Lewis Carroll’s Arithmetical Croquet

1. The first player names a number [positive integer] not greater than 8: the second does the same: the first then names a higher number, not advancing more than 8 beyond his last; and so on alternately — whoever names 100, which is the “winning peg,” wins the game.

NOTE: for this version of the game, players are required to choose how many steps they wish to move forward, rather than which number they wish to move to.

2. The numbers 10, 20, etc. are the “hoops”. To “take” a hoop, it is necessary to go, from a number below it, to one the same distance above it: e.g. to go from 17 to 23 would “take” the hoop 20: but to go to any other number above 20 would “miss it,” in which case the player would have, in his next turn, to go back to a number below 20, in order to “take” it properly. To miss a hoop twice loses the game.

3. It is also lawful to “take” a hoop by playing *into* it, in one turn,
and out of it, to the same distance above it in the next turn: e.g. to
play from 17 to 20, and then from 20 to 23 in the next turn, would
“take” the hoop 20. A player “in” a hoop may not play out of it with
any other than the number so ordered.

4. Whatever step one player takes, bars the other from taking an equal
step, or the difference between it and 9: e.g. if one player advances
2, the other may not advance 2 or 7. But a player has no “barring”
power when playing *into* a hoop, or when playing from any number between 90 and 100,
unless the other player is also at such a number.

5. The “winning peg,” like the hoops, may be “missed” once, but to miss it twice loses the game.

6. When one player is “in” a hoop, the other can keep him in, by playing the number he needs for coming out; so as to bar him from using it. He can also do it by playing the difference between this and 9. And he may thus go on playing the 2 barring numbers alternately: but he may not play either twice running: e.g. if one player has gone from 17 to 20, the other can keep him in by playing 3, 6, 3, 6, etc.

Player A's Turn

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Player B's Turn

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