3045: AlphaMove

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AlphaMove
It struggles a little with complex positions, like when there are an even number of moves and it has to round down, but when run against itself it's capable of finding some novelties. At one point I saw six knights on the board at once; Stockfish rarely exceeds four.
Title text: It struggles a little with complex positions, like when there are an even number of moves and it has to round down, but when run against itself it's capable of finding some novelties. At one point I saw six knights on the board at once; Stockfish rarely exceeds four.

Explanation

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Created by THE SEVENTH KNIGHT, WAITING IN ANTICIPATION FOR THE BETA RELEASE. Do NOT delete this tag too soon. If you can address this issue, please edit the page!

This comic shows a new chess engine, presumably created by Randall, which takes a list of all legal moves (in algebraic notation) in alphabetical order and chooses the median.

A playable implementation of this game can be found here: AlphaMove.

Algebraic notation begins with a symbol for which piece is being moved, which is always the first letter of the piece name, with the exception of knights (N) and pawns (nothing). This is then followed by the square that the piece is being moved to. For example, 'Rc4' would indicate a move that moved a rook to c4. Other symbols include a lowercase x before the destination, indicating that the move is a capture; a plus sign (+) after the destination, indicating that the move places the opposing king in check; and a hash sign (#) after the destination, indicating that the move places the opposing king in checkmate, thus winning the game. There are also O-O and O-O-O notations, which indicate that a player is castling kingside or queenside, respectively.

In practice, this algorithm runs into a few issues. As seen in the comic, the algorithm rarely moves bishops and rooks due to their relative lack of moves in the early game, and their tendency to inhabit the edges of any list when they do have sortable moves. Among basic moves, only pawns destined to move in the first two files of a board can ever sort higher than bishops, and nothing other than another rook can be closer to the far end than a rook. The algorithm favors knight and king moves, with entries starting with the most alphabetically middling "K" and "N" list entries, and (to a lesser extent) pawns destined to move up the right side of the board, the "h"-file pawn generally having the greatest statistical chance. Castling moves would also occur near the middle of the list, as they are denoted with letter 'O' characters as O-O or O-O-O. The shortcomings of AlphaMove are instantly apparent from looking at the game board presented in the comic; roughly ten moves into the game, White has lost three pawns, captured nothing, and advanced their king into the open rather than developing any pieces, while Black (presumably being played by a 'stronger' conventional chess engine) has taken control of the center with a knight and two pawns, developed a bishop, and advanced their queen to f2.

The actual middle of the list might vary away from the usual alphabetic median if the moves (and the pieces removed by the opponent) are heavily biased to a particular subset of player-pieces. It is conceivable that an opponent could identify the AlphaMove strategy as being used, and then use their foreknowledge of the algorithm's 'developing game' to strategically make (normally non-optimal) moves designed explicitly to force the algorithm down their own choice of path, such as targeting undefended rooks and queens (either capturing them with impunity, or just strategically restricting their movements by moving into contact with them in a way that would normally be a suicidal sacrifice), in order to make certain other pieces take moves more advantageous to the opponent. However, given the established failings of uncritically sticking to the algorithmic plan, it is probably vastly more effort to precisely engineer a given game-state than to merely play properly and respond with half-decent responses to the overwhelmingly sub-optimal series of moves generated by AlphaMove. For example, setting Stockfish (Black) against AlphaMove (White) results in the following fifteen-move victory for black:

  1. f3 e5
  2. e4 Bc5
  3. d4 Bxd4
  4. f4 d5
  5. g4 Qh4+
  6. Ke2 Qf2+
  7. Kd3 dxe4+
  8. Kxe4 Nf6+
  9. Kd3 e4+
  10. Kc4 Be6+
  11. Kb5 a6+
  12. Ka5 Bc3+
  13. Ka4 b5+
  14. Ka3 Qc5+
  15. b4 Qxb4#

On the other hand, a person playing black who knew that white was using AlphaMove could win in six moves (possibly fewer):

  1. f3 e5
  2. e4 Qh4+
  3. Ke2 b6
  4. g3 Ba6+
  5. Ke1 Qh3
  6. c3 Qxf1#

However, chess tournaments do not award more points for quicker victories, and playing like this would be risky. If White initially uses AlphaMove and Black goes for the six-move checkmate, White could capture Black's undefended queen on move five, revealing the AlphaMove emulation to just be a ruse to get Black to expose a queen. White would then be in a winning position after 5. Bxh3 or 5. Nxh3 and could play smartly for the rest of the game and would likely win, so opting for the fifteen-move mate would likely be safer. Indeed, playing Stockfish against itself after 5. Nxh3 yields the following 41-move win for white:

  1. f3 e5
  2. e4 Qh4+
  3. Ke2 b6
  4. g3 Ba6+
  5. Ke1 Qh3
  6. Nxh3 c5
  7. f4 Bb7
  8. Nc3 Nc6
  9. d3 Be7
  10. Nb5 Rd8
  11. Nc7+ Kf8
  12. Bg2 d6
  13. Kf2 Nf6
  14. Rf1 exf4
  15. Nxf4 Rc8
  16. Ncd5 Ne5
  17. Nxf6 Bxf6
  18. Kg1 h6
  19. c3 Rd8
  20. d4 cxd4
  21. cxd4 Nd7
  22. Be3 Kg8
  23. h4 Kh7
  24. Nh5 Rhg8
  25. Qf3 Ba6
  26. Rfc1 Kh8
  27. Bh3 Bd3
  28. Bxd7 Bxh4
  29. Qxf7 Bxe4
  30. gxh4 Rdf8
  31. Qe7 Bg6
  32. Rc7 Rf7
  33. Nf4 Rxe7
  34. Nxg6+ Kh7
  35. Nxe7 Rf8
  36. Rf1 Rb8
  37. Rf7 Kh8
  38. Be6 Kh7
  39. Bf5+ Kh8
  40. Ng6+ Kh7
  41. Rxg7#

(While White technically does let Black capture White's undefended queen on move 34, this is not the same as what Black did on move 5 because after 34. … Rxe7, the rook doing the capturing has moved into a position where 35. Nxg6+ forks it and Black's king while capturing a bishop. This allows White to recoup eight points in the following two moves, which represents a greater proportion of Black's remaining firepower than the nine points that White just lost. Indeed, with Black having only one piece (besides the king) left to help with defense, White can force checkmate in six moves. Thus, the AlphaMove ruse, where White pretends to use AlphaMove in order to trick Black into hanging the black queen, can be advantageous for White if Black falls for it. However, even after 1. f3 e5 2. e4, White has a weakened kingside early in the game and has not been the most productive at allowing for future development, so Black should focus on development (e.g., 2. … Nc6 or 2. … Bc5) and use the advantage that Black already has instead of risking falling into a trap. (Of course, the AlphaMove ruse would only have any chance of working if the opponent reads xkcd, which is another reason to not try it.)

Even if AlphaMove ever found one or more of its potential moves to be one that happens to result in checkmate, it has no reason to do anything other than choose its "mid-list move", as described, and the chances are high that such a mate would never be invoked. Along those lines, Qa4+ is a relatively safe move to create a short-term check, to put immediate pressure upon the Black king, and potentially a longer term inconvenience with 'only' a predictable response preventing it from developing into a mate. But it is not in the right list position to attempt, never mind whether it would then be correctly followed up.

This engine may be named for and inspired by the real chess engine AlphaZero, or AlphaGo which plays a different game but has a more similar name. Another real name, mentioned in the title text, is Stockfish, a widely used (and powerful) chess engine.

On this board, Black can win the game instantly with ...Bb4#. Rather than do anything to defend against this, White just moves an unrelated piece, almost certainly losing immediately afterward. Randall has also chosen a setup where the king is placed in a position where it cannot make any legal moves, thus removing it from the list of pieces that can perform any moves. Almost certainly this was a choice, both to make the list without king moves and also to make it pretty easy to see how one more move would be checkmate.

The title of the comic is a play on words. As the name of the chess engine, it refers to the strategy of choosing moves based on alphabetical ordering, while in popular usage, an "alpha move" is an action that would assert dominance over someone else. This makes it an ironic name for the chess engine; rather than asserting dominance, it loses quickly.

