Answers.Body: <p>In tiger hunt you could try to find setups for white in which the tiger can attack nothing and has no possibility to cross the pawn phalanx. Then you only have to show that you can always transform one of these setups into another, with further progressed pawns, without allowing captures or escapes. </p>
  
  <p>These transformations should be calculable by brute force. And if you can actually find these setups and transformations, the tiger will be forced back until it is captured.</p>
  
  <p>The point is of course that you don't really have a complete search tree. You only use a search tree to get from one stable position to another more advanced stable position.</p>
  
  <p>Edit: At first I had proposed a simple solution that unfortunately hinged on pawn promotions, which aren't allowed.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-08-10T06:49:39.083Z
Answers.Text: According to the link for the rules given by Ying Zhou, pawns do not promote. Presumably this is to stop such trivial wins as the one you give.
Answers.UserDisplayName: Brian Towers
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-08-10T07:26:35.733Z
Answers.Text: Ah, true. I managed to miss that although I reread it.
Answers.UserDisplayName: BlindKungFuMaster
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-08-10T12:42:02.113Z
Answers.Text: I have thought about the same. It might start with 1.c3,2.b3,3.d3,4.h3. It seems not as easy as Marahaja and Sepoys which seems to have been solved in this way.
Answers.UserDisplayName: Ying Zhou
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Answers.CreationDate: 2015-08-10T05:39:31.003Z
Answers.LastActivityDate: 2015-08-10T11:04:19.437Z
Answers.LastEditDate: 2015-08-10T11:04:19.437Z
Answers.UserDisplayName: BlindKungFuMaster
Answers.Body: <p>Even without a computer one can prove that
  "<strong>Tiger Hunt</strong>" (a.k.a. Maharajah Chess) is a forced win.
  Certainly the "tiger" can't hope for more than a draw
  if White starts with 1 Na3 and then repeats with say
  Nf3-g1-f3-... ad infinitum.  But in fact the "tiger"
  can be gradually corralled as <strong>BlindKungFuMaster</strong> suggests;
  for instance:</p>
  
  <pre><code>[Title "Tiger Hunt"]
  [fen "4q3/8/8/8/8/8/PPPPPPPP/RNB1KBNR w - - 0 0"]
  
  1.Na3 null
  2.c3 null
  3.d3 null
  4.Nf3 null
  5.g3 null
  6.Bg2 null
  7.h3 null
  8.Rh2 null
  9.Nd2 null
  10.Ndc4 null
  11.Be3 null
  12.Bd4 null
  13.b3 null
  14.Nc2 null
  15.Nb4 null
  16.Nd5 null
  17.Nf4 null
  18.Bd5 null
  19.Rg2 null
  20.f3 null
  21.h4 null
  22.Kd2 null
  23.Kc2 null
  24.a3 null
  25.a4 null
  26.e3 null
  27.e4 null
  28.Re1 null
  29.Re3 null
  30.Be5 null
  31.Ne6 null
  32.Rge2 null
  33.d4 null
  34.Nd6 null
  35.Kd2 null
  36.Re1 null
  37.Rh1 null
  38.g4 null
  39.h5 null
  40.g5 null
  41.f4 null
  42.h6 null
  43.f5 null
  44.g6 null
  45.h7 null
  46.Ree1 null
  47.Ra1 null
  48.b4 null
  49.a5 null
  50.b5 null
  51.c4 null
  52.a6 null
  53.c5 null
  54.b6 null
  55.a7 Qe7
  </code></pre>
  
  <p>The tiger is now limited to the squares d7 and e7.  White can now finish
  immediately by Zugzwang (56 f6 or 56 c6 respectively) or continue in
  the same fashion:</p>
  
  <pre><code>[Title "Tiger suffocates"]
  [fen "8/P3q2P/1P1NN1P1/2PBBP2/3PP3/8/3K4/R6R w - - 0 55"]
  
