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		<id>https://www.hexwiki.net/index.php?action=history&amp;feed=atom&amp;title=Passing</id>
		<title>Passing - Revision history</title>
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		<updated>2026-04-15T02:22:17Z</updated>
		<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://www.hexwiki.net/index.php?title=Passing&amp;diff=8621&amp;oldid=prev</id>
		<title>Selinger: /* Implementations of passing */ SGF now permits passing</title>
		<link rel="alternate" type="text/html" href="https://www.hexwiki.net/index.php?title=Passing&amp;diff=8621&amp;oldid=prev"/>
				<updated>2024-07-30T10:09:42Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Implementations of passing: &lt;/span&gt; SGF now permits passing&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 10:09, 30 July 2024&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 41:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 41:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Most online playing sites do not currently permit passing. However, this ought to be changed. [[Board Game Arena]] allows passing in Hex since release 211104-1253 (November 2021).&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Most online playing sites do not currently permit passing. However, this ought to be changed. [[Board Game Arena]] allows passing in Hex since release 211104-1253 (November 2021).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;for Hex does not provide for &lt;/del&gt;a passing move. It &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;does&lt;/del&gt;, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;however, permit &lt;/del&gt;consecutive moves by the same player. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;It would be desirable to add &lt;/del&gt;an explicit passing move to &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;the file format, as this would allow passing moves to be recorded and documented&lt;/del&gt;. For example, a comment &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;attached to such a move &lt;/del&gt;might explain why the player passed (e.g., to give a handicap)&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;. This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no explicit way of passing, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot; before the first player can move again. This is not elegant. A passing move would permit this information to appear in the game tree&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;includes &lt;/ins&gt;a passing move. It &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;was added in December 2021. In addition&lt;/ins&gt;, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;the file format permits &lt;/ins&gt;consecutive moves by the same player. &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;On advantage of having &lt;/ins&gt;an explicit passing move &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;is that comments can be attached &lt;/ins&gt;to &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;such a move&lt;/ins&gt;. For example, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;such &lt;/ins&gt;a comment might explain why the player passed (e.g., to give a handicap).&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: Definition]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: Definition]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: Theory]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: Theory]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: Rules and Conventions]]&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;[[category: Rules and Conventions]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Selinger</name></author>	</entry>

	<entry>
		<id>https://www.hexwiki.net/index.php?title=Passing&amp;diff=7566&amp;oldid=prev</id>
		<title>Selinger: /* Reasons for passing */ wording</title>
		<link rel="alternate" type="text/html" href="https://www.hexwiki.net/index.php?title=Passing&amp;diff=7566&amp;oldid=prev"/>
				<updated>2021-11-05T21:23:42Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Reasons for passing: &lt;/span&gt; wording&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 21:23, 5 November 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 17:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 17:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Strategy puzzles: many Hex strategy puzzles, such as [http://www.mseymour.ca/hex_puzzle/hexpuzzle.html Matthew Seymour's puzzles], are concerned with a particular area of the board. The object of the puzzle is to make sure that certain groups are [[strong connection|connected]] or not connected. If a player's groups are already connected, moving in that area of the board would waste a move for that player. In a real game, the player might choose to play elsewhere on the board. In a strategy puzzle, the player should be allowed to pass instead. Recognizing situations where one can or cannot pass, or equivalently, recognizing which groups are connected, is an important learning objective of the puzzles.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Strategy puzzles: many Hex strategy puzzles, such as [http://www.mseymour.ca/hex_puzzle/hexpuzzle.html Matthew Seymour's puzzles], are concerned with a particular area of the board. The object of the puzzle is to make sure that certain groups are [[strong connection|connected]] or not connected. If a player's groups are already connected, moving in that area of the board would waste a move for that player. In a real game, the player might choose to play elsewhere on the board. In a strategy puzzle, the player should be allowed to pass instead. Recognizing situations where one can or cannot pass, or equivalently, recognizing which groups are connected, is an important learning objective of the puzzles.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Clearer game record: Even in games where passing is not formally allowed, a player usually has the &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;effective &lt;/del&gt;ability to pass anyway, namely by deliberately making an [[irrelevant move]] (such as playing in a cell that is already captured by that player). Explicitly passing is more informative than deliberately making a bad move.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Clearer game record: Even in games where passing is not formally allowed, a player usually has the ability to &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;effectively &lt;/ins&gt;pass anyway, namely by deliberately making an [[irrelevant move]] (such as playing in a cell that is already captured by that player). Explicitly passing is more informative than deliberately making a bad move.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== The ability to pass does not affect the outcome ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== The ability to pass does not affect the outcome ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Selinger</name></author>	</entry>