The title text mentions games with "six knights", which implies that two pawns have been promoted to knights. Pawns can promote to bishop, knight, queen or rook, so the middle of this list is tied between knight and queen. It is rare that a pawn is promoted to a knight; in most situations a queen would be preferred. The exceptions (perhaps where promoting to queen would cause either an immediate stalemate from what was a winnable position, or let the king survive on a square that's a knight's move away from the newly-promoted queen) are common in contrived chess puzzles but rare in actual gameplay. Promotion to rook or bishop would be even rarer, as these pieces have fewer move possibilities than a queen without the alternative moves of the knight. It would probably be due to a 'forced' promotion, in lieu of moving a more vital piece currently perfectly positioned for the endgame, and the player concerned should be perfectly aware of they must or must not promote to, ahead of time. However, when AlphaMove plays itself, the pawns tend to preferentially move up (and down) the right-hand side of the board, and may meet each other in double-files, or more, possibly with the opportunity to cross over to capture an opponent. If the alphabetical balance of moves becomes such that multiple right-hand files of pawns are dodging past each other, it is not unrealistic that multiple pawns would reach the respective back ranks and 'choose' to promote to knights.

Chess is a recurring theme on xkcd, with another recent example being 3036: Chess Zoo.

Transcript

[A standard chessboard is shown with Black at the top. The boards "black squares" are light gray. Black (which is drawn as dark gray) has made moves resulting in Qf2, Nd4, e4, a5, Bc5, e5 and Ne7 while other black pieces are in starting positions. White has made moves resulting in c4, f4, h4, Kc3, Ne2 and three white pawns are removed from the board while other white pieces including a- and b-pawns are in starting positions. Two squares associated with white's move Ne2 are highlighted in yellow, it has moved there from its starting position g1.]
[To the right of the chess board is a vertical list of possible moves listed in alphabetical order. The text is in light gray, except the move Ne2 in the middle which is black and highlighted in yellow. Two light gray double arrows with a line at the end of each arrow head goes from the top to just above the yellow move, and from just below this to the bottom. A short but thick black arrow points in between the space between the two gray arrows pointing at the yellow move.]
a3
a4
b3
b4
Bd2
Bd3
Be2
Be3
Bg2
Bh3
f5
fxe5
h5
Na3
Nd2
Ne2
Nf3
Nh3
Qa4+
Qb3
Qc2
Qd2
Qd3
Qe1
Qe2
Qf3
Qg4
Qh5
Qxd4
Rh2
Rh3
[Caption below the panel:]
My new AlphaMove chess engine, which sorts the list of legal moves alphabetically and picks the middle one, was quickly defeated by stronger engines.


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Discussion

Ask Tom Murphy VII to get on this 141.101.99.103 22:50, 31 January 2025 (UTC)

This has actually been done and tested against other strange algorithms: https://youtu.be/DpXy041BIlA?t=729

I have attempted to run the proposed bot against itself — if I haven't made any errors, here are the resulting games:

Rounding down:

 1. e4 e6 2. f3 f5 3. e5 g5 4. d4 d5 5. exd6 g4 6. d7+ Kf7 7. dxc8=N Ke8 8. fxg4 h6 9. gxf5 Kd7 10. g4 h5 11. fxe6+ Ke8 12. g5 Na6 13. h3 Nc5 14. h4 Ne7 15. Kd2 Ne4+ 16. Ke1 Nf5 17. g6 Nf6 18. g7 Ng3 19. gxf8=N Nge4 20. Ke2 Ng4 21. Kf3 Ngf2 22. Ke2 Nh3 23. Ke3 Nhf2 24. Nb6 Nh3 25. Na4 Nhf2 26. Nac3 Nxc3 27. Kxf2 Nxd1+ 28. Kf3 Qc8 29. c4 Ne3 30. Ke4 Nf5 31. Kd3 Ng3 32. e7 Nxh1 33. Kc2 Qb8 34. d5 Kxe7 35. d6+ Kf6 36. dxc7 Nf2 37. c8=R Ng4 38. Kd2 Nh2 39. Ke3 Ng4+ 40. Kd4 Nh2 41. Kd5 Nxf1 42. Nc3 Nh2 43. Nce2 Ng4 44. Nd4 Nh6 45. Nd7+ Kf7 46. Ndf3 Qd6+ 47. Ke4 Qd2 48. Nf8 Qd5+ 49. Ke3 Qd2+ 50. Ke4 Qd5+ 51. Ke3 Qd2+ 52. Ke4

Rounding up:

