Monday, December 31, 2018

Jerome Gambit: Took Less Time Than It Takes to Tell

If you know your Jerome Gambit, and can think and move quickly, bullet chess can be a successful arena of play for you.

Check out the following online game from angelcamina, who has a whole minute to get the Jerome Gambit to work for him, and does just fine.

angelcamina - janpecsok18
1 0 bullet, lichess.org, 2018

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+




4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+ g6

So far, so good for Black - but is this part of a defense he knows, or is this a reflex reaction to the check?

7.Qxe5 Nf6

Reflex. Black returns a second piece, and tries to find his way in an opening he doesn't know - two pawns down.

8.Qxc5 d6 9.Qe3 Rf8

Castling-by-hand is a standard defensive maneuver, and maybe Black should have continued.

10.O-O Be6

Sometimes this move is okay, and sometimes it is bad, but it always screams "throw a pawn at me!" to White.

11.d4 Qd7

This might be aimed at preventing f2-f4-f5, or it might be a bit of quick development (the clock is ticking), but 11...Kg8 was probably more consistent.

12.f4 c5

Aimed at the growing White mass of pawns.

13.e5 

Or 13.d5

White's position is better, the first player knows what he is doing - and he might even be ahead on the clock.

13...dxe5 14.fxe5 Bf5

Trying to block the dangerous f-file, but Black can not afford to return any more material.

15.exf6 Kxf6 16.Qe5+ Kf7 17.g4 Black resigned



And that's that. Reminds me of the action sequence that "took less time than it takes to tell".

Nicely done.

Saturday, December 29, 2018

Jerome Gambit: A Positional Dance

I have struggled to appreciate the Human + Computer vs Computer Jerome Gambit games that Bill Wall has sent me, and this has slowed my presentation of some of them. (For an over-all look, see "Jerome Gambit: Centaurs".)

I suppose that I had expected a series of one-sided crushes, revealing brutal new Jerome Gambit refutations and uncovering scintillating dynamic defenses. It didn't turn out that way - at times the game looks like a positional dance. Let's take a look.

Wall/Stockfish - Crafty
centaur match, 2018

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+ 



Okay, we all should be expecting a win for White - Stockfish is a higher-rated computer program than Crafty, and it is partnered with Bill, who is pretty knowledgeable when it comes to the Jerome Gambit.

4...Kxf7 5.Nxe5+ Nxe5 6.Qh5+

Bill played two games with White with Critter as his partner, two with Houdini, two with Rybka, and two wth Stockfish. Each time, he played one 6.Qh5+ game and one 6.d4 game. (6.Qh5+ scored 2 - 4 - 2, while 6.d4 scored 2 - 5 - 1.)

6...Ke6 7.f4 Qf6 

Interesting: Black avoids 7...d6, which I have called the annoying or silicon defense, because it annoyingly drains much of the dynamism out of the position, and because it has been a primary choice of computer programs.

The Database has 208 games with 7...d6, with White winning 54% of the time. Instead, it has 133 games with 7...Qf6, with White winning 56% of the time.  

8.Rf1 g6

Even computers like to kick the enemy Queen, but 8...d6, working toward development, is probably a little bit better.

9.Qh3+ Ke7 10.fxe5 Qxe5



White has to be careful here (he cannot castle, Black threatens the pawn at e4) and probably should not go into this line without some preparation. That is one suggestion that 6...Qf6 might have been a "book" move inserted by a knowledgeable human.

11.Qf3 Nf6 12.Nc3 c6

The computers tut-tut at this move, which keeps White's Knight off of d5 and prepares ...d7-d5, preferring the more complicated 12...Bd4. They still give Black the advantage after the text.

13.Ne2

Wow. This move has a tactical justification that comes from silicon thinking. Of course, now, 13...Qxe4? would blunder a piece to 14.Qxf6+. It takes a bit more work, however, to see that 13...Nxe4 is met by 14.d4 Bxd4 15.Bf4!?, when 15...Qa4+ 16.c3 d5 17.Nxd4 allows White to recover his sacrificed piece, with a roughly equal game. "Equal", as in mutually complicated; not "drawn".