	<entry>
		<id>https://www.hexwiki.net/index.php?title=Passing&amp;diff=7563&amp;oldid=prev</id>
		<title>Selinger: Added &quot;clearer game record&quot;</title>
		<link rel="alternate" type="text/html" href="https://www.hexwiki.net/index.php?title=Passing&amp;diff=7563&amp;oldid=prev"/>
				<updated>2021-11-05T13:30:25Z</updated>
		
		<summary type="html">&lt;p&gt;Added &amp;quot;clearer game record&amp;quot;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 13:30, 5 November 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 16:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Strategy puzzles: many Hex strategy puzzles, such as [http://www.mseymour.ca/hex_puzzle/hexpuzzle.html Matthew Seymour's puzzles], are concerned with a particular area of the board. The object of the puzzle is to make sure that certain groups are [[strong connection|connected]] or not connected. If a player's groups are already connected, moving in that area of the board would waste a move for that player. In a real game, the player might choose to play elsewhere on the board. In a strategy puzzle, the player should be allowed to pass instead. Recognizing situations where one can or cannot pass, or equivalently, recognizing which groups are connected, is an important learning objective of the puzzles.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Strategy puzzles: many Hex strategy puzzles, such as [http://www.mseymour.ca/hex_puzzle/hexpuzzle.html Matthew Seymour's puzzles], are concerned with a particular area of the board. The object of the puzzle is to make sure that certain groups are [[strong connection|connected]] or not connected. If a player's groups are already connected, moving in that area of the board would waste a move for that player. In a real game, the player might choose to play elsewhere on the board. In a strategy puzzle, the player should be allowed to pass instead. Recognizing situations where one can or cannot pass, or equivalently, recognizing which groups are connected, is an important learning objective of the puzzles.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* Clearer game record: Even in games where passing is not formally allowed, a player usually has the effective ability to pass anyway, namely by deliberately making an [[irrelevant move]] (such as playing in a cell that is already captured by that player). Explicitly passing is more informative than deliberately making a bad move.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== The ability to pass does not affect the outcome ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== The ability to pass does not affect the outcome ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Selinger</name></author>	</entry>

	<entry>
		<id>https://www.hexwiki.net/index.php?title=Passing&amp;diff=7562&amp;oldid=prev</id>
		<title>Selinger: /* Implementations of passing */ Added that BGA now allows passing.</title>
		<link rel="alternate" type="text/html" href="https://www.hexwiki.net/index.php?title=Passing&amp;diff=7562&amp;oldid=prev"/>
				<updated>2021-11-05T13:22:18Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Implementations of passing: &lt;/span&gt; Added that BGA now allows passing.&lt;/span&gt;&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 13:22, 5 November 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 37:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 37:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Implementations of passing ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Implementations of passing ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;No &lt;/del&gt;online playing sites currently permit passing. However, this ought to be changed.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Most &lt;/ins&gt;online playing sites &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;do not &lt;/ins&gt;currently permit passing. However, this ought to be changed&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. [[Board Game Arena]] allows passing in Hex since release 211104-1253 (November 2021)&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] for Hex does not provide for a passing move. It does, however, permit consecutive moves by the same player. It would be desirable to add an explicit passing move to the file format, as this would allow passing moves to be recorded and documented. For example, a comment attached to such a move might explain why the player passed (e.g., to give a handicap). This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no explicit way of passing, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot; before the first player can move again. This is not elegant. A passing move would permit this information to appear in the game tree.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] for Hex does not provide for a passing move. It does, however, permit consecutive moves by the same player. It would be desirable to add an explicit passing move to the file format, as this would allow passing moves to be recorded and documented. For example, a comment attached to such a move might explain why the player passed (e.g., to give a handicap). This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no explicit way of passing, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot; before the first player can move again. This is not elegant. A passing move would permit this information to appear in the game tree.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Selinger</name></author>	</entry>

