The players can split the finger count any way they want. If they have a 4/1 distribution, they can split that to 3/2. This variation is sometimes played instead of allowing transfers or redistributions.
The Japanese version of the game does not allow splitting to be performed unevenly (i.e. if one hand has 1 and the other has 2 the only split possible is a pure split of 3 onto one hand).
The knubs variation is played the same as regular Chopsticks except that there can now be half-fingers or "knubs". A knub is created by extending the finger upwards and curling it down. Since a knub represents a half of a finger, two knubs will equal one regular finger, which means that everything can be split, so 1:0 would become 0.5:0.5 and 3:0 would become 1.5:1.5 and 4.5:0 becomes 2.5:2, etc. Because of all of the possible splits the game can last a while. A good strategy for a player to use is to reduce the opponent's hands to 0:0.5 and transfer until the player has 4.5:4.5.
This variation is played the same way as Knubs except that each knub can further be divided into half-knubs which represents a quarter of a finger. This variation can be somewhat confusing and will last a long time.
Game of Five
In this variation, a player does not lose when he gets 5 fingers on one hand, instead losing when they have more than 5 fingers on a hand. When this variation is played in conjunction with the Splits variation, the game is a win for the second player to go.
In this variation, the objective of the game is to force your opponent to defeat you. When played in conjunction with the Splits variation you may defeat yourself by combining both your hands to get more than or equal to 5.
- "Chopsticks Game". Activity Village. Retrieved 2014-03-27.
- Rigney, Ryan (2012-11-07). "You May Win Every Time, But You Haven’t Solved This Game Yet". Wired. Retrieved 2014-03-27.
- "Chopsticks". Childhood, Tradition & Change. 2011. Retrieved 2014-03-27.
- Unbeatable Chopsticks AI Bot. This bot plays the game with remainders and transfers.