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Domineering
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===Horizontal rows=== [[Image:20x20square.png]][[Image:20x20square.png]] 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 number|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 <nowiki>{|</nowiki>0} = β1. This makes sense, as this grid is a 1-move advantage for Right. [[Image:20x20square.png]][[Image:20x20square.png]][[Image:20x20square.png]] This game is also <nowiki>{|</nowiki>0} = β1, because a single box is unplayable. [[Image:20x20square.png]][[Image:20x20square.png]][[Image:20x20square.png]][[Image:20x20square.png]] This grid is the first case of a choice. Right ''could'' play the left two boxes, leaving β1. The rightmost boxes leave β1 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 <nowiki>{|</nowiki>0,β1}. This is β2. 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 2''n'' or 2''n''+1 boxes, it counts as β''n''. A column of such size counts as +''n''.
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