Chess variants
This is the second of a series of now four articles by Nikolas Axel Mellem on Shatranj. The first instalment was included in AG19.
by Nikolas Axel Mellem
Introduction
It seems likely that Shatranj was introduced into Europe in the 10th and 11th centuries. According to Kluge-Pisker (1994) board games reached a new peak of popularity in the 11th and 12th century. We know at least that Chess, Backgammon, Nine-men's Morris, and Tablut were played over vast European areas. The abstract Sunni-Arabic piece design also served as the basis for creating a new synthetic style that combined Islamic pieces shapes with Western figurative motifs.
It seems likely that Shatranj was introduced into Europe in the 10th and 11th centuries. According to Kluge-Pisker (1994) board games reached a new peak of popularity in the 11th and 12th century. We know at least that Chess, Backgammon, Nine-men's Morris, and Tablut were played over vast European areas. The abstract Sunni-Arabic piece design also served as the basis for creating a new synthetic style that combined Islamic pieces shapes with Western figurative motifs.
Chess was especially popular among the upper classes in the European Middle Ages, and never did so many woman play Chess as in this period. There is a saying that things were much better in earlier times, and the statement seems at least correct with respect to Chess prizes. A knight could in fact play a lady, wagering his money against the possibility of winning her for himself (Bubczyk 2009).
The level of play in the Middle Ages in Europe was very weak compared with Moslem Chess. Murray (1913) points that the European player was suspicious of the Elephant piece, which he found to be a destructive creature for forking two stronger pieces. The Fers was given the role of King's bodyguard, and hence lost all of its offensive potential. There exist no recorded games from this period, just relatively static setups. We miss endgame literature, which seems a bit surprising given the fact that new bare King and stalemate rules created many new interesting theoretical endgames.
Our main question is to answer how the European rule changes through the Middle Ages affected the game. Below I have listed a table for six different countries, at three different moments (ca 1400, 1600 and 1800), to show the frequency of nine selected rule changes from Shatranj.
The level of play in the Middle Ages in Europe was very weak compared with Moslem Chess. Murray (1913) points that the European player was suspicious of the Elephant piece, which he found to be a destructive creature for forking two stronger pieces. The Fers was given the role of King's bodyguard, and hence lost all of its offensive potential. There exist no recorded games from this period, just relatively static setups. We miss endgame literature, which seems a bit surprising given the fact that new bare King and stalemate rules created many new interesting theoretical endgames.
Our main question is to answer how the European rule changes through the Middle Ages affected the game. Below I have listed a table for six different countries, at three different moments (ca 1400, 1600 and 1800), to show the frequency of nine selected rule changes from Shatranj.
The earliest rule changes are still in the Middle Ages and four of them seem to be imported from outside—either from Arabia or India. The three most important of the six rule changes dating from the Middle ages rules are:
Bare King does not win, but stalemate wins
Probably late in 13th century Italians abandoned the bare King win rule, and this new variation spread to the rest of Europe, as Italian rules were held in the highest esteem for most of the 1000-1800 period. In Germany when bare King was no longer a win, a victory could still be obtained by stalemating the opponent. Below is the longest King-Knight-Elephant versus King stalemate win, created by H.G. Muller's Tablebase.
- Bare King no win,
- Stalemate no win,
- Pawn promotion limited to an available Fers.
Bare King does not win, but stalemate wins
Probably late in 13th century Italians abandoned the bare King win rule, and this new variation spread to the rest of Europe, as Italian rules were held in the highest esteem for most of the 1000-1800 period. In Germany when bare King was no longer a win, a victory could still be obtained by stalemating the opponent. Below is the longest King-Knight-Elephant versus King stalemate win, created by H.G. Muller's Tablebase.