Instead, a decade ago a couple of computers fought it out after the solid 13.d3 -   13...Bb4 14.Bd2 d6 15.d4 Qe6 16.O-O-O Ng4 17.d5 Qg8 18.Qg3 Ke8 19.dxc6 bxc6 20.Nb5 cxb5 21.Bxb4 Ne5 22.Rxd6 Nc4 23.Qg5 Nxd6 24.Qe5+ Qe6 25.Qxh8+ Kd7 26.Rd1 h5 27.Rxd6+ Qxd6 28.Bxd6 Kxd6 29.Qd8+ Black resigned, Fritz 8 - Fritz 5.32, D1N5TWD1, 2008

13...Rf8 14.d4

I (sort of) warned you about this move (and the next) in the previous post.

14...Bxd4 15.Bf4 Qc5

It was okay, instead, to take the e-pawn with 15...Qxe4 16.Qxe4+ Nxe4 17.Nxd4, as after 17...g5!? the game would resolve itself into a pawn-plus Queenless middlegame favoring Black with 18.Be3 Rxf1+ 19.Kxf1 d5.

Interestingly enough, 17...d5 (instead of 17...g5!?) would have led to a human game where White ground down his opponent: 18.O-O-O Bg4 19.Rde1 Kd7 20.h3 Bf5 21.Bh6 Rf7 22.Nf3 Re8 23.g4 b6 24.gxf5 Rxf5 25.Nd2 Ng3 26.Rxe8 Kxe8 27.Rxf5 Nxf5 28.Bf4 h5  29.Nf3 Ke7 30.Ne5 Kf6 31.Nxc6 g5 32.Bc7 g4 33.hxg4 hxg4 34.Nxa7 g3 35.Nb5 Kg5  36.Bxb6 Kg4 37.a4 g2  38.Bg1 Kg3 39.a5 Nh4 40.Nd4 Kf4 41.a6 Nf3 42.Nxf3 Black resigned, Vlastous 2344 - Daboa 1799, Chessmaniac.com, 2016.

Black is still for choice, but this is how computer games go - a small slip here, a slight goof there... it all adds up.

16.O-O-O Be5 17.b4 

Again: Wow.

Black is close to stabilizing his position with ...d7-d6, so White has to do something.

17...Qb5 

This doesn't work. The other (stronger) computers suggest 17...Bxf4+ 18.Qxf4 Qxb4, when 19.Qe5+ Kd8 accents Black's uneasy King and unfinished development. Stockfish 9 then likes 20.Nf4, while Komodo 9 prefers 20.Nd4, both leading to a balanced game, or the slightest edge to Black.

A decade ago, a computer vs computer game saw this continuation: 20.Rxf6 Re8 21.Re6 Rxe6 22.Qxe6 Qf8 23.Qe5 Qe7 24.Qd4 b6 25.e5 Bb7 26.Nc3 c5 27.Qg4 Bc6 28.Qf4 h5 29.Nd5 Bxd5 30.Rxd5 Rc8 31.Qa4 Rc7 32.Qe4 Rc6 33.Qa4 Qe6 34.c4 Rc7 35.Qd1 a6 36.Qe2 Rc6 37.g3 b5 38.h4 bxc4 39.Qxc4 Qf7 40.Qb3 Kc7 41.Qd3 Kc8 42.Rd6 Rxd6 43.Qxd6 Qf1+ 44.Kd2 Qg2+ 45.Kc1 Qc6 46.Qd2 Kc7 47.Qa5+ Kb7 48.Qd2 Qe6 49.Qb2+ Kc6 50.Qg2+ Kb5 51.Qb7+ Ka5 52.Qc7+ Kb4 53.Qb7+ Kc3 54.Qb2+ Kd3 55.Qc2+ Kd4 56.Qb2+ Kd5 57.a3 Qg4 58.Qb7+ Kxe5 59.Qc7+ d6 60.Qe7+ Kd5 61.Qb7+ Ke6 62.Qb3+ Ke5 63.Qb2+ Qd4 64.Qe2+ Kd5 65.Qg2+ Qe4 66.Qd2+ Ke5 67.Qb2+ Kf5 68.Qb8 Qd3 69.Qc8+ Ke5 70.a4 Qc4+ 71.Kd2 Qxa4 72.Qc7 Qd4+ 73.Ke2 Qe4+ 74.Kf2 Qd3 75.Qe7+ Kd5 76.Qe8 Qf5+ 77.Kg1 Kd4 78.Qb8 Ke3 79.Qb3+ Qd3 80.Qf7 Kd2 81.Qa2+ Ke1 82.Qa5+ Qd2 83.Qa1+ Qd1 84.Qc3+ Ke2+ 85.Kh2 Qd4 86.Qa3 Qf2+ White resigned, Fritz 8-Fritz 5.32/D1N5TWD1 2008

