Journey to IM Title…and More
By IM Jason Wang
Hi everyone! I’m Jason Wang, Co-President here at Chess4Unity. Earlier this year, I achieved the title of International Master through a combination of motivation, genuine insight, and, of course, a preponderance of luck.
The coveted title of International Master in chess — the second-highest title awarded by the International Chess Federation — had always been somewhat elusive, at least to me. To gain this title, one needs to achieve an international (FIDE) rating of 2400 as well as earn three norms, which are awarded based on excellent tournament performance — a 2450 performance rating, to be exact.
I’d like to share some important parts of my journey toward this title, most of which occurred over the course of the last year. And near the end, I’d like to talk about how the confidence gained throughout the journey has affected me, even outside of the realm of chess. Let’s get straight into the journey.
Part 1: North American Open
It would not be entirely untruthful to say that I was struggling on my path toward the International Master title immensely, all the way up until December of 2022. In October 2019, my FIDE rating hit 2343; incidentally, it was during the Southwest Open that month, where I spectacularly won the final two rounds on demand, that I gained my first IM norm.
Half a year later, Covid-19 struck. Chess tournaments in the US went on involuntary hiatus. I studied chess for many hours a day over quarantine, but my results did not reflect it. Over the course of the next three years, my rating would go up and down — by November of 2022 my rating charged up to a new peak of 2345, a dazzling and fantastic 2 points higher than it had ever been before. Needless to say, I was not extremely impressed…
Entering the North American Open held in Las Vegas in December 2022, I was not expecting much. My playing style had been far too complaisant; I’d been scared of players who had significantly higher ratings than me, like Grandmasters. Because of this mental block, I had been hardly able to progress, despite the substantial amount of training I was undergoing.
It’d been prophesied that — having not studied as much chess as perhaps would have been desired — I wouldn’t achieve any more IM norms, let alone the title. One of the leading advocates of this theory was indeed my father, and to be fair I’d entirely embraced his prophecy. Looking back in retrospect, I think that both of us were happy that it ended up being incorrect…Anyways, let’s return back to the tournament.
It was quite evident from the start that I was not warmed up. In the second game in particular, I managed to swindle my way out of a losing position to achieve a winning one, only to blunder again into a drawn game, only to win after a miraculous mistake by my opponent. It was a nightmare and a half, but I’d come out alive and unscathed.
Then came my hectic fourth round game against International Master Jason Liang. Just as I was feeling optimistic about my position, Liang surprised me with an excellent exchange sacrifice, changing the character of the position. Objectively, the sacrifice was solid, but even more importantly his move shattered my morale; even though the position was still complicated, I put up a very feeble defense and lost unpretentious!
Something about this game, however, affected me in a way no other had before. Instead of being downtrodden and dejected by my loss, a cord struck in me — I became motivated. If my memory does not serve me wrong, I believe that right after this game I said aloud that I would achieve an IM norm in that tournament. As it turned out, this would be true. Indeed, it would be quite perfectly true.
In the sixth round, I was paired against Grandmaster Arman Mikaelyan from Armenia. Despite my expert navigation through the opening, I soon found myself outplayed into a losing position. Suddenly, Mikaelyan made a motion toward his queen, sliding it fatefully to f5. As I stared up in disbelief into his eyes, he instantly realized the grave mistake he had made: he’d blundered Ne7, forking his queen on f5 and his rook on c6. And in just the matter of a few moves, the game was over. The end of this game made me very happy, but it also made me realize that Grandmasters were susceptible to blunders all the same.
In any normal tournament, I would’ve become increasingly anxious — to be quite frank, I was never very good at calming my nerves in these tournaments. But to my surprise, I felt no such anxiety. Maybe it was some sort of teenage imprudence, or some sort of indifference toward the result, but I was undisturbed.