 1. f3 f5 2. e4 f4 3. d4 e6 4. e5 g6 5. g3 fxg3 6. c3 g2 7. d5 gxf1=Q+ 8. Kxf1 exd5 9. Ke2 d6 10. Kd3 g5 11. Kd2 dxe5 12. Ke2 d4 13. Kd3 dxc3+ 14. Ke3 e4 15. Ne2 exf3 16. Ng1 f2 17. Nxc3 fxg1=N 18. Qc2 Kd7 19. Ne2 h6 20. Qa4+ Ke6 21. Qb3+ Ke7 22. Qb4+ Ke8 23. Qb5+ Kf7 24. Qa6 Kg7 25. Qa4 Kg6 26. Qb3 Kg7 27. Qb4 Kh7 28. Qb5 Kg7 29. Qa6 Nc6 30. Nxg1 Na5 31. Qb6 Kh7 32. Qb3 Kg6 33. Qb4 Kg7 34. Qb6 Kh7 35. Qb3 Kg6 36. Qb4 Kg7 37. Qb6

Rounding down code:

 const { Chess } = require("chess.js");
 
 const chess = new Chess();
 while (!chess.isGameOver()) {
   const moves = chess.moves();
   moves.sort((a, b) => b.localeCompare(a));
   const move = moves[Math.floor(moves.length / 2)];
   chess.move(move);
 }
 console.log(chess.pgn());

To round up, swap the a and b in the sort function.

Both games end in a threefold repetition draw. The game with rounding down does, in fact, have 6 knights in it, so I believe he did code this to see what would happen.

Ohpointfive (talk) 22:52, 31 January 2025 (UTC)

To elaborate on the Tom VII point - this is the YouTube video that possibly inspired the comic: https://www.youtube.com/watch?v=DpXy041BIlA 141.101.98.179 22:55, 31 January 2025 (UTC)

Specifically, it's the Arithmetic Player at 24:43 set to ½. ChaoticNeutralCzech (talk) 17:52, 1 February 2025 (UTC)

Unfortunately for white, it's mate in 1 with Bb4# 162.158.90.124 23:25, 31 January 2025 (UTC)

Even if white makes a different move, its still forced mate in one. RIP XKCD Bot. Redacted II (talk) 00:53, 1 February 2025 (UTC)

Well, for most options. Queen to a4 puts Black in check, forestalling an immediate move to mate White; capturing the knight de-threatens enough squares around the king that Black can't check next turn without leaving an escape route. 172.70.176.28 17:45, 1 February 2025 (UTC)

Although it wouldn't change the outcome much (either by changing black's move or white's general options), I'm currently not understanding why Kd4 isn't on the list of options at this point in time. So long since I played serious(ish) chess, and the only reason I could think of is that it's probibited by some strict ortbodox game rule recognising the potential moving of the knight out of the way (in the next white move-cycle). But I'd have treated that later option as forbidden, as a revealing-mate. But, as I said, it's been a while, so maybe I'm just blind to something like a sweeping bishop-range that disbars this (much as the near knight, bishop and pawn disbars four out of the five moves). ...darn, it's just clicked. That's the AlphaMoved white-knight's destination (before that, the black queen was entirely covering that square, and double-teaming one of the adjacent black-knight covered squares), I'd been thinking that was the piece's origin (with the empty highlighted square as its destination) until I'd finally read the highlighted movelist item properly and deciphered it as Knight To King Two (done), not the (intention of) Knight To King's Bishop One. So ignore the above. Although, just to note, for the Black Queen to have even achieved that position would probably have required at least one normally-sacrificial exposure to the deadly white Q/B/R pieces guarding the obvious entry, give or take the algorithmic development of their (and the "gateway pawns"') current positions. 141.101.99.104 02:00, 1 February 2025 (UTC)

Follow-up... As far as the black queen is concerned, I suppose she could have done d6, (x?)g3 then f2, in-between the other black and white moves made, largely safe from the white 'defence'. Or to d4 then f2, if white Queen's Pawn was shielding still. (Appears to have been taken, but it would have been bold to have done that with the queen, for a normally immediate pawn-queen exhange!) A bolder/more opportunistic set of moves than I would have tried, either. Even (unknowingly) against AlphaMove, I'd have been wary of the unconventionally developing white disposition actually being an idiot-trap (and I'm really not that far off being an idiot, insofar as chess). 172.70.162.162 02:17, 1 February 2025 (UTC)