	<entry>
		<id>https://www.hexwiki.net/index.php?title=Passing&amp;diff=7220&amp;oldid=prev</id>
		<title>Selinger: Added categories</title>
		<link rel="alternate" type="text/html" href="https://www.hexwiki.net/index.php?title=Passing&amp;diff=7220&amp;oldid=prev"/>
				<updated>2020-12-28T21:30:09Z</updated>
		
		<summary type="html">&lt;p&gt;Added categories&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 21:30, 28 December 2020&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 40:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 40:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] for Hex does not provide for a passing move. It does, however, permit consecutive moves by the same player. It would be desirable to add an explicit passing move to the file format, as this would allow passing moves to be recorded and documented. For example, a comment attached to such a move might explain why the player passed (e.g., to give a handicap). This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no explicit way of passing, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot; before the first player can move again. This is not elegant. A passing move would permit this information to appear in the game tree.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] for Hex does not provide for a passing move. It does, however, permit consecutive moves by the same player. It would be desirable to add an explicit passing move to the file format, as this would allow passing moves to be recorded and documented. For example, a comment attached to such a move might explain why the player passed (e.g., to give a handicap). This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no explicit way of passing, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot; before the first player can move again. This is not elegant. A passing move would permit this information to appear in the game tree.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[category: Definition]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[category: Theory]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[category: Rules and Conventions]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Selinger</name></author>	</entry>

	<entry>
		<id>https://www.hexwiki.net/index.php?title=Passing&amp;diff=6872&amp;oldid=prev</id>
		<title>Selinger: Added proof that the ability to pass does not affect the outcome.</title>
		<link rel="alternate" type="text/html" href="https://www.hexwiki.net/index.php?title=Passing&amp;diff=6872&amp;oldid=prev"/>
				<updated>2020-10-10T21:21:22Z</updated>
		
