World
Game
Of
Sprouts
Association

## A Sprouts Glossary

AB - Aunt Beast.

air bag - A hollow sphere.

AJS - The pattern, discovered and computer-proved through n = 11 by Applegate, Jacobson, and Sleator, that Left wins in normal sprouts iff n divided by 6 leaves a remainder of 3, 4, or 5, and the pattern, also proved by these researchers through n = 9, that Left wins in misere sprouts iff n divided by 5 leaves a remainder of 0 or 1

anago - A line floating in white space, to which live spots are affixed.

antipharisaic adj. Describing a move which tends to increase ultimately the total number of survivors.

Aunt Beast - The computer program of Josh Purinton introduced with revolutionary effect in the year 2006.

biosphere - A hermetically sealed life zone. A sphere with no outer pivots.

black and white sprouts - A sprouts variant in which the mover can opt not to place a spot on a newly drawn line. See Black and White Sprouts, by Holger Matties.

Brussels sprouts - A joke variant of sprouts which uses crosses instead of spots, with each spoke of a cross capable of attaching to a single line, and with new crosses born with alternate spokes already filled. The joke is that every "game" is predestined to last exactly 5n - 2 moves.

cannibal - A spot with zero or two lines attached.

cannibal war - A struggle not to move first to a trap. Iff the number of survivors which will be produced outside of the trap is of different parity than the number of cannibals outside of the trap, then the player to move will win this struggle.

closed move - A move which creates a new region.

component - For any mathematical game, a portion of a total position such that no move involving that portion can have any effect upon upon the remainder of the position. In sprouts, component and biosphere are synonymous.

crash vt. - To move into a Type 2 UT without being forced, in the hopes that the move will produce a favorable configuration of double switches.

dead spot - A spot with three lines attached.

dot - A spot.

double switches - A total position containing two switches.

dry up vt. - To reduce the potential for survivors.

dynamic component - A trap or switch.

enclosing move - A move that creates an additional region.

endgame - A biosphere with a small number of liberties.

exhausted position - A position with no legal moves.

eye spot - A pivot.

fecundity - The ability of a position to produce survivors.

fianchetto - A nonlooping opening move.

fickle component - A tame component that can be correctly treated in misere play as if it were a sum of nim heaps of size 0 or 1. Part of Conways's "Genus theory" for finding good moves in misere games. The precise definition is rather technical; for details see the article Firm and Fickle Games. See also: tame component, firm component. A sprouts example is 0P1. (See the article Playing Sprouts with Misere Grundy Tables for an explanation of 0P1.)

field vt. - To be required to move (to a position).

firm component - A tame component that can be correctly treated in misere play as if it were a sum of nim heaps containing at least one heap of size 2 or greater. Part of Conways's "Genus theory" for finding good moves in misere games. The precise definition is rather technical; for details see the article Firm and Fickle Games. See also: tame component, fickle component. A sprouts example is the type 1 UT.

first player - In regards to a given biosphere, the first player to move to that biosphere.

flipflop - A switch.

ghost - A spot with one line attached.

guardian - In an exhausted position, one of the two dead spots closest to some survivor.

hermitic adj. - Describing a sphere which, if played as a game, could be forced by either player to produce a single survivor.

hollow sphere - A region with two or more pivots on its outer boundary but otherwise empty. H(a) designates a hollow sphere with pivot a.

Hudson conjecture - The former conjecture, now disproven, that, for n > 9, Left wins in misere sprouts iff N divided by 6 leaves a remainder of 3, 4, or 5.

inverter - A biosphere which if played as a game wins for the first player in normal sprouts and for the second player in misere sprouts.

isolani - Survivors.

Khorkov conjecture - The conjecture that, for n > 4, Left wins in misere sprouts iff N divided by 6 leaves a remainder of 0, 4, or 5.

Left - The player who moves first in a given game.

liberty - A capability of a spot to receive a line. Original spots have three liberties.

life force - The total number of liberties in a sphere.

line - One of the two elements of a sprouts position, the other being the "spot". A line is a narrow but inviolate corridor, each end of which attaches to a spot.

linguini - A line attached at one end to a region boundary and otherwise floating in white space, to which one or more live spots are affixed.

live spot - A spot with fewer than three lines attached.

loop vi. - To form an enclosure.

match - One or more sets played as a contest between two players. See "Richman method".

misere sprouts - Sprouts such that the winner is the player to field an exhausted position.

mystical principle - The rule of thumb that a biosphere which can be forced by either player to produce N moves will with best play actually produce N moves.

n - The number of spots in an initial position.

neighbor - A connected spot, alive or dead, with no intervening spots.

nim - A mathematical game in which two players take turns reducing nim heaps, with the object of making the last legal move.

nim heap - A nim entity with an integral value not less than zero. In nim, a legal move consists of selecting a nim heap with value greater than zero and converting it to a nim heap of any lesser value not less than zero.

normal sprouts - Sprouts such that the loser is the player to field an exhausted position.

novice cannibal - A spot with no lines attached.