Entering the eighth round, I was paired against Ukrainian Grandmaster Viktor Matviishen; both of us were on 5.5/7. I was again outplayed in the beginning, but later on I capitalized on an opportunity. Four hours and 54 moves later, I’d done it — I’d secured my second IM norm with a round to spare. The next day would be the last of the tournament — and, perhaps, the most fateful. On 6.5/8, I was one of four players tied for first. Instead of anxiously preparing for my game against Grandmaster Vladimir Belous the next day, however, I preferred to go to In-N-Out Burger for a quick snack, for I did not feel the need to fret over the impending game. With a clear mind, I entered the playing hall the following morning, confident in my abilities.
Two hours into the game, Belous offered me a draw. I suppose that this was the real test of this tournament, for I’d never declined one against a Grandmaster before — not once, in my entire chess career. I could have continued this streak, taken it, and tied for first. But in a moment of inspiration, I decided that I wanted more. I think that it is not difficult to infer where the story goes from here…
It was really something special, though. I’d never before won a tournament comparable to this one; I’d never been close. I’m often asked how I managed this feat. And to be frank, I’m not entirely sure. One thing that I did, however, was remove myself from the mental block that had once plagued my play. I no longer focused on the results or on the idea that Grandmasters were superior to me, but instead on the journey, on the beauty of the pieces and the subtlety of the game. It was, indeed, quite a profound shift in thought.
Perhaps the most telling consequence of this was the fact that I wrote my personal statement for college about this game. The final line of my statement goes like this: “Maybe I overcame Belous. But more than anything, I overcame myself. Pushing aside the concept of titles has allowed me to fully embrace the beauty of this analytical art and mental war — a beauty no longer diluted by the internal politics that had once come with it.”
For once, I was not shackled to the confines that I’d built for myself. With this clearer mind, I was able to reach territories I could not have thought possible before. I was changed, I was confident, and for the first time in three years, I believed that I could do it.
Mastering the Moves: Chess Players and their Career Stories
By FM Arthur Xu
In March 2023, I ran into a math problem in an article from GM Jonathan Mestel. In July 2023, I had the opportunity to engage in a delightful conversation with him and talk about chess and math.
GM Jonathan Mestel is a Professor of Applied Mathematics at Imperial College London. GM Jonathan Mestel won the World Cadet Championship in 1974 and held the title of British Chess Champion in 1976, 1983, and 1988. He was awarded the Grandmaster (GM) title in 1982. Between 1976 and 1988, GM Jonathan Mestel was a member of the English Chess Olympiad team, winning three team medals (two silver and one bronze). He earned a Ph.D. in mathematics from Trinity College, the University of Cambridge in 1982. In the interview, GM Jonathan Mestel shared his views on chess and how chess may have influenced his career as a mathematician.
GM Jonathan Mestel learned to play chess from his dad at about five or six years old and began playing chess seriously at 11. When discussing what lured him into chess, he mentioned that chess appealed to something about geometry.
GM Mestel: The pawns are really great. The fact that they give some sort of rigid structure to the position, and yet it’s not always rigid. Obviously, they can be blocked, but as the pawns move, they alter the position. So, that really works very well in my view. And en passant works, it’s important for that to work. The other thing which is a complete coincidence is that knights and bishops are almost the same. No one could predict that just by looking at the two pieces. It’s just we know from experience that they are. And that really makes a lot of very interesting interplay between when the knight is better than the bishop and vice versa.
Chess and mathematics seem to have some connections. In childhood, GM Mestel followed his academic career while concurrently engaging in chess competitions- a practice mirrored by many young chess players nowadays. While some of his contemporaries became full-time chess players and the younger players followed suit, he realized that it was challenging to maintain his position at the top of the British chess scene. In his days, he played one Interzonal Chess Tournament (a similar role replaced by the World Cup in 2005) in Las Palmas in 1982. He said he played the Interzonal well enough but did not go further. GM Mestel decided to begin his career as a professional mathematician after earning his doctoral degree in mathematics.
So, how did he think about the influences chess has on his mathematician career? He first pointed out that chess and math both require thought and visualization.