		<summary type="html">&lt;p&gt;Added proof that the ability to pass does not affect the outcome.&lt;/p&gt;
&lt;table class='diff diff-contentalign-left'&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;col class='diff-marker' /&gt;
				&lt;col class='diff-content' /&gt;
				&lt;tr style='vertical-align: top;'&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan='2' style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Revision as of 21:21, 10 October 2020&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To ''pass'' means not to make a move when it is one's turn to do so. It then becomes the other player's turn again.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;To ''pass'' means not to make a move when it is one's turn to do so. It then becomes the other player's turn again.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The most common formulations of the rules of Hex do not envision passing as a possibility. For example, most [[online playing]] sites do not allow passing. Indeed, &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;it is easy to see that &lt;/del&gt;passing is theoretically unnecessary in Hex: &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;if &lt;/del&gt;passing &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;were allowed, it &lt;/del&gt;is never to a player's advantage to pass. &lt;del class=&quot;diffchange diffchange-inline&quot;&gt; &lt;/del&gt;In other words, playing a piece (no matter which piece) always leaves the player in an equal or better position than passing would do.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;The most common formulations of the rules of Hex do not envision passing as a possibility. For example, most [[online playing]] sites do not allow passing. Indeed, &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;offering the possibility of &lt;/ins&gt;passing is theoretically unnecessary in Hex: &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;since &lt;/ins&gt;passing is never to a player's advantage&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, a rational player in a normal game should never want &lt;/ins&gt;to pass&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;, and therefore the outcome of the game is not affected by whether passing is permitted or not&lt;/ins&gt;. In other words, playing a piece (no matter which piece) always leaves the player in an equal or better position than passing would do&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. Nevertheless, there are a number of good reasons for why the rules of Hex (on game sites or otherwise) should include the ability to pass&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Reasons for passing ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Reasons for passing ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;However, there &lt;/del&gt;are several theoretical and practical uses for passing:&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;There &lt;/ins&gt;are several theoretical and practical uses for passing:&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Theory: many theoretical arguments about winning positions become easier to state and analyze if passing is allowed. For example, the well-known property that Hex (without the swap rule) is a [[Hex theory#No_winning_strategy_for_Blue|first-player win]] is easiest to prove with passing: if the second player had a winning strategy, the first player could simply pass, thereby effectively becoming the second player. Since this would be a winning strategy for the first player, the second player cannot have had a winning strategy.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Theory: many theoretical arguments about winning positions become easier to state and analyze if passing is allowed. For example, the well-known property that Hex (without the swap rule) is a [[Hex theory#No_winning_strategy_for_Blue|first-player win]] is easiest to prove with passing: if the second player had a winning strategy, the first player could simply pass, thereby effectively becoming the second player. Since this would be a winning strategy for the first player, the second player cannot have had a winning strategy&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. More generally, strategy-stealing arguments are often easier to formulate if passing is permitted&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Handicap: for unevenly matched players, the game is often more enjoyable if the more experienced player gives the less experienced player a [[handicap]]. One way of implementing a handicap is for the weaker player to be permitted two or more consecutive moves at the beginning of the game. In practice, the stronger player would do this by passing one or more times at the beginning of the game. However, since many online sites do not permit passing, playing with handicap is difficult on these sites. Players sometimes have to resort to playing deliberately weak moves instead of passing.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Handicap: for unevenly matched players, the game is often more enjoyable if the more experienced player gives the less experienced player a [[handicap]]. One way of implementing a handicap is for the weaker player to be permitted two or more consecutive moves at the beginning of the game. In practice, the stronger player would do this by passing one or more times at the beginning of the game. However, since many online sites do not permit passing, playing with handicap is difficult on these sites. Players sometimes have to resort to playing deliberately weak moves instead of passing.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Strength of win: sometimes a player's position is so strong that they can pull off a win even if the opponent gets two or more moves in a row. In that case, the player may choose to pass as a way of demonstrating the strength of their position to the opponent. In a friendly or teaching game, this can have a pedagogical value by illustrating a point. In a competitive game, it can be a way of making a win more impressive.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Strength of win: sometimes a player's position is so strong that they can pull off a win even if the opponent gets two or more moves in a row. In that case, the player may choose to pass as a way of demonstrating the strength of their position to the opponent. In a friendly or teaching game, this can have a pedagogical value by illustrating a point &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;about the strength of connections&lt;/ins&gt;. In a competitive game, it can be a way of making a win more impressive.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Losing play: once a player realizes that they will lose the game, they would customarily resign. However, sometimes resigning is not possible or desirable for some reason. For example, some game sites do not allow resigning unless a certain percentage of the board has been filled. In that case, the losing player often resorts to playing nonsense moves to allow the winning player to complete a connection as quickly as possible. Passing would be more elegant than playing nonsense moves.