null - A biosphere which if played as game is a win for the second player in normal sprouts and for the first player in misere sprouts.

open move - A move which does not create a new region.

original spot - A spot with no lines attached.

outer pivot - A pivot contained in a given sphere such that the pivot accesses a live spot not contained in the given sphere.

parity - 1. Evenness or oddness. 2. Survivor parity.

parity conservation principle - The principle that the parity of the number of cannibals in a sphere will not change after an even number of moves to that sphere.

partisan sprouts - A sprouts variant which accords differing sets of possible moves to the two players. See Partisan Sprouts, by Gregory Van Patten.

pharisaic adj. Describing a move which tends to reduce ultimately the total number of survivors.

pharisee - In an exhausted position, a dead spot p such that for any live spot l at least two dead spots are closer to l than is p.

pier spot - A spot with two lines attached which accesses only one region.

pivot - A spot with two lines attached and accessing two regions.

quasiswitch - A biosphere of stable parity that can be adjusted in one move to either contain or not contain a hidden trap.

receiver - For a given game, the player designated to determine who shall play Left. The receiver makes this determination after the server has determined the number of spots and type of play.

region - An undivided area such that a game begins with one region, which is gradually divided into more and more regions. (An area of white space, possibly containing spots, entirely bounded by lines or else running to infinity outside the castle walls.)

Richman method - A method of conducting a competition between two players using the concepts of set, match, server and receiver.

Right - The player who moves second in a given game.

second player - In regards to a given biosphere, the second player to move to that biosphere.

server - For a given game, the player designated to determine the number of spots to be used and whether play is to be normal or misere.

set - A pair of consecutive games in a match such that the first of these games is odd numbered (with the first game of the match being game 1). Matches are comprised of some number of sets. See "Richman method".

SGN - Sprague-Grundy number.

sphere - An aggregation of regions. The sphere S(a,b,...) is the aggregation including all regions containing or touching at least one of the live spots a, b,..., or at least one live spot accessible to at least one of the spots a, b,...,.

spice worm - An anago with five or more live spots.

split - A sphere consisting of two regions sharing a single pivot, with novice cannibals in each region but with no ghosts or veteran cannibals in either (apart from the shared pivot). In an m-n split the two regions have m and n novice cannibals, respectively.

spot - One of the two elements of a sprouts position, the other being the "line". Spots are demarcated junctions to which lines attach.

Sprague-Grundy number - An integer S assigned to a given biosphere B such that: (1) If B is exhausted then S = 0; (2) If B is not exhausted, S is the lowest integer greater than or equal to 0 to which B cannot branch, where "biosphere B can branch to integer N" means that B can be transformed in one move to a biosphere with Sprague-Grundy number N.

sprouts notation - The WGOSA system of recording sprouts games.

static component - A null or inverter.

survivor - A live spot in an exhausted position.

survivor parity - The evenness or oddness of projected survivors apart from any as yet unplayed traps.

switch - A biosphere which, if played as a game, would be won by the first player, both in normal and misere play.

switchman - A live spot after waiting moves have been depleted.

tame component - A component that can be correctly treated in misere play as if it were a sum of nim heaps. Part of Conways's "Genus theory" for finding good moves in misere games. The precise definition is rather technical; for details see the article Firm and Fickle Games. See also: fickle component, firm component.

TM - An advantage wherein all immediately forming traps create winning cannibal wars.

two-thirds rule - The rule of thumb that 2n/3 is a good approximation of the number of survivors a beginning position will produce.

tranquil adj. - Describing a position for which it is possible that every survivor will be a Zen master or a move leaving such a position.

trap - A biosphere which, if played as a game, would be won by the second player, both in normal and misere play.

trapeze move - A move from a pivot to an adjacent pivot.

ubiquitous trap - A UT.

unicorn - A hermitic sphere.

universal trap - A UT.

UT - A region containing two original spots and no other live spots (Type 1) or a region containing two original spots and an outer pivot, such that the pivot accesses a live spot in another region (Type 2). A Type 1 UT is a biosphere and a trap and is also a firm component, while a Type 2 UT is not a biosphere but often behaves as a trap.

veteran cannibal - A spot with two lines attached.

Zen master - A survivor which is a pier spot.

Zen sprouts - The sprouts variant played exactly like standard sprouts except that every move must be tranquil.

### Notation

In the following notational designations, i and j represent integers.

Ai - A biosphere consisting of the anago comprised of a ghost connected to a veteran cannibal connected to another ghost, along with i - 2 novice cannibals.

iLj - A biosphere consisting of two spheres sharing two pivots, one of these spheres consisting of i novice cannibals and the shared pivots, the other consisting of j novice cannibals and the shared pivots.

iPj - A biosphere consisting of two spheres sharing one pivot, one of these spheres consisting of i novice cannibals and the shared pivot, the other consisting of j novice cannibals and the shared pivot.

PPi - The biosphere consisting of the anago comprised of a veteran cannibal connected to a ghost, along with i - 1 novice cannibals.