18.Nd4 Bxd4 

Have to get rid of that annoying Knight, but the exchange opens up dark squares in Black's position. White is now a bit better.

19.Rxd4 

19...Kd8

Black's two problems are related: uneasy King and under-development. In the game he works to move the King to a safer place. He should have chosen, instead, 19...d5, unblocking the Bishop that blocks the Rook - a standard defense ailment in the Jerome Gambit. Then, after 20.Bg5 Bg4 21.Bxf6+ Kf7!? 22.Qf4 Kg8, White will probably be able to untangle his pieces, with an edge.

The problem is that White has a powerful response to the text move. 

20.Bd6

Remember when the doctor told you "Okay, this is going to hurt  a bit"?

20...Qg5+ 

What else?

21.Kb1 Re8

White now has a forced checkmate in 17 (!), but it is hard to find any acceptible alternative for Black.

Perhaps you are used to seeing computers display their brutal tactical skills, and this game is a good example of how many "positional" games are underlaid by tactical themes.  

22.h4 Qxh4 23.e5 Black resigned



Simply brutal. The more you look, the more painful it becomes for Black.

Thursday, December 27, 2018

The Jerome Gambit Article: Followup

Readers who have kept up with the 8 posts of my "Jerome Gambit Article" probably now know more about the opening than almost anyone else in the world!

Of course, those who checked out the "Afterword" for the list of names of people I thanked, personally, for their help saw only about 100 mentions - by now, the list would be twice as long. Many additional thanks to those who have shared games and analysis!

Finally, I have to touch on the most in/famous of Jerome Gambit games, Amateur - Blackburne, London, 1884, and recall, from an earlier blog post 
...the uncertainties mentioned by Brazilian chess master Hindemburg Melão, Jr. in his article for the online chess site, SuperAjedrez,
...Some sources indicate year of the game as 1868, others indicate 1888, and others indicate 1880. Some sources affirm that it was played in Manchester, others in London. Normally the name of the adversary is not given, having only "NN" or "Amateur", but in at least one source "Millner" is indicated as the name. Also it is not known if it was an individual game or part of a simultaneous display... [T]he game deserves to be cited as one of most beautiful pearls of blindfold Chess...

In the years since my Jerome Gambit article was written - 5 years after Melão's - Blackburne expert Tim Harding has clarified the location and year
That was "Mr M" v Blackburne, first published in the Illustrated London News on 10 May,1884 

Still, who is the amateur named "Millner"? Was the game part of a simultaneous exhibition? Was the game really played "blindfold"? (Blackburne did not mention either of the last two in his notes to the game in Mr. Blackburne's Games at Chess - I would think he would.)

What to do? Something I couldn't do when Melão first wrote - I posted on his Facebook page, (with the help of Google translation).
15 years ago you wrote an article for SuperAjedrez.com about a Jerome Gambit game by Blackburne. You named "Millner" as his opponent and said it was a "blindfold" game. Do you remember your source? Thank you, very much!
Very quickly I received a response.
Probably the source was " Ajadrez a la ciega " (by Benito Lopes Esnaola) or " Manuel de chess " (by Idel Becker), in both of which is the match. I don't remember the name of the black player, but I found 2 Milner (with 1 L) from that time: 
http://www.edochess.ca/players/p1627.html 
 http://www.edochess.ca/players/p4055.html
I hope I helped.

Very interesting. Of course, I immediately put in a request, through InterLibrary Loan, for the two books Melão mentioned. They were written many years after the Illustrated London News article, but you never know what research will turn up.

I also checked out the links to the Edo Historical Chess Ratings.