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* Losing play: once a player realizes that they will lose the game, they would customarily resign. However, sometimes resigning is not possible or desirable for some reason. For example, some game sites do not allow resigning unless a certain percentage of the board has been filled. In that case, the losing player often resorts to playing nonsense moves to allow the winning player to complete a connection as quickly as possible. Passing would be more elegant than playing nonsense moves.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* Strategy puzzles: many Hex strategy puzzles, such as [http://www.mseymour.ca/hex_puzzle/hexpuzzle.html Matthew Seymour's puzzles], are concerned with a particular area of the board. The object of the puzzle is to make sure that certain groups are [[strong connection|connected]] or not connected. If a player's groups are already connected, moving in that area of the board would waste a move for that player. In a real game, the player might choose to play elsewhere on the board. In a strategy puzzle, the player should be allowed to pass instead. Recognizing situations where one can or cannot pass, or equivalently, recognizing which groups are connected, is an important learning objective of the puzzles.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== The ability to pass does not affect the outcome ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== The ability to pass does not affect the outcome ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;To do&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;In Hex, passing never gives the player who passes an advantage. Specifically:&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;* If a player can win by passing, then the same player can also win by moving anywhere.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;The intuitive reason for this is that, since the objective of Hex is to connect a player's two edges, having additional pieces of that player's color on the board cannot hurt the player.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;More formally, consider Hex without passing. Given two Hex positions P and Q, we say that P ≤ Q if Q is obtained from P by adding zero or more red stones and removing zero or more blue stones. We claim that if Red has a winning strategy for P (with some player to move), then Red also has a winning strategy for Q (with the same player to move). This is easily proved by induction on the number of empty cells in the position P. The base case is when P has no empty cells; since we assumed P is winning for Red, Red's two edges are connected in P, and therefore in Q, so Q is also winning for Red. For the induction step, first consider the case where it is Red's turn. Red's winning strategy calls for playing in some empty cell of the position P to arrive at a new position P' that is a second-player win for Red. If the corresponding cell is empty in Q, then Red can just play there. If the corresponding cell is not empty in Q, then it must be occupied by a red stone (since P ≤ Q). In that case, Red can play anywhere. In either case, Red arrives at a new position Q' that satisfies P' ≤ Q'. Since P' is a second-player win for Red, by induction hypothesis, so is Q', and therefore Q was winning for Red. Second, consider the case where it is Blue's turn. We have assumed that Red has a second-player winning strategory for P, and we must show that Red has a second-player winning strategy for Q. Suppose Blue moves in some empty cell of Q, arriving at a new position Q'. If the corresponding cell in P is empty, imagine that Blue moves there. If the corresponding cell in P is not empty, then it must be occupied by a blue stone (since P ≤ Q). In that case, imagine Blue moves anywhere in P. Let P' be the resulting position. In either case, we have P' ≤ Q'. Since P' is a first-player win for Red, by induction hypothesis, so is Q', and therefore, since Blue's move in Q was arbitrary, Q was a second-player win for Red, as required.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;The above statement, &amp;quot;If a player can win by passing, then the same player can also win by moving anywhere&amp;quot;, now follows. Namely, if it is Red's turn in a position P, then passing would result in the same position P (with Blue to move), and not passing would result in a position Q with one additional red piece (and Blue also to move). Since P ≤ Q, if P is winning then so is Q.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;The analogous result of course also holds from Blue's point of view.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;In particular, any player who has a winning strategy with passing also has a winning strategy without passing that is just as easy to carry out. Therefore, the outcome of the game does not depend on whether passing is permitted or not.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;Many sites seem to take the above fact as a reason why passing 'should not' be allowed. But it is equally valid as a reason for why passing 'should' be allowed&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Implementations of passing ==&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Implementations of passing ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 23:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 39:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* No online playing sites currently permit passing. However, this ought to be changed.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* No online playing sites currently permit passing. However, this ought to be changed.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class='diff-marker'&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] for Hex does not provide for a passing move. It does, however, permit consecutive moves by the same player. It would be desirable to add an explicit passing move to the file format, as this would allow passing moves to be recorded and documented. For example, a comment attached to such a move might explain why the player passed (e.g., to give a handicap). This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;possibility of an &lt;/del&gt;explicit passing &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;move&lt;/del&gt;, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot;&lt;del class=&quot;diffchange diffchange-inline&quot;&gt;, which &lt;/del&gt;is not elegant &lt;del class=&quot;diffchange diffchange-inline&quot;&gt;and will not be recorded &lt;/del&gt;in the game tree.&lt;/div&gt;&lt;/td&gt;&lt;td class='diff-marker'&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;* The current version of the [[Smart Game Format|SGF file format]] for Hex does not provide for a passing move. It does, however, permit consecutive moves by the same player. It would be desirable to add an explicit passing move to the file format, as this would allow passing moves to be recorded and documented. For example, a comment attached to such a move might explain why the player passed (e.g., to give a handicap). This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no explicit &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;way of &lt;/ins&gt;passing, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot; &lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;before the first player can move again. This &lt;/ins&gt;is not elegant&lt;ins class=&quot;diffchange diffchange-inline&quot;&gt;. A passing move would permit this information to appear &lt;/ins&gt;in the game tree.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Selinger</name></author>	</entry>