The first phase and first 10 moves is about saving the pieces from the raging Blue King. 1...Kc5 2.Ed3 Kd4 3.Ef1 Ke3 4.Ng4 Kf3 5.Nf6 Kf2 6.Ed3 Ke3 7.Eb5 Kd4 8.Ka7 Kc5 9.Ka6 Kc6 10.Nd7 Kd5 (Now Red can start thinking about pushing Blue's King into the corner.) 11.Kb6 Kd6 12.Ka5 Kd5 13.Kb4 Kd4 14.Nc5 Kd5 15.Nb3 Ke5 16.Kc4 Ke4 17.Ed7 Ke5 18.Nc5 Kf4 19.Kd4 Kf3 20.Ne6 Kg4 21.Ke4 Kg3 22.Nd4 Kg4 23.Nf3 Kg3 24.Ne5 Kf2 25.Kd3 Kg2 26.Ke2 Kg3 27.Ke3 Kh3.
Driving the King to the last row seems relatively easy, the last part however requires more subtle play with sophisticated Knight moves. 28.Kf3 Kh4 29.Kf4 Kh5 30.Eb5 Kh4 31.Ng6 Kh5 32.Kf5 Kh6 33.Nf4 Kg7 34.Ke6 Kg8 35.Ke7 Kg7.
36.Ed7 Kg8 37.Nh5 Kh7 38.Kf6 Kh6 39.Ng7 Kh7 40.Nf5 Kg8 41.Nh6 Kh7 42.Nf7 Kg8
43.Ef5 Kf8 44.Nd8! (The trick! Now if the King goes towards the centre with the natural 44...Ke8 Red takes the advantage of the Elephant's leaping ability and stalemates on the spot with 45.Ne6!) 44….Kg8 45.Ne6 Kh8 46.Kf7 ‡# (Stalemate).
A hard 4-1 endgame
Leaving out the Rook, because King-Rook versus King is easily won, most 4-1 piece endgames are still won. However, the wins are hard like this King-Elephant-Fers-Fers versus King, which could have occurred in Italy, where multiple Ferses were allowed.
A hard 4-1 endgame
Leaving out the Rook, because King-Rook versus King is easily won, most 4-1 piece endgames are still won. However, the wins are hard like this King-Elephant-Fers-Fers versus King, which could have occurred in Italy, where multiple Ferses were allowed.
1.Ee3 Ka8 2.Fd6 Kb8 3.Fc5 Ka8 4.Fb4
The first part of the plan is completed—the b4-Fers blocks the Blue King along the a-file making it possible for the Red King to leave b6 and setup a Kc6-Fb7 mating net. 4…Kb8 5.Kc6 Ka7 6.Fc8 Kb8 7.Fb7.
Now the King is locked to a7-b8 squares and it is time to bring the b4-Fers and Elephant in to action. 7...Ka7 8.Fc5 (The Fers heads for d6.) 8...Kb8 9.Fd6 Ka7 10.Ec5 Kb8 11.Fc7#
The reader can now try to solve the KNFE-K ending. Is it still possible to mate within the 70-move limit with concordant Fers and Elephant?
An unusual 3-1 endgame
However, if the King has been unlucky and got stuck in the wrong corner, even the lonely Knight and Fers can mate him!
An unusual 3-1 endgame
However, if the King has been unlucky and got stuck in the wrong corner, even the lonely Knight and Fers can mate him!
Red's first plan is simple—keep the Blue King in the corner and simultaneously win a tempo so the Fers can approach the King. 1.Kd6 Kc8 2.Ne6 Kb7 3.Kc5 Ka6 4.Nd4 Kb7 5.Nb5 Kc8 6.Kd6 Kd8 7.Nc7 Kc8.
The procedure has been successful and Red now has time to move the Fers. 8.Fg4 Kb7 9.Nb5! Kb6 10.Nc3 Ka5 11.Kc5 Ka6 12.Ff5 Kb7 13.Nb5 Kc8 14.Kd6 Kd8 15.Nc7 Kc8 16.Fe6 Kb7 17.Fd5 Kb6 18.Fc4!