  1.Ra6 null
  2.c6 null
  3.Rh6 null
  4.f6
  </code></pre>
  
  <p>and the tiger is completely out of squares (NB there are no legal moves from
  d7/e7 to a8 or h8), <strong>QEF</strong>.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-12-08T20:44:47.397Z
Answers.Text: You're welcome :-)  I see that a few steps can be done more quickly
  (e.g. Bf4-e5 instead of Be3-d4-e5), though I deliberately avoided pawn
  double-moves in case the rules change to remove them.
  If win by stalemate is not allowed then we can end with
  56 Kc3, 57 Kb4, 58 Ra6, 59 b7, 60 Rc6, 61 Rc7#.
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-12-08T20:50:34.347Z
Answers.Text: I suppose the path I chose is seasonally appropriate because 
  the final position is reminiscent of a Hanukkah menorah!
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-12-09T14:58:26.933Z
Answers.Text: Happy Hanukkah! In the original definition of Tiger Hunt chess we also have the white tiger version (i.e. you can consider it using the same board, just white does a null move first.) Does (some variant of) your proof also work in this case, may I ask? By the way I really like your detailed solution, Professor Elkies..though I can not accept it as the correct answer because we have the other two variants in the problem whose solutions should be encouraged..
Answers.UserDisplayName: Ying Zhou
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-12-09T15:32:44.543Z
Answers.Text: 1) Thanks for the Hanukkah wishes! 2) Yes it works; the tiger can start anywhere as long as it doesn't attack c2 (or c7 with colors reversed) - after Na3 (or Na6) everything's defended, and stays defended (or unattackable) for the rest of the long sequence.  3) Do you really expect somebody to solve all three games in one answer? . . .
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-12-09T15:34:43.923Z
Answers.Text: Thanks..I will put the fact that it is solved on my blog: https://categoriesandfelines.wordpress.com/2015/12/08/game-solving-professor-noam-elkies-has-solved-tiger-hunt-chess/
Answers.UserDisplayName: Ying Zhou
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2015-12-08T05:08:31.380Z
Answers.LastActivityDate: 2015-12-08T05:08:31.380Z
Answers.UserDisplayName: Noam D. Elkies
Body: <p><a href="https://www.chessvariants.com/unequal.dir/tigerhnt.html" rel="nofollow noreferrer">Tiger Hunt</a> is a chess variant where an entire army without a queen fight against a royal amazon (tiger, queen+knight). I believe it is certainly a win for the army just like Marahaja and Sepoys. I also believe this can easily be solved. Perhaps we can modify stockfish code to do so..</p>
  <p><a href="http://www.chessvariants.org/boardrules.dir/atlantis.html" rel="nofollow noreferrer">Atlantis Chess</a> is a variant where one can sink an empty space on the edge of the board (which changes as more spaces are sunk) as a legitimate move which is intuitively a draw simply because both sides can sink the board to protect their own king since nothing moves across sunk spaces. Putting the king in absolute safety requires at least 14 steps. I believe it is easily solvable. If we can generate all moves up to depth 40 or 50, I believe it can be solved since most attempts to disrupt the 14 steps involve bad piece trades or sacrifices.</p>
  <p>I have also been looking at a variant called <a href="http://www.chessvariants.org/large.dir/peasantrevolt.html" rel="nofollow noreferrer">Peasants' Revolt Chess</a> for a while. I strongly believe that the original four knights form is a black victory based on results of Stockfish, even as the author of the variant believes it to be biased towards black. A search depth of 80 may be required based on what I have done, also a tablebase of K3N against K+several pawns will be very helpful and can reduce search depths by at least 20.</p>
  <p>In addition, I believe the three knights form might also be a black victory based on what Stockfish tells me. But this time search depth may have to be 110 or more.</p>
  <p>So how do we weakly solve these chess variants? Any strategy?</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-08-10T07:30:50.913Z
Comments.Text: +1 for such a creative question. Do we know the approx complexity for those variants? If we know the numbers, maybe we can compare with checkers which have already been solved.
Comments.UserDisplayName: SmallChess
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-08-10T14:11:15.470Z
Comments.Text: Atlantis Chess is interesting in a mathematical sense only because practically we see easily that it is a draw. Statistically most random moves from the other side can not stop the 14 steps to safety (also there can be two less spaces sunk if you have eliminated knights from the other side). So if we generate random steps from one side to counter the other which is determined to put the king to a corner and sink all spaces around him. I believe the game will not exceed ply 50.
Comments.UserDisplayName: Ying Zhou
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-08-10T14:14:13.110Z
Comments.Text: For tiger hunt it may not be as easy as it seems (see the answer below). If white is the tiger side I do not believe restricting where the tiger can be (i.e. deformation) works since you might need to choose what you do after 1.Tc1 c6 based on what 2. is about, though I believe theoretically the tiger is lost. Perhaps an engine is necessary. In order to move all pawns to row 7 we need 40 steps at least, though I believe in reality we may need even more.
Comments.UserDisplayName: Ying Zhou
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2015-08-10T14:19:30.397Z
Comments.Text: Peasants' Revolt might be the most interesting among the three variants. We need to first start from the 4 knights version. Generating all K3N vs K+some P and K2N vs K+some P tablebases will be helpful, if not outright necessary. The game is likely to be long.
  