The explanation gives both O-O and 0-0 as notations for castling and then explains why 0-0 can never occur, even though O-O can be sorted pretty centrally. So, which is the correct notation? 172.71.250.91 09:14, 1 February 2025 (UTC)

According to the pgn spec, section 8.2.3.3: they are capital Os and not zeros 172.68.3.96 15:10, 1 February 2025 (UTC)

I'm pretty sure we're looking at a retrograde puzzle. Ohpointfive is onto something here, with the six knights on the board a strong indicator. The question is, of course, where is the joke? White plays Alphamove all along and must have started with e4 (rounding down) or f3 (rounding up). Both are consistent with the end position. So from my point of view, the joke is

  • either that the "stronger engine" is not a strong engine at all but maybe the same algorithm, rounding up instead of down
  • or that black doesn't win this position (in real chess, White is of course toast) because its algorithm is even worse

@Ohpointfive, could you run the two versions against each other? --Pganon (talk) 15:55, 1 February 2025 (UTC)

I created a playable version of this game in like 10 minutes using ChatGPT  ;)

https://enn-nafnlaus.github.io/AlphaMove/alphamove.html

Git page here:

https://github.com/enn-nafnlaus/AlphaMove

-- Rei 17:52, 1 February 2025 (UTC)

I checked, castling and en passant both work. 172.68.245.25 19:26, 1 February 2025 (UTC)

@Pganon certainly: White rounding down vs. black rounding up:

 1. e4 f5 2. f3 f4 3. d4 e6 4. e5 g6 5. d5 exd5 6. g3 fxg3 7. c4 g2 8. h3 gxf1=Q+ 9. Kd2 Kf7 10. Kc3 Ke8 11. Kc2 Kf7 12. Kb3 Ke8 13. Kc2 Kf7 14. Kb3 Ke8 15. Kc2

White rounding up vs. black rounding down:

 1. f3 e6 2. e4 f5 3. e5 g5 4. d4 d5 5. f4 gxf4 6. h3 h5 7. h4 Kd7 8. Kd2 Kc6 9. Kd3 Kb6 10. Ke2 Kb5 11. Ke1+ Kb4 12. Ke2 Kb5 13. Ke1+ Kb4 14. Ke2 Kb5

The first game is quite exciting, with black at one point having a chance at checkmate in one, but alas too many available pawn moves drives the winning move Qxc4# far past the center of the list. The second game is much less exciting.

Ohpointfive (talk) 21:30, 1 February 2025 (UTC)

Here's a question: What is the quickest way to checkmate AlphaMove? Here's the quickest that I have found so far:

  1. f3 d5
  2. e4 d5xe4
  3. f4 e5
  4. g3 Bg4
  5. d4 Qxd4
  6. f5 e3
  7. f6 Qxd1#

Thus, we have mate in seven. This might be good to mention outside the comments section as a demonstration tha AlphaGo is not very good (not to mention failing to attack black's queen with a less valuable piece), but a quicker checkmate might be possible, in which case we should mention that instead.172.70.207.159 11:08, 2 February 2025 (UTC)

Checkmating Alphamove is easy. Getting checkmated *by* Alphamove is challenging. You basically have to forget everything you know about normal chess. -- Rei (talk) 14:48, 2 February 2025 (UTC)
Fastest mate against Alphamove playing Black 3 moves (natural max), White 5 moves (exhaustive search), selfmate 9 moves - problem composers and mathematicians solve that in a jiffy. See here: https://chess.stackexchange.com/questions/46651/fastest-win-against-xkcds-alphamove 172.70.248.29 09:11, 3 February 2025 (UTC)

One possible move, Kd2, is missing! /141.101.76.164 17:41, 2 February 2025 (UTC)

That can't be done. The Knight isn't between d2 and the Q@f2 at the point that the moves are being compiled. The Ne2 hasn't happened yet (we now see it, as having moved there, as a result of Ne2 being selected from the list, so next turn the King could move there, assuming the game isn't lost (or black decides to do something else which prevents it, for some strange reason). 162.158.74.25 18:47, 2 February 2025 (UTC)

I put the position before White's move into Lichess and it says it's mate in 12 for Black.

