Arithematic Croquet is a two-person game that was created by Lewis Caroll in 1876. Lewis Caroll wrote the children stories "Alice in Wonderland" and "Through the Looking Glass". In the Alice story there is a croquet game between Alice and the Red Queen. It is played on a grass croquet court with hedgehogs and flamagos. This game is nothing like that.

In Carroll's Arithematic Croquet players advance in steps of 1 through 8 to 100 -- their moves are subject to serveral rules.

- The player that gets to 100 first wins.
- The players take turns.
- The current player may be able to choose 1, 2, 3, 4, 5, 6, 7, or 8 but not the number just played by the other player or its nines complement. If the other player played 6, then the current player cannot play 6 or 3.
- Numbers that are multiples of ten are called hoops. The hoops are 10, 20, 30, 40, 50, 60, 70, 80, and 90. If a player move into a hoop they must player the same number to get out that they used to get in. Alternately, they can "take the hoop" by playing a number that advances the same number of steps to the hoop as its steps after the hoop. For example, if a player is at 37 they can take it by playing 6; they move 3 steps to the hoop and 3 steps out to position 43. In each group of ten numbers, a hoop can be taken from positions 6, 7, 8, and 9 by playing 8, 6, 4, and 2. On the other side of the hoop they land at positions 4, 3, 2, and 1.
- When a player is in a hoop, they can be barred by the other player who can play the number needed to leave the loop. Or, they can play the nines complement of the number needed to get out. There is, however, a restriction. The needed number cannot be played over and over; it must alternated with its complement. So, if a player needs a 6 to exit the hoop, the other player can play 6, 3, 6, 3 ... and keep the player in the hoop, effectively causing them to lose turns to advance toward 100. (The other player could also have played 3, 6, 3, 6 ... .)
- When a player is in a hoop they lose the power to bar the other player. Also, when a player is between 90 and 100 they are not subject to barring unless the other player is also between 90 and 100.
- There are play position from 1 through 108 so a player can over run the 100 position and then come back to get to 100 exactly to win. However, a player can only do this once. If they had moved from 97 to 103, then back to 97, they can win by playing 3. If they played 2 to 99 and then 2 to 101, they would lose because they passed 100 twice.

By default, the two players are Alice and the Red Queen represented by blue and red, respectively.