18…Kb7 (If 18…Ka5 Red has 19.Kc5 Ka4 20.Nb5 ready, keeping the King under control.) 19.Nd5 Ka6 20.Kc5 Kb7 21.Fb5 Kc8 22.Kd6 Kd8 23.Nc7 Kc8 24.Ne6 Kb8 25.Kd5! (Using the triangular King technique to press the Blue King.) 25…Kb7 26.Kc5 Ka7 27.Kc6 Kb8 28.Kb6 Kc8 29.Fc6
Finally things are looking very simple, where the King will be doomed to move back and forth on the a8 and b8 squares. 29…Kb8 30.Fd7 Ka8 31.Nd8 Kb8 32.Nc6 Ka8 33.Na7 Kb8 34.Fc8 Ka8 35.Fb7 Kb8 36.Nc6#
Restrictions on winning due to the rule changes
As even the 4-1 endings were very hard to win and the original Shatranj game was relatively drawish, Johannes Kohtz concluded in his discussion with Benary and Murray around 1910-1912 that Shatranj without the bare-King-wins would have been a disfunctional game due to the difficulty of giving check mate or stalemate. Kohtz (1916) also claimed that his three problemist friends, Holzhausen, Brunner, and Dehler played 25 Shatranj games where mate occurred only once.
Kohtz attitude is better informed than Murray and later scholars, who describe positively the European ban on bare King and stalemate wins, not recognizing how Europeans restricted the winning chances. Secondly, the European rules made an already slow game last longer.
However a 400 Shatranj game sample consisting of two matches I played against the Zillion of Games (ZoG) engine and two auto-matches ZoG played against itself showed that 60-75% of games might have been won with mate only, and the stalemate win gained another 10-25 % decided games. Combined mate and stalemate alone gave 73-89% of decided games, which proves that the game was playable, with Bare King not being a win.
As even the 4-1 endings were very hard to win and the original Shatranj game was relatively drawish, Johannes Kohtz concluded in his discussion with Benary and Murray around 1910-1912 that Shatranj without the bare-King-wins would have been a disfunctional game due to the difficulty of giving check mate or stalemate. Kohtz (1916) also claimed that his three problemist friends, Holzhausen, Brunner, and Dehler played 25 Shatranj games where mate occurred only once.
Kohtz attitude is better informed than Murray and later scholars, who describe positively the European ban on bare King and stalemate wins, not recognizing how Europeans restricted the winning chances. Secondly, the European rules made an already slow game last longer.
However a 400 Shatranj game sample consisting of two matches I played against the Zillion of Games (ZoG) engine and two auto-matches ZoG played against itself showed that 60-75% of games might have been won with mate only, and the stalemate win gained another 10-25 % decided games. Combined mate and stalemate alone gave 73-89% of decided games, which proves that the game was playable, with Bare King not being a win.
Bare King is a loss for the stronger side
Sometimes local rules could take a bizarre form. Stalemate had for instance different negative consequences for the strong side in India, Russia, and later in England, where it was a loss. So we should not be shocked when the Kraków manuscript (1422) claims that in some places in Poland baring the opponent's King is a loss. Here is an example.
Sometimes local rules could take a bizarre form. Stalemate had for instance different negative consequences for the strong side in India, Russia, and later in England, where it was a loss. So we should not be shocked when the Kraków manuscript (1422) claims that in some places in Poland baring the opponent's King is a loss. Here is an example.
1.Ra8! g6 (1…Re1 2.Re1 Ra8 3.Re8 Kh7 4.Ra8 wins) 2.Rh8 Kg7 3.Raf8 f5 (3…Re1 4.Kd2 wins) 4.Rh7 Kf6 5.Rff7 Rf7 6.Rf7, and Red wins.
Only one Fers per player
The third important drawish rule was implemented at least in Germany, Spain, France and England, and abolished having more than one Fers on the board per player. This meant that Pawn promotion was not possible for both players until their original Fers was gone. Murray (1913) argues this rule was implemented on moral grounds, not allowing more than one Queen at the same time. This rule really makes things harder for the strong side. Let us look at the position below featuring no bare King win, no stalemate win, and no more than one Fers.
Only one Fers per player
The third important drawish rule was implemented at least in Germany, Spain, France and England, and abolished having more than one Fers on the board per player. This meant that Pawn promotion was not possible for both players until their original Fers was gone. Murray (1913) argues this rule was implemented on moral grounds, not allowing more than one Queen at the same time. This rule really makes things harder for the strong side. Let us look at the position below featuring no bare King win, no stalemate win, and no more than one Fers.