On a related note, I'm also wondering how they got to the comic position in the first place. Anyone want to try constructing a proof game? Arcorann (talk) 03:30, 3 February 2025 (UTC)

A lot of the explanation is based on a round-up version of AlphaMove. It should round down for even lists like the title text says. The example implementation is wrong too. The first move should be e4, not f3. 162.158.187.55 07:25, 3 February 2025 (UTC)

If there ever was an explanation that needed to be broken up into three paragraphs and a Detail section, this is it. 172.71.142.30 17:19, 3 February 2025 (UTC)

It is not mentioned what happens when there is a tie for the middle move (for an even number of possible moves). Is it then chosen "at random"? 162.158.155.102 19:38, 3 February 2025 (UTC)

The title text discusses it, so presumably that's the principle we should consider at play. 162.158.6.110 21:23, 3 February 2025 (UTC)

Why is there still a pawn on a2? It would seem that a3 would be the first move, followed by a4. 172.69.135.191 (talk) 23:20, 3 February 2025 (UTC) (please sign your comments with ~~~~)

a3 would be the first in the list for the compilation of first move (then a4, then [b-h] x [2-3], then four "N"-moves. The middle of the list would therefore (depending upon round-up or round-down) "e4" or "f3". Assuming e4, the next white move list is going to be seven pawns that can move to self.3 or self.4, one that can move to self.5, with some B-moves between b4 and c3, a K-move, five N-moves and a number of Q-moves. pawn on a2 just doesn't get a look-in, move-wise, at least not until after a lot of moves (possibly designed by the opponent specifically' to remove moves from anything that isn't pawn-move from a2 to a3 or a4. 162.158.33.252 15:48, 4 February 2025 (UTC)

What does this mean? The current explanation includes a paragraph starting with "The actual middle of the list might vary away from the usual alphabetic median if the moves (and the pieces removed by the opponent) are heavily biased to a particular subset of player-pieces." I can't make head or tail of this, but maybe that's just 'cause I'm dumb. Why would the middle of the list be different from the median? It should be re-worded to be clearer, or perhaps removed. DKMell (talk) 22:43, 3 February 2025 (UTC)

As an example, when the King is in check, there are far fewer legal moves, but they might include (or be limited to) interposing with a bishop, so that a bishop actually does get moved. That differs from the _usual_ median, even though the median function is still being used. JimJJewett (talk) 06:56, 4 February 2025 (UTC)
Several ways of reading "alphabetic median", one is that, in a-z, the m/n point is the median, or divide between the two halves. But of course not all letters are used (a-h as no-prefix pawn-destinations, B, K, N, Q, R as non-pawn prefices to destinations, a capturing pawn-move will start with x (of a-h and then an x, if needing disambiguationg, and then there's O-O and O-O-O). That's already overbalanced, so that 'g' is the 'middle' of the first-letters (unweighted by whatever actual opportunities, or lack of them, there are).
But, in any given board position, the lower-case letters tend to be pawns with (initially) two possible moves, generally just one move, maybe up to four (a first-move pawn given 1/2-step forward options and given two different options to capture away from its current file, where near-neighbour pawns require the disambiguation to be used) A queen can (where not restrained, until (possible capturing whilst) hitting the edge-of-board) have 28 moves (seven positions front/back, seven left/right, similar on the two diagonals). Rooks and Bishops might have 14 move-to positions. The kNight might have up to 8 'landing spots'. Initially, apart from the kNight with two moves, they of course have no opportunity to do anything. As the game develops, though, whatever you prior preconceived 'median' might be, in the alphabetically-sorted list, the gaining (by gaining opportunity to move) eand losing (by a piece being capture) adjusts the move-state's 'middle' of all valid-moves up and down the alphabet. Probably never as far as an unambiguous pawn-capture, or a first-file pawn move (or disambiguated capture from that positions), but it'll change a lot.
How to concisely explain this, I don't know. Especially as I'm just running off the various possibilities off the top of my head, and might have forgotten some of the 'algebraic' notation's subtleties. 162.158.33.252 15:48, 4 February 2025 (UTC)

This comic reminds me of suckerpinch's "Elo World" video, where he made a whole bunch of similarly single-minded chess engines and ranked them against each other. https://www.youtube.com/watch?v=DpXy041BIlA - If I recall correctly there was an alphabet-based one but it picked the first result rather than the middle result. 172.68.23.136 01:01, 11 February 2025 (UTC)

Is there any series of moves to be checkmated by alphamove?799571388 (talk) 11:34, 14 February 2025 (UTC)