  I used stockfish to do both 4 knights and 3 knights versions. In 4 knights version it ends before 40 and in 3 knights version it went before 60. But note that the last 15 steps can be removed because up to that point the knights have already won but just need to finish the checkmate.
Comments.UserDisplayName: Ying Zhou
Tags: <chess-variants><solving>
Title: How to weakly solve Tiger Hunt, Atlantis Chess and Peasants' Revolt
ThreadText: # How to weakly solve Tiger Hunt, Atlantis Chess and Peasants' Revolt
  
  (Asked by: username_0 on 2015-08-09)
  
  [Tiger Hunt](https://www.chessvariants.com/unequal.dir/tigerhnt.html) is a chess variant where an entire army without a queen fight against a royal amazon (tiger, queen+knight). I believe it is certainly a win for the army just like Marahaja and Sepoys. I also believe this can easily be solved. Perhaps we can modify stockfish code to do so..
  
  [Atlantis Chess](http://www.chessvariants.org/boardrules.dir/atlantis.html) is a variant where one can sink an empty space on the edge of the board (which changes as more spaces are sunk) as a legitimate move which is intuitively a draw simply because both sides can sink the board to protect their own king since nothing moves across sunk spaces. Putting the king in absolute safety requires at least 14 steps. I believe it is easily solvable. If we can generate all moves up to depth 40 or 50, I believe it can be solved since most attempts to disrupt the 14 steps involve bad piece trades or sacrifices.
  
  I have also been looking at a variant called [Peasants' Revolt Chess](http://www.chessvariants.org/large.dir/peasantrevolt.html) for a while. I strongly believe that the original four knights form is a black victory based on results of Stockfish, even as the author of the variant believes it to be biased towards black. A search depth of 80 may be required based on what I have done, also a tablebase of K3N against K+several pawns will be very helpful and can reduce search depths by at least 20.
  
  In addition, I believe the three knights form might also be a black victory based on what Stockfish tells me. But this time search depth may have to be 110 or more.
  
  So how do we weakly solve these chess variants? Any strategy?
  
  **Tags:** chess-variants, solving
  
  > **Comments:**
  > **username_1**: +1 for such a creative question. Do we know the approx complexity for those variants? If we know the numbers, maybe we can compare with checkers which have already been solved.  
  > **username_0**: Atlantis Chess is interesting in a mathematical sense only because practically we see easily that it is a draw. Statistically most random moves from the other side can not stop the 14 steps to safety (also there can be two less spaces sunk if you have eliminated knights from the other side). So if we generate random steps from one side to counter the other which is determined to put the king to a corner and sink all spaces around him. I believe the game will not exceed ply 50.  
  > **username_0**: For tiger hunt it may not be as easy as it seems (see the answer below). If white is the tiger side I do not believe restricting where the tiger can be (i.e. deformation) works since you might need to choose what you do after 1.Tc1 c6 based on what 2. is about, though I believe theoretically the tiger is lost. Perhaps an engine is necessary. In order to move all pawns to row 7 we need 40 steps at least, though I believe in reality we may need even more.  
  > **username_0**: Peasants' Revolt might be the most interesting among the three variants. We need to first start from the 4 knights version. Generating all K3N vs K+some P and K2N vs K+some P tablebases will be helpful, if not outright necessary. The game is likely to be long.  I used stockfish to do both 4 knights and 3 knights versions. In 4 knights version it ends before 40 and in 3 knights version it went before 60. But note that the last 15 steps can be removed because up to that point the knights have already won but just need to finish the checkmate.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_4 on 2015-12-08. Score: 8 | Accepted answer
  
  Even without a computer one can prove that
  "Tiger Hunt" (a.k.a. Maharajah Chess) is a forced win.
  Certainly the "tiger" can't hope for more than a draw
  if White starts with 1 Na3 and then repeats with say
  Nf3-g1-f3-... ad infinitum.  But in fact the "tiger"
  can be gradually corralled as username_2 suggests;
  for instance:
  [Title "Tiger Hunt"]
  [fen "4q3/8/8/8/8/8/PPPPPPPP/RNB1KBNR w - - 0 0"]
  