	<entry>
		<id>https://www.hexwiki.net/index.php?title=Passing&amp;diff=6870&amp;oldid=prev</id>
		<title>Selinger: Added a page on passing.</title>
		<link rel="alternate" type="text/html" href="https://www.hexwiki.net/index.php?title=Passing&amp;diff=6870&amp;oldid=prev"/>
				<updated>2020-10-10T17:43:44Z</updated>
		
		<summary type="html">&lt;p&gt;Added a page on passing.&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;To ''pass'' means not to make a move when it is one's turn to do so. It then becomes the other player's turn again.&lt;br /&gt;
&lt;br /&gt;
The most common formulations of the rules of Hex do not envision passing as a possibility. For example, most [[online playing]] sites do not allow passing. Indeed, it is easy to see that passing is theoretically unnecessary in Hex: if passing were allowed, it is never to a player's advantage to pass.  In other words, playing a piece (no matter which piece) always leaves the player in an equal or better position than passing would do.&lt;br /&gt;
&lt;br /&gt;
== Reasons for passing ==&lt;br /&gt;
&lt;br /&gt;
However, there are several theoretical and practical uses for passing:&lt;br /&gt;
&lt;br /&gt;
* Theory: many theoretical arguments about winning positions become easier to state and analyze if passing is allowed. For example, the well-known property that Hex (without the swap rule) is a [[Hex theory#No_winning_strategy_for_Blue|first-player win]] is easiest to prove with passing: if the second player had a winning strategy, the first player could simply pass, thereby effectively becoming the second player. Since this would be a winning strategy for the first player, the second player cannot have had a winning strategy.&lt;br /&gt;
&lt;br /&gt;
* Handicap: for unevenly matched players, the game is often more enjoyable if the more experienced player gives the less experienced player a [[handicap]]. One way of implementing a handicap is for the weaker player to be permitted two or more consecutive moves at the beginning of the game. In practice, the stronger player would do this by passing one or more times at the beginning of the game. However, since many online sites do not permit passing, playing with handicap is difficult on these sites. Players sometimes have to resort to playing deliberately weak moves instead of passing.&lt;br /&gt;
&lt;br /&gt;
* Strength of win: sometimes a player's position is so strong that they can pull off a win even if the opponent gets two or more moves in a row. In that case, the player may choose to pass as a way of demonstrating the strength of their position to the opponent. In a friendly or teaching game, this can have a pedagogical value by illustrating a point. In a competitive game, it can be a way of making a win more impressive.&lt;br /&gt;
&lt;br /&gt;
* Losing play: once a player realizes that they will lose the game, they would customarily resign. However, sometimes resigning is not possible or desirable for some reason. For example, some game sites do not allow resigning unless a certain percentage of the board has been filled. In that case, the losing player often resorts to playing nonsense moves to allow the winning player to complete a connection as quickly as possible. Passing would be more elegant than playing nonsense moves.&lt;br /&gt;
&lt;br /&gt;
== The ability to pass does not affect the outcome ==&lt;br /&gt;
&lt;br /&gt;
To do.&lt;br /&gt;
&lt;br /&gt;
== Implementations of passing ==&lt;br /&gt;
&lt;br /&gt;
* No online playing sites currently permit passing. However, this ought to be changed.&lt;br /&gt;
&lt;br /&gt;
* The current version of the [[Smart Game Format|SGF file format]] for Hex does not provide for a passing move. It does, however, permit consecutive moves by the same player. It would be desirable to add an explicit passing move to the file format, as this would allow passing moves to be recorded and documented. For example, a comment attached to such a move might explain why the player passed (e.g., to give a handicap). This is not quite the same as simply omitting the move; for example, for some handicapping methods, after the first move, the second player can choose to swap (and then the first player will get two consecutive moves) or not to swap (and then the first player gets to move again). If there is no possibility of an explicit passing move, the second player must verbally announce &amp;quot;I am not going to swap&amp;quot;, which is not elegant and will not be recorded in the game tree.&lt;/div&gt;</summary>
		<author><name>Selinger</name></author>	</entry>

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