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.^[1] 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.^[2]

Rules

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. ^[3]

Splitting

If you have 5/2 (Dead hand and other hand has 2 points) you can split 1/1. (one hand has 1 point the other has 1 point) If you have 5/3 you can split 2/1 or 1/2. If you have 5/4 you can split 2/2 or 3/1 or 1/3.

Variations of play

Leftovers

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.

Exact Play

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.

Half Splits Only

In this variation, a player can only split if he has one dead hand and an even number of fingers on the other, and the split can only be in half. This means that there are only two possible splits in the game, splitting 4:0 into 2:2 and splitting 2:0 into 1:1. This best strategy here is to try to make your opponent have odd numbers so they can't split.

Knubs

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.

Quarters

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.

Committing Suicede

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.

References

1. "Chopsticks Game". Activity Village. Retrieved 2014-03-27.
2. Rigney, Ryan (2012-11-07). "You May Win Every Time, But You Haven’t Solved This Game Yet". Wired. Retrieved 2014-03-27.
3. "Chopsticks". Childhood, Tradition & Change. 2011. Retrieved 2014-03-27.

External links

• Unbeatable Chopsticks AI Bot. This bot plays the game with remainders and transfers.