The first, John Joseph Milner [note the single "l"], does not have a lot of information, but, given that one reference is given as  Bignold's Australian Chess Annual, and that the one tournament mentioned is the 6th New Zealand championship at Christchurch in 1893 - unless he is a very well-travelled chess player, he may not have been Blackburne's victim. A search with Google Books provided me with a copy of Volume 1 of the Australian Chess Annual of 1896, and there J.J. Milner is listed as Treasurer of the Canterbury Chess Club, in Christchurch.

The second, J. Milner [again, the single "l"], has even less information, but mentions a drawn game with A.C. Haines, played in the 1899 Lancashire - Yorkshire County Match, at Huddersfield. That's about a couple hundred miles away from Simpson's Divan, in London, much less of a travel for a dedicated pawnpusher. As for the reference given, Forster's book on Amos Burn, I have requested that from ILL as well.

So - more puzzles, more clues. Many thanks to master Hindemburg Melão, Jr., and I will share what more I discover.      


Tuesday, December 25, 2018

Merry Christmas!

Image may contain: one or more people and people sitting

Santa says, "Remember that when it comes to the Jerome Gambit (1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+) it is better to give than to receive!"

{That's my college roommate. I think he's checking out the new, mobile version of the Chess Openings Wizard}

Sunday, December 23, 2018

The Jerome Gambit Article (Part 8)

Here continues the Jerome Gambit article that I wrote for Kaissiber, a decade ago.


Alonzo Wheeler Jerome

            Alonzo Wheeler Jerome was born March 8, 1834 at Four Mile Point, New York. Little is known about his life, and nothing of his early years.
At the age of almost 30, with the United States fighting its Civil War, Jerome was drafted into the Union army in September of 1863, where he served as quartermaster until he was transferred, in April 1865, as quartermaster sergeant, to the 26th infantry regiment of the United States Colored Troops, under the command of Colonel William B. Guernsey, on Long Island, New York.
The 26th USCT served under the Department of the South (Union Army) in South Carolina and was very active on Johns and James Island, Honey Hill, Beaufort, and a number of other locations. While it is not know when Jerome took up playing chess, it is known that shortly after arriving at their first camp, the soldiers of the 26th immediately went about building both a chapel and a school; the latter, as many of the soldiers expressed an interest in learning to read and write. Might there have been time for the royal game, as well?
Jerome was mustered out of the army as a 2nd Lieutenant in August 1865, at Hilton Head, North Carolina. He returned to Mineola, New York, where he worked in a factory that manufactured agricultural machinery. It was here that Jerome first played his gambit, he said, against G.J. Dougherty.
He moved to Paxton, Illinois in 1868, where he took up the position of manager of a hemp and flax company.
On March 6, 1873, Jerome married 21-year old Jane “Jennie” A. Ostrom, of Paxton. Like Jerome, Jenny had been born in New York.
The Jeromes had one child, a boy, born 1874, who apparently died young, as he appears in one census at age 6, but not in future censuses.
Jerome’s public life as a chess player apparently began when a game of his, a King’s Gambit, appeared in the March 1874 issue of the Dubuque Chess Journal. The next issue carried the “New Chess Opening” article. The July issue carried the first Jerome Gambit game that he played against William Shinkman.
            In 1875, Jerome and Brownson met and played their games, later printed in the Journal. In one game Brownson offered the McDonnell Double Opening – 1.e4 e5 2.Bc4 Bc4 3.b4 Bxb4 4.f4. It is not surprising that he was intrigued by the Jerome Gambit.
            Two 1876 games by Jerome were published by the Dubuque Chess Journal, one, a Jerome Gambit, against Shinkman, and the other, a postal odds game (Queen for Queen’s Rook) against the child chess prodigy (later, chess problemist) Frank Norton.
            When the Dubuque Chess Journal stopped publication in 1876, it was replaced by the American Chess Journal, and Jerome continued his campaign on behalf of “Jerome’s Double Opening” in its pages for two more years.
            News about Jerome then grows scarce. J.W. Miller occasionally mentioned him in his chess column of the Cincinnati Commercial Gazette and by S.A. Charles referred to him in his Jerome Gambit writings.
            In 1884, of course, Jerome was healthy enough to travel to the Cincinnati Mercantile Library and play a few games with his gambit against Miller.
In 1899, citing diabetes and heart problems, Jerome applied for a disability pension. By that time he and Jennie were living in Springfield, Illinois, where he was working as a guide in the state capital building. 
Alonzo Wheeler Jerome died from the complications of a gastric ulcer March 22, 1902 in Springfield, Illinois. He was survived by his wife.