1…Ne6! 2.Kc2 Ng5 3.hg5 Ke3 and the King escapes behind the Pawns and can not be mated as Red is unable to deliver mate with only one Fers. Red can instead try 3.Kd2, but after 3…Nf3 he must let the Blue King in anyway, which secures Blue's draw.
Conclusion
There are two important factors that made the drawish rules possible. Firstly, in the period around the Middle Ages there was a tendency in different chess variants around the world to develop drawish rules, probably in order to make games between opponents with different playing strengths more interesting—see below.
Conclusion
There are two important factors that made the drawish rules possible. Firstly, in the period around the Middle Ages there was a tendency in different chess variants around the world to develop drawish rules, probably in order to make games between opponents with different playing strengths more interesting—see below.
Secondly, and even more importantly, the draw ratio increases with the playing strength. Based on Western Chess numbers extracted from Chessbase by Morten Lilleøren we can compute and get following predicted draw probabilities by using the logistic regression formula:
This gives us in turn the following draw expectation curve:
Of course the numbers are statistical and caution is needed when dealing with the extreme values. We can mention H.G. Muller's remark that his randomly moving Chess engines make approximately 84 % draws, and in a similar way most of the first self-play games of Alpha Zero ended with draws. Therefore, the same might be said of the opposite end of the scale. Although today the best Chess engines are rated around 3500, and their draw percentage fits our curve, lying around 80%, I would argue that these computer ratings are inflated and victims of the overfit effect (Sadler & Regan 2019). The overfit effect, which potentially can also be seen in human-versus-engine games, means that agent(s) are taken advantage of by other agent(s) by means of exploiting weaknesses to such an extent that their rating gain is bigger than their actual playing strength. My guess is that a real rating strength of around 3100-3200 should lead to agents that play almost 100% draws.
Because the level of skill in European Chess of the Middle Ages was, as Murray (1913) points out, very low the draw percentage would still have stayed low, even with the new drawish rules. In fact, based on a small Shatranj game sample, even the best historical players would have had problems making 2000 Elo strength.
Because the level of skill in European Chess of the Middle Ages was, as Murray (1913) points out, very low the draw percentage would still have stayed low, even with the new drawish rules. In fact, based on a small Shatranj game sample, even the best historical players would have had problems making 2000 Elo strength.
The findings in the table follow the history of strength in Western chess, where for instance Paul Morphy in the1850's was the only player before the rise of tournaments in the 1870's to have Master level strength of at least 2200 Elo (Regan & Macieja, 2011). Hence, you would expect most European Shatranj amateurs to have a playing strength of well below the 1500 rating mark. ◾️
Literature list
The full list of background sources for the Shatranj articles is included in AG19. The references below were used just for the current article.
Acknowledgement
Header image: Public domain image from Wikipedia Commons. Chess Problem #35, showing Templars playing Chess, from the 1283 Libro de los juegos.
Literature list
The full list of background sources for the Shatranj articles is included in AG19. The references below were used just for the current article.
- Bubczyk, Robert (2009). Gry na szachownicy. Lublin.
- Kluge-Pinsker, Antje (1994). "Brettspiele, isnbesondere 'tabuale' und 'schacchis' im Alltag der Gesellschaft des 11. und 12. Jahrhundert." Homo Ludens, 4, pp. 69-79. München.
- Kohtz, Johannes (1910). "Von Ur-Schach." Desutsches Wochensschach. Potsdam.
- Kohtz, Johannes (1916). Kurtze Geschichte des Schachspiels. Dresden.
- Murray, H. J. R. (1913). A History of Chess. Oxford. (Retrieved May 4, 2020)
- Regan, Kenneth W., Macieja, Bartolomiej, & Haworth, Guy McC. (2011). "Understanding Distributions of Chess Performances." Warszawa. (Retrieved May 4, 2020)
- Sadler, Matthew & Regan, Natasha (2019). Game Changer: Alpha Zero's Groundbreaking Chess Strategies and Promise of AI. New in Chess.
Acknowledgement
Header image: Public domain image from Wikipedia Commons. Chess Problem #35, showing Templars playing Chess, from the 1283 Libro de los juegos.