to make such that the human opponent will experience a somewhat complicated or perhaps a position that is not that easy to calculate. This is from an inspiration of the match Komodo giving knight odds to a human master.
Given a position, a computer will search for a move that it considered best for him, considering contempt and other things.
I am examining game 4 of that match. Say white to play (Komodo) at move 12.
Code: Select all
Calculate complexity at move no. 12
FEN: 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
Player move: g3White played g3 in actual game.
To see the possible alternative moves here I let SF6 analyze this position for 5 minutes at multipv 5 on 4 threads, and it comes up with.
Code: Select all
engine : id name Stockfish 6 64 POPCNT
hash : 256 MB
threads : 4
Top pv at 300s of analysis on multipv 5
[30, 1, 190170, -322, 'g2g3 h7h5 f3f4 e5f6 f1d3', 'g2g3']
[30, 2, 263947, -331, 'f1d3 h7h5 h3h4 g8e7 g2g3', 'f1d3']
[30, 3, 263947, -338, 'h3h4 d4d3 b2e5 c6e5 c2c3', 'h3h4']
[30, 4, 263947, -346, 'a1e1 h7h5 h3h4 g8h6 g2g3', 'a1e1']
[30, 5, 263947, -348, 'f1b5 g8e7 h3h4 a7a6 b5d3', 'f1b5']Code: Select all
[30, 1, 190170, -322, 'g2g3 h7h5 f3f4 e5f6 f1d3', 'g2g3']depth, multipv num, time in ms, eval in cp, pv in uci format, first move in pv in uci format.
Important to look here is the eval and the move, since we will not choose a move whose score is too far from the best score of the best move found in multipv 1. This early into the game the eval is minus because Komodo is giving a knight at the start of the game.
Here I set an eval margin of 30 cp, meaning that any move score that is more than 30 cp worst from the bestmove will not be considered in the calculation of complexity.
Code: Select all
analyze each move at 75s on multipv 1
eval margin : +30cp
ref. score : -322cpgap = score_in_pv1 - score_in_pv2
gap = -322 - (-331) = 9
This would mean that move2 is not that bad, and it will be included in the calculation of complexity. If the gap > eval margin 30cp in this case then it will not be included in complexity calculation.
In the calculation of complexity we will save two things, one is the number of move changes during engine analysis, and second the complexity number that is the sum of the depth at which there is move change.
Example, comparison starts at depth 3. At depth 4 the pv move has changed from g8e7 to d4d3, that would count move_change = 1, and complexity_value of 4, because of depth 4. Then suceeding moves will be examined as we go deeper.
Once completed we have move changes and complexity value. The idea is that whenever an engine changes its bestmove, it has difficulties assessing the position. Best move changes that happened at higher depths is an indication that there is something in the position that is difficult to evaluate, and we covered it by adding the depth to complexity value.info depth 1 seldepth 1 multipv 1 score cp 336 nodes 38 nps 19000 tbhits 0 time 2 pv g8e7
info depth 2 seldepth 2 multipv 1 score cp 373 nodes 86 nps 43000 tbhits 0 time 2 pv g8e7 d2d3
info depth 3 seldepth 3 multipv 1 score cp 374 nodes 152 nps 76000 tbhits 0 time 2 pv g8e7 d2d3 g7g6
info depth 4 seldepth 4 multipv 1 score cp 339 nodes 467 nps 233500 tbhits 0 time 2 pv d4d3 b2e5 c6e5 c2d3
info depth 5 seldepth 6 multipv 1 score cp 248 nodes 1565 nps 521666 tbhits 0 time 3 pv d4d3 b2e5 c6e5 f3f4 d3c2
info depth 6 seldepth 6 multipv 1 score cp 248 nodes 1957 nps 652333 tbhits 0 time 3 pv d4d3 b2e5 c6e5 f3f4 d3c2 f4e5
info depth 7 seldepth 8 multipv 1 score cp 248 nodes 3268 nps 817000 tbhits 0 time 4 pv d4d3 b2e5 c6e5 f3f4
info depth 8 seldepth 9 multipv 1 score cp 289 nodes 5269 nps 1053800 tbhits 0 time 5 pv d4d3 b2e5 c6e5 f3f4 g8e7 f4e5
info depth 9 seldepth 12 multipv 1 score cp 246 nodes 52209 nps 3263062 tbhits 0 time 16 pv g8f6 f1c4 c8b8 h1e1 h8f8 f3f4
info depth 10 seldepth 12 multipv 1 score cp 272 nodes 82703 nps 3308120 tbhits 0 time 25 pv d4d3 c2c3 g8e7 f3f4
info depth 11 seldepth 12 multipv 1 score cp 280 nodes 93505 nps 3339464 tbhits 0 time 28 pv d4d3 c2c3 g8e7 f3f4
info depth 12 seldepth 14 multipv 1 score cp 287 nodes 140187 nps 3594538 tbhits 0 time 39 pv d4d3 b2e5 c6e5 f3f4
info depth 13 seldepth 20 multipv 1 score cp 277 nodes 639221 nps 5113768 tbhits 0 time 125 pv e5f6 f3f4 g8e7 b3b4 e7d5
info depth 14 seldepth 20 multipv 1 score cp 269 nodes 889843 nps 5265343 tbhits 0 time 169 pv e5f6 b3b4 h7h5 b4b5
