# Dictionary Definition

domineering adj : tending to domineer [ant:
submissive]

# User Contributed Dictionary

#### Synonyms

#### Translations

overbearing, dictatorial or authoritarian

- French: dominateur
- Hebrew:

# Extensive Definition

Domineering (also called Stop-Gate or Crosscram)
is a mathematical
game played on a sheet of graph paper,
with any set of designs traced out. For example, it can be played
on a 6×6 square, a checkerboard, an entirely
irregular polygon, or
any combination thereof. Two players have a collection of dominoes which they place on the
grid in turn, covering up squares. One player, Left, plays tiles
vertically, while the other, Right, plays horizontally. As in most
games in combinatorial
game theory, the first player who cannot move loses.

## Basic examples

### Single box

Other than the empty game, where there is no grid, the simplest game is a single box.In this game, clearly, neither player can move.
Since it is a second-player win, it is therefore a zero
game.

### Horizontal rows

This game is a 2-by-1 grid. There is a convention
of assigning the game a
positive number when Left is winning and a negative one when
Right is winning. In this case, Left has no moves, while Right can
play a domino to cover the entire board, leaving nothing, which is
clearly a zero game. Thus in surreal
number notation, this game is = −1. This makes sense, as this
grid is a 1-move advantage for Right.

This game is also = −1, because a single box is
unplayable.

This grid is the first case of a choice. Right
could play the left two boxes, leaving −1. The rightmost boxes
leave −1 as well. He could also play the middle two boxes, leaving
two single boxes. This option leaves 0+0 = 0. Thus this game can be
expressed as . This is −2. If this game is played in conjunction
with other games, this is two free moves for Right.

#### Vertical rows

Vertical columns are evaluated in the same way. If there is a row of 2n or 2n+1 boxes, it counts as −n. A column of such size counts as +n.### More complex grids

is a more complicated game. If Left goes first,
either move leaves a 1×2 grid, which is +1. Right, on the other
hand, can move to −1. Thus the surreal
number notation is . However, this is not a surreal number,
because 1 > −1. This is a Game, but not a number. The notation
for this is ±1, and it is a hot game,
because each player wants to move here.

is a 2×3 grid, which is even more complex, but
just like any Domineering game, it can be broken down by looking at
what the various moves for Left and Right are. Left can take the
left column (or equivalently, the right column), and move to ±1,
but it is clearly a better idea to split the middle, leaving 2
separate games, each worth +1. Thus Left's best move is to +2.
Right has four "different" moves, but they all leave the following
shape in some rotation:

This game is not a hot game (also called a
cold
game), because each move hurts the player making it, as we can
see by examining the moves. Left can move to −1, Right can move to
0 or +1. Thus this game is = = −½.

Our 2×3 grid, then, is , which can also be
represented by the mean value, ¾, together with the bonus for
moving (the "temperature"), 1¼, thus: \textstyle\left\ = \frac \pm
\frac

## High-level play

The
Mathematical Sciences Research Institute held a Domineering
tournament, with a
$500 prize for the winner. This game was played on an 8×8 board,
which proved sufficiently large to be interesting. The winner was
mathematician Dan Calistrate, who defeated David Wolfe in the
final. The tournament is detailed in Richard J. Nowakowski's Games
of No Chance (p. 85).

## External links

# Synonyms, Antonyms and Related Words

Olympian detachment, Olympian loftiness, absolute, absolutist, absolutistic, arbitrariness, arbitrary, argumentum
baculinum, aristocratic, arrogance, arrogant, arrogantness, assumption of
superiority, authoritarian, authoritarianism,
authoritative,
authoritativeness,
autocratic, autocraticalness,
big, big stick, bossism, bossy, condescendence, condescending, condescension, despotic, despotism, dictatorial, domination, domineeringness,
fascism, feudal, grinding, hard, harsh, haughtiness, haughty, haughty airs, hauteur, heavy hand, high and
mighty, high hand, high horse, high-faluting, high-flown,
high-handed, high-headed, high-nosed, hoity-toitiness, hoity-toity,
imperative, imperativeness, imperial, imperious, imperiousness, insolent, iron boot, iron hand,
iron heel, loftiness,
lofty, lordliness, lordly, magisterial, magisterialness,
magistral, magistrality, masterful, masterfulness, monocratic, officious, oppression, oppressive, overbearance, overbearing, overbearing
pride, overbearingness,
overruling,
overweening pride, patronization, patronizing, patronizing
attitude, peremptoriness, peremptory, pride, proud, proudness, purse-pride,
purse-proud, pushy, reign
of terror, repressive, severe, side, stiff-necked pride, strict, stuck-up, superbia, superior, suppressive, terrorism, thought control,
toploftiness,
toplofty, tough, tyrannical, tyrannicalness, tyrannous, tyranny, uppish, uppishness, uppity, uppityness, upstage