Unanswered Questions

 1) Arguably the most influential Jerome Gambit article was the one by Sorensen, May 1877, in Nordisk Skaktidende – it was translated into English and reprinted in the Chess Player’s Chronicle August, 1877, and in the September & October 1877 issue of the American Chess Journal; and it was translated into Italian and appeared in the December, 1887, Nuova Rivista Degli Scacchi. In what other magazines, in what other languages did it appear?
2) The first player in the Blackburne game has been referred to as "NN" or "Anonymous" or "Stranger." Occasionally (e.g. www.superajedrez.com; or, with the wrong year, at www.chesslab.com ) the player has been given as "Millner." Was it Millner? Who was Millner? Documentation would be helpful.
3) Charlick of Australia was familiar with the Jerome Gambit. The Adelaide Observer (5/28/1881) published a Jerome Gambit correspondence game of his, as well as a game with (AO, 5/12/1877) Charlick’s own “Evans-Jerome Gambit” 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4 Bxb4 5.c3 Bc5 6.Bxf7+. Are there other Jerome or Jerome-ish examples from this openings explorer to be found?
4) Abrahams in The Chess Mind (1951) refers to “the once popular Jerome Gambit” – 1.e4 e5 2.Bc4 Bc5 3.Bxf7+. Fletcher’s Gambits Accepted A Survey of Opening Sacrifices (1954) notes “Some authors have called the opening with the moves 1.P-K4, P-K4; 2.B-B4, B-B4; 3.BxPch, by the name Jerome.” Is this a typographical error, or does the Jerome, of the Giuoco Piano have an evil twin brother in the Bishop’s Opening?       5) Half-way between the creativity of Charlick (of 1.d4 e5!? notoriety) and the possible misnomer of Abrahams and Fletcher lie two other Jerome Gambit “variants.”
The Dubuque Chess Journal, November, 1874 carried the game Wright – Hunn, USA, 1874, which began 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.d4 - “brilliant but not sound” according to Brownson - ed 5.Bxf7+. The DCJ said that this was “an unsound variation of Jerome’s double opening” and suggested that after 5…Kxf7, the move 6.Ne5+ “a la Jerome” would have improved upon the game continuation of 6.Ng5+. The Italian Gambit (2004) by Jude Acers and George Laven, the current reference on 4.d4 in the Giuoco Piano, covers 4.d4 ed 5.c3 dc 6.Bxf7+, but does not mention Wright’s rash 5.Bf7+.
James Mason, in the August 1895 British Chess Magazine, gave a game “played recently by correspondence between Brandfort and Bloemfontein, South Africa” which went 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Qe2 d6. Mason suggested the move 4…Nf6, because “there would be plenty of time to play the Pawn - perhaps two squares instead of one. For, as the Cape Times remarks, if White adopts the ‘Jerome Gambit’ 5.Bxf7+ Black replies 5…Kxf7 6.Qc4+ d5 7.Qxc5 Nxe4 with advantage.” This assessment was confirmed in Albin – Schlechter, Vienna 1914 (0-1,31).
The odd 1.e4 e5 2.Nf3 Nc6 3.Bc4 Na5 sometimes received the “Jerome treatment” (without the title) 4.Bxf7+ Kxf7 5.Nxe5+ (e.g. Sidran – Vong, Compuserve e-mail 1992, [1-0, 8]) when 4.Nxe5 would have been adequate.
These lines are interesting; but they did not show up in the work of Jerome, Sorensen, Charles, etc. Are there other Jerome gambit off-shoots out there?
6) Traxler, concerning his gambit in the Two Knights Defense, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 Bc5 wrote in Golden Prague on October 11, 1892 (quoted by Lubomir Kavalek in The Washington Post, April 14, 2003)

 An original combination that is better than it looks. A small
mistake by white can give black a decisive attack. It is not easy to
find the best defense against it in a practical game and it is probably
theoretically correct. It somewhat resembles the Blackmar-Jerome
gambit: 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+?! Kxf7 5.Nxe5?!.