info depth 15 seldepth 20 multipv 1 score cp 281 nodes 1464434 nps 5464305 tbhits 0 time 268 pv g8e7 f3f4 e5f6 b3b4 e7d5
info depth 16 seldepth 20 multipv 1 score cp 282 nodes 1868486 nps 5447481 tbhits 0 time 343 pv g8e7 f3f4 e5f6 b3b4 e7d5
info depth 17 seldepth 20 multipv 1 score cp 284 nodes 2929273 nps 5665905 tbhits 0 time 517 pv g8e7 f1c4 e7d5 a1e1
info depth 18 seldepth 23 multipv 1 score cp 287 nodes 4306924 nps 5828043 tbhits 0 time 739 pv g8e7 f3f4 e5f6 f1c4 e7d5
info depth 19 seldepth 25 multipv 1 score cp 294 nodes 6630447 nps 5920041 tbhits 0 time 1120 pv g8e7 f1c4 e7d5 h3h4 h7
info depth 20 seldepth 27 multipv 1 score cp 297 nodes 9457413 nps 5918280 tbhits 0 time 1598 pv g8e7 f3f4 e5f6 b3b4 e7d5 b4b5
info depth 21 seldepth 29 multipv 1 score cp 292 nodes 13887733 nps 5912189 tbhits 0 time 2349 pv g8e7 f1c4 e7d5 h3h4 h7
To get the complexity for our opponent (human) we will give the engine the current position + the move in each of the 5 pvs, because the engine will calculate the complexity of the position when the computer is to move.
Example.
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multipv num : 1
old fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
new move : g2g3
new fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3PPP/1BPP1K2/R4B1R b - - 0 12
move changes : 5
complexity : 51
expected reply: g8e7 a1e1 h7h5 f3f4 e5f6The new move is the move in one of the move in the 5 pvs.
The new fen is the old fen + the new move, meaning we make the move in the board and get the fen.
This new fen is the fen that we sent to the engine to get the complexity, and it is opponent to play, meaning human to play, we try to determine if the engine difficulties could also be a difficulty to the human opponent.
The move changes 5 is what we get when we let SF6 on 4 threads analyze the position at 75s on multipv 1.
Complexity is the sum of depth where move changed has happened.
expected reply is the a move or pv output of the engine analyzing the given new fen. It is this line that has the complexity.
After analyzing those alternatives the tool will give us the move that would generate high complexity among the moves.
Here is the complete analysis at move no. 12.
[d]2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
Code: Select all
Calculate complexity at move no. 12
FEN: 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
Player move: g3
engine : id name Stockfish 6 64 POPCNT
hash : 256 MB
threads : 4
Top pv at 300s of analysis on multipv 5
[30, 1, 190170, -322, 'g2g3 h7h5 f3f4 e5f6 f1d3', 'g2g3']
[30, 2, 263947, -331, 'f1d3 h7h5 h3h4 g8e7 g2g3', 'f1d3']
[30, 3, 263947, -338, 'h3h4 d4d3 b2e5 c6e5 c2c3', 'h3h4']
[30, 4, 263947, -346, 'a1e1 h7h5 h3h4 g8h6 g2g3', 'a1e1']
[30, 5, 263947, -348, 'f1b5 g8e7 h3h4 a7a6 b5d3', 'f1b5']
analyze each move at 75s on multipv 1
eval margin : +30cp
ref. score : -322cp
multipv num : 1
old fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
new move : g2g3
new fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3PPP/1BPP1K2/R4B1R b - - 0 12
move changes : 5
complexity : 51
expected reply: g8e7 a1e1 h7h5 f3f4 e5f6
multipv num : 2
old fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
new move : f1d3
new fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP1B1P1P/1BPP1KP1/R6R b - - 3 12
move changes : 3
complexity : 29
expected reply: h7h5 h3h4 g7g6 g2g3 e5f6
multipv num : 3
old fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
new move : h3h4
new fen : 2kr2nr/ppp2ppp/2n5/4b3/3p3P/PP3P2/1BPP1KP1/R4B1R b - - 0 12
move changes : 1
complexity : 5
expected reply: d4d3 b2e5 c6e5 c2c3 g8f6
multipv num : 4
old fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
new move : a1e1
new fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/4RB1R b - - 3 12
move changes : 5
complexity : 43
expected reply: h7h5 h3h4 g8h6 g2g3 h6f5
multipv num : 5
old fen : 2kr2nr/ppp2ppp/2n5/4b3/3p4/PP3P1P/1BPP1KP1/R4B1R w - - 2 12
new move : f1b5
new fen : 2kr2nr/ppp2ppp/2n5/1B2b3/3p4/PP3P1P/1BPP1KP1/R6R b - - 3 12
move changes : 0
complexity : 0
expected reply: g8e7 g2g3 d4d3 b2e5 c6e5
The move that will generate the most complex position is: g2g3 Which move you would like to make so that your human opponent will have difficulties assessing the position when it his turn to move. Note in the actual game white played Bd3.
