[ Help | Earliest Comments | Latest Comments ][ List All Subjects of Discussion | Create New Subject of Discussion ][ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]Comments/Ratings for a Single Item Earlier ⇧Reverse Order⇩ Later Overprotection Chess. If an attacked piece is more often defended than it is attacked, it gains extra powers. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]Peter Aronson wrote on 2002-04-08 UTCExcellent ★★★★★This looks like fun! I particularly like that once you overprotect a Pawn by two (easy enough -- just take an unattacked Pawn and give it two supporters), suddenly it captures forward and to the side. <p> I find myself wondering if overprotection is calculated recursively. That is, when determining overprotection, is overprotection taken into account? <p> Consider the following: <blockquote> White Pawns at <b>a3</b>, <b>b4</b> and <b>c3</b>; <p> Black Pawns at <b>a6</b>, <b>b5</b> and <b>c6</b>. </blockquote> Assume white's move. Can the white Pawn on <b>b4</b> capture the black Pawn on <b>b5</b>? If you apply white's Wazir capture first, then it can (since it is overprotected by two, black not having a Wazir capture as it is only overprotected by one), if you apply black's Wazir capture first, it can not (since then the white Pawn will only be overprotected by one). Curious, no? gnohmon wrote on 2002-04-09 UTCExcellent ★★★★★A Pawn or piece must be attacked in order to be overprotected. I said that, right? 'and dynamic' ... 'where checkmating the opponent could also checkmate you!' means that the enemy K is defended several times (but of course not attacked) so that when you attack the enemy K it becomes overprotected and gives check to your nearby King. I could have made that clearer, right? But you're correct, even the closest reading of this doesn't really say whether it's recursive. Yes, why not recursive, gosh darn it and gosh darn it again? If you could overprotect an unattacked piece, this would 'merely' be a new (and perhaps an excellent) form of Relay Chess. So, should add a line that the powers gained by an overprotected piece can be used to overprotect another piece. Should add a line 'therefore you can destroy your opponent's overprotection by moving your attacker away'. And should add the explanation of how giving check[mate] can check[mate] yourself. Better now? Peter Aronson wrote on 2002-04-09 UTCBusy editorial beavers have made the requested edits to this page, all the while whistling the 'Happy Editor' song. <p> Ok, I read the part about having to be attacked to be overprotected, but somehow it didn't sink in. But there's still a lovely paradox here. <p> Consider: <blockquote> White has Pawns on <b>a3</b>, <b>b4</b> and <b>c3</b>, and a Rook on <b>b1</b>. <p> Black has Pawns on <b>a6</b>, <b>b5</b> and <b>c6</b>, a Rook on <b>b8</b>, and a Bishop on <b>d6</b>. </blockquote> The white Pawn on <b>b4</b> is attacked by one piece, and defended by three, so it can move and capture as a Wazir. Which means it attacks the black Pawn on <b>b5</b>. The black Pawn is then attacked by one, and defended by three, so <em>it</em> can now move and capture like a Wazir. But this reduces the white Pawn on <b>b4</b> from being overprotected by two to being overprotected by one, which means it can no longer capture the black Pawn at <b>b5</b>. But if it can not capture the black Pawn at <b>b5</b>, the black Pawn isn't attacked, and so can't capture the white Pawn which suddenly overprotected by two, which means it <em>can</em> capture the black Pawn. But it can't . . . Tony Paletta wrote on 2002-04-09 UTCApart from the paradox problem, the need to take into account temporary powers makes assessment of overprotection a bit complicated. I would suggest ignoring temporary powers in assessing overprotection. gnohmon wrote on 2002-04-10 UTCExcellent ★★★★★You have trapped me and won the game of game-making! You suggested recursive, and I said 'sure, okay', and then you hoisteded me with me own petard by pointing out a most ingenious paradox, more ingenious than Doctors Einstein and Schweitzer. I am bereft, like an apprentice to Pilate. Where can I find an mp3 of busy editorial beavers whistling the 'Happy Editor' song as they undo a previous change? Peter Aronson wrote on 2002-04-10 UTCShall we go with Tony Paletta's suggestion, and avoid all temporary powers when calculating overprotection? It does make it simpler, and importantly improves clarity. gnohmon wrote on 2002-04-10 UTCYes, I'm afraid that recursion (drat and drat again) must be explicitly forbidden, which is too bad because it sounded like fun. Peter Aronson wrote on 2002-04-10 UTCChanges made as best I understood. <p> Alas, the Happy Editor song can never be written down or recorded, lest the secret society of web editors silence y 8 comments displayedEarlier ⇧Reverse Order⇩ LaterPermalink to the exact comments currently displayed.