What connection did Blackmar, of Blackmar-Diemer Gambit fame, have with the Jerome Gambit?
            7) Although Alonzo Wheeler Jerome (1834 - 1904) was the "inventor," of the Jerome Gambit, it was extensively analyzed and popularized by S. A. Charles. There are scant clues today as to who Mr. Charles was. Jeremy Gaige's classic book on chess players, for example, lists the name "S. A. Charles," but not a date of birth or death; and Gaige's entry indicates only that Mr. Charles seemed to have been on the chess scene from 1890 to 1910. In the early 1870s he worked for the Covington and Cincinnati Bridge Company, residing in Covington, Kentucky, although a September, 1881 chess column in the New Orleans Times-Democrat referred to Mr. Charles as "formerly of this city." Mr. Charles was identified in a January, 1881 chess column in the Pittsburgh Telegraph as being the President of the Cincinnati Chess Club. Does anyone know more?
8) Finally, was Jerome’s inspiration for his opening the sacrificial attack in the well-known game Hamppe - Meitner, Vienna, 1872:  1.e4 e5 2.Nc3 Bc5 3.Na4 Bxf2+ 4.Kxf2 Qh4+ 5.Ke3 Qf4+ 6.Kd3 d5 7.Kc3 Qxe4 8.Kb3 Na6 9.a3 Qxa410.Kxa4 Nc5+ 11.Kb4 a5+ 12.Kxc5 Ne7 13.Bb5+ Kd8 14.Bc6 b6+ 15.Kb5 Nxc6 16.Kxc6 Bb7+ 17.Kb5 Ba6+ 18.Kc6 Bb7+ draw

Afterword

Many people helped me gather the information in this article, and I want to express my heartfelt thanks to each of them: Deanna Austin, Kent Ball, Pete Banks, Martin Bennedik, Eric Bentzen, John Blackstone, Harold Bohn, Neil Brennen, Paul Broekhuyse, Stefan Bucker, J. Gayle Camarda, Franklin Campbell, Geoff Chandler, Adailton Chiaradia, Sarah Cohen, Kristina Daily, Todor Dimitrov, Paul Dunn, Bob Durrett, Wayne Everard, Steve Farmer, Steve Frymer, Sam Fore, Richard Forster, Ken Fraser, Gary Gifford, Michael Goeller, A.B. Hailey, Tim Harding, Keith Hayward, Dan Heisman, Adam Henderson, John Hilbert, Owin Hindle, James F. Holwell, Colin James III, Thomas Johansson, Fyhn Karsten, Ara L. Kaye, Paul Keiser, Libby Ford Kennedy, Rick Kinkaid, Tom Klem, Michael Kramer, Robert Kruszynski, Rosemary Kurtz, Gary Lane, Heather Lang, George Laven, Jeff Martin and the staff of the John G. White Collection at the Cleveland Public Library, Missi Matt, Tim McGrew, Hindemburg Melao, Anna Maria Mihalega, Louis Morin, Mark Morss, Robert Murnan and the staff at the Cleveland Research Center, Clyde Nakamura, Christopher Nelson, Anne Newman, Russ Newman, Reg Nonni, William Paulsen, James Pratt, Tyrin Price, Tom Purser, Marianne Reynolds, Magnus Rosenstielke, Tim Sawyer, Eric Schiller, Daaim Shabazz, Jeremy Spinrad, Peter Stockhausen, Susan Strahan, Jason Stratman, David Surratt, Joseph Tanti, Pat Tavenner, Attila Turzo, Cindy Ulrich, Olimpiu Urcan, Bill Vallicella, Lissa Waite, Andrew Walker, Art Wang, Bill Wall, Brian Wall, Ken Whyld, Jaap van der Kooij, Jeroen van Dorp, Ed Yetman, Bradley Zang, Lev Zilbermints
Please note that in almost all cases concerning source quotes, I have changed descriptive notation to algebraic notation.

Bibliography


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