[d]2kr2nr/ppp2p2/2n4p/4b1p1/3p3P/PP3PP1/1BPP1K2/R4B1R w - - 0 14
Code: Select all
Calculate complexity at move no. 14
FEN: 2kr2nr/ppp2p2/2n4p/4b1p1/3p3P/PP3PP1/1BPP1K2/R4B1R w - - 0 14
Player move: Bd3
engine : id name Stockfish 6 64 POPCNT
hash : 256 MB
threads : 4
Top pv at 300s of analysis on multipv 5
[29, 1, 260229, -286, 'h4g5 h6g5 h1h8 e5h8 f1h3', 'h4g5']
[29, 2, 287739, -307, 'a1b1 g8e7 f1d3 a7a6 h1h2', 'a1b1']
[29, 3, 298724, -310, 'a1d1 g8e7 f1d3 a7a6 d1e1', 'a1d1']
[29, 4, 298724, -312, 'a1e1 g8e7 f1d3 a7a6 h1h3', 'a1e1']
[29, 5, 298724, -316, 'f1d3 g8e7 h1h2 d8g8 h4g5', 'f1d3']This is the record in game 4.
[pgn]
[Event "Computer chess game"]
[Site "Brussels"]
[Date "2015.08.02"]
[Round "4"]
[White "Kt-1460.00"]
[Black "Bolzoni, V"]
[Result "0-1"]
[BlackElo "2189"]
[BlackType "human"]
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/R1BQKBNR w KQkq - 0 1"]
[SetUp "1"]
[Termination "abandoned"]
[Time "13:57:30"]
[TimeControl "2700+15"]
[WhiteElo "3300"]
[WhiteType "program"]
1.f4 d5 2.b3 e5 3.fxe5 Nc6 4.Bb2 d4 5.Nf3 Bg4 6.a3 Qd5 7.h3 Bxf3 8.exf3 Qxe5+
9.Qe2 Bd6 10.Qxe5+ Bxe5 11.Kf2 O-O-O 12.g3 g5 13.h4 h6 14.Bd3 Nge7 15.Rag1
Rdg8 16.Bb5 a6 17.Bd3 Kd7 18.h5 f5 19.Rd1 Rf8 20.Bc4 Nd8 21.Rhe1 Nec6 22.b4
b5 23.Ba2 Re8 24.Bb1 Rhf8 25.Bc1 Re7 26.d3 Rfe8 27.Bd2 Ne6 28.Re2 Ng7 29.f4
gxf4 30.gxf4 Bd6 31.Rxe7+ Rxe7 32.Rh1 Ne6 33.Rh4 Rg7 34.Ba2 Ncd8 35.Bd5 c6
36.Bg2 Nc7 37.c3 Nd5 38.Bxd5 cxd5 39.cxd4 Ne6 40.Be3 Rg8 41.Rh1 Bxf4 42.Bxf4
Nxf4 43.Ke3 Ne6 44.Kf2 Rg4 45.a4 Rxd4 46.axb5 Rxb4 47.bxa6 Ra4 48.Kg3 Rxa6
49.Rf1 f4+ 50.Kg4 Ra3 51.Kf5 Rxd3 52.Ra1 f3 53.Ra7+ Nc7 54.Ra2 Re3 55.Rf2 Ne6
56.Kg6 Nf4+ 57.Kg7 0-1[/pgn]
. This is how it would look so far.