Post History
#2: Post edited
by
r~~
·
2026-05-07T18:05:53Z (4 months ago)
Yes. A simple example is \(G = \{1\mathop|* \mathop- 1\}\).- If Left goes first in \(G + G\), their only move is to \(G + 1\), after which Right's only move is to \(* \mathop- 1 + 1 = *\), after which Left moves to 0 and wins.
- If Right goes first in \(G + G\), their only move is to \(G + * - 1\). Left has two options: play in \(G\) or in \(*\).
- * If Left moves to \(1 + * - 1 = *\), Right moves to 0 and wins.
- * If Left moves to \(G - 1\), Right may move to \(* - 2\), after which Left must move to \(-2\), and Right wins.
- \(G + G\) is thus a win for the first player, and therefore a fuzzy game.
- Yes (such games exist). A simple example is \(G = \{1\mathop|* \mathop- 1\}\).
- If Left goes first in \(G + G\), their only move is to \(G + 1\), after which Right's only move is to \(* \mathop- 1 + 1 = *\), after which Left moves to 0 and wins.
- If Right goes first in \(G + G\), their only move is to \(G + * - 1\). Left has two options: play in \(G\) or in \(*\).
- * If Left moves to \(1 + * - 1 = *\), Right moves to 0 and wins.
- * If Left moves to \(G - 1\), Right may move to \(* - 2\), after which Left must move to \(-2\), and Right wins.
- \(G + G\) is thus a win for the first player, and therefore a fuzzy game.
#1: Initial revision
by
r~~
·
2026-05-07T18:05:07Z (4 months ago)
Yes. A simple example is \(G = \{1\mathop|* \mathop- 1\}\).
If Left goes first in \(G + G\), their only move is to \(G + 1\), after which Right's only move is to \(* \mathop- 1 + 1 = *\), after which Left moves to 0 and wins.
If Right goes first in \(G + G\), their only move is to \(G + * - 1\). Left has two options: play in \(G\) or in \(*\).
* If Left moves to \(1 + * - 1 = *\), Right moves to 0 and wins.
* If Left moves to \(G - 1\), Right may move to \(* - 2\), after which Left must move to \(-2\), and Right wins.
\(G + G\) is thus a win for the first player, and therefore a fuzzy game.