  1.Na3 null
  2.c3 null
  3.d3 null
  4.Nf3 null
  5.g3 null
  6.Bg2 null
  7.h3 null
  8.Rh2 null
  9.Nd2 null
  10.Ndc4 null
  11.Be3 null
  12.Bd4 null
  13.b3 null
  14.Nc2 null
  15.Nb4 null
  16.Nd5 null
  17.Nf4 null
  18.Bd5 null
  19.Rg2 null
  20.f3 null
  21.h4 null
  22.Kd2 null
  23.Kc2 null
  24.a3 null
  25.a4 null
  26.e3 null
  27.e4 null
  28.Re1 null
  29.Re3 null
  30.Be5 null
  31.Ne6 null
  32.Rge2 null
  33.d4 null
  34.Nd6 null
  35.Kd2 null
  36.Re1 null
  37.Rh1 null
  38.g4 null
  39.h5 null
  40.g5 null
  41.f4 null
  42.h6 null
  43.f5 null
  44.g6 null
  45.h7 null
  46.Ree1 null
  47.Ra1 null
  48.b4 null
  49.a5 null
  50.b5 null
  51.c4 null
  52.a6 null
  53.c5 null
  54.b6 null
  55.a7 Qe7
  
  The tiger is now limited to the squares d7 and e7.  White can now finish
  immediately by Zugzwang (56 f6 or 56 c6 respectively) or continue in
  the same fashion:
  [Title "Tiger suffocates"]
  [fen "8/P3q2P/1P1NN1P1/2PBBP2/3PP3/8/3K4/R6R w - - 0 55"]
  
  1.Ra6 null
  2.c6 null
  3.Rh6 null
  4.f6
  
  and the tiger is completely out of squares (NB there are no legal moves from
  d7/e7 to a8 or h8), QEF.
  
  > **Comments:**
  > **username_4**: You're welcome :-)  I see that a few steps can be done more quickly (e.g. Bf4-e5 instead of Be3-d4-e5), though I deliberately avoided pawn double-moves in case the rules change to remove them. If win by stalemate is not allowed then we can end with 56 Kc3, 57 Kb4, 58 Ra6, 59 b7, 60 Rc6, 61 Rc7#.  
  > **username_4**: I suppose the path I chose is seasonally appropriate because  the final position is reminiscent of a Hanukkah menorah!  
  > **username_0**: Happy Hanukkah! In the original definition of Tiger Hunt chess we also have the white tiger version (i.e. you can consider it using the same board, just white does a null move first.) Does (some variant of) your proof also work in this case, may I ask? By the way I really like your detailed solution, Professor Elkies..though I can not accept it as the correct answer because we have the other two variants in the problem whose solutions should be encouraged..  
  > **username_4**: 1) Thanks for the Hanukkah wishes! 2) Yes it works; the tiger can start anywhere as long as it doesn't attack c2 (or c7 with colors reversed) - after Na3 (or Na6) everything's defended, and stays defended (or unattackable) for the rest of the long sequence.  3) Do you really expect somebody to solve all three games in one answer? . . .  
  > **username_0**: Thanks..I will put the fact that it is solved on my blog: https://categoriesandfelines.wordpress.com/2015/12/08/game-solving-professor-noam-elkies-has-solved-tiger-hunt-chess/  
  
  ---
  
  ### Answer by username_2 on 2015-08-10. Score: 2
  
  In tiger hunt you could try to find setups for white in which the tiger can attack nothing and has no possibility to cross the pawn phalanx. Then you only have to show that you can always transform one of these setups into another, with further progressed pawns, without allowing captures or escapes.
  
  These transformations should be calculable by brute force. And if you can actually find these setups and transformations, the tiger will be forced back until it is captured.
  
  The point is of course that you don't really have a complete search tree. You only use a search tree to get from one stable position to another more advanced stable position.
  
  Edit: At first I had proposed a simple solution that unfortunately hinged on pawn promotions, which aren't allowed.
  
  > **Comments:**
  > **username_3**: According to the link for the rules given by username_0, pawns do not promote. Presumably this is to stop such trivial wins as the one you give.  
  > **username_2**: Ah, true. I managed to miss that although I reread it.  
  > **username_0**: I have thought about the same. It might start with 1.c3,2.b3,3.d3,4.h3. It seems not as easy as Marahaja and Sepoys which seems to have been solved in this way.  
  
  ---
  
  