GM Mestel: There’s not a direct link. I mean, obviously there are some chess things which are very logical, and obviously logic and math and chess go together. But you know, I mentioned chess problems rather than chess playing. Chess problems
are really much more mathematical than chess playing, because in chess problems you have an idea and you can make it work. In a game you have an idea. Maybe it works, but probably it doesn’t. You know, you just live with that. Oh, it’s a nice idea. If you have an idea, you can compose a position such that it works. And so, you can get lots of beautiful things happening in chess problems and studies.
FM Xu: So, what are some things that you learned from chess that helped you in your life or your career?
GM Mestel: Not really, not really. I mean obviously people think, oh, you play chess, you must be very good at plotting and whatever, but they don’t seem to realize that in chess, of course, the rules are really clear. Yeah, you tend to be good at certain kinds of visualizations, that you can play in your head blindfold, some people just can’t understand at all how you could do it. But why shouldn’t you be able to, when you look at a position and think ahead, you’re essentially thinking and looking at a position that isn’t there.
FM Xu: Yeah, so that’s the other thing. Chess is a lot about patterns, right? Pattern recognition. That’s why, when you study chess, of course you look at thousands of games, thousands of positions, and that’s also how they teach computers to play chess and feed it millions of positions. And then it gets better and better because it learns from those positions and experiences. It’s kind of the same with math, right? You do a lot of math problems and start to see patterns.
At the end of the interview, GM Mestel offered some suggestions for young chess players who love chess and math and do them simultaneously. He suggested managing time in a reasonable, balanced way. He further shared his insights into decision-making and strategic thinking in chess that may affect a person’s math thinking.
GM Mestel: …you get used to thinking, making quick decisions sometimes. Yeah, that’s kind of the fun of chess sometimes too. And of course, in chess you have this dual approach. There’s the short-range tactics, there, there, there, I win. And then there’s this long term strategic (play), well this is a weak pawn, maybe if I can swap these rooks and I can build a bishop here and eventually I can do that. And that certain kind of math is a bit like that. You can prove things using logic. You can say for this, then that, then that, and then that’s like calculation. But then if I come up with a conjecture, you can sort of think that’s probably not true.
Last, as a mathematician, GM Mestel raised this chess-related math question at the end of the interview. Can you solve it?
You can mate with a bishop and a knight on an eight-by-eight board. Can you do it on a ten-by-ten board?
Chess and Math Connection for Fun!
Knight’s Tour
By IM Jason Wang
Chess is, of course, a serious game. It is seriously complex and filled with, of course, serious strategy. But that doesn’t mean that we can’t take some time to enjoy the less chessical (or is it chessy?) aspects the game has to offer once in a while. Here, we’re going to explore a concept widely known in chess literature as a knight’s tour — an enigmatic puzzle nominally related to the game of chess.
For the computer scientist, the mathematician, and the chess enthusiast, the knight’s tour has always been a fascinating puzzle. A knight’s tour is a sequence of moves with a knight such that the knight lands on every square exactly once. Indeed, the knight is essentially giving a “tour” around the board.
The Chess Player:
The chess player sees this as a curious game embedded naturally into chess. Perhaps a challenge to bet a dollar or two on with a friend.
Anecdotal evidence suggests, curiously, that stronger chess players tend to perform better on this tour, i.e. they can land their knight on more squares before it runs out of moves. This is strange, because it would seem initially that any player who understood how a knight moved would be on level playing ground in this game.
The best explanation for this is that stronger players are able to envisage where the knight can land many moves in the future, which makes it inherently easier to complete a successful “tour.”
The Mathematician:
The mathematician sees this game as a puzzle with bountiful possibilities.
The mathematician calls a knight’s tour a Hamiltonian Cycle, and treats the board as a graph where each square is a vertex, with edges protruding from each vertex to every legal square the knight can jump to.
The mathematician attempts to generalize this game to an m x n board, where m≤n and m and n are not necessarily 8. And in doing so, the mathematician distinguishes between a closed tour, where the knight ends one move away from where it starts (so the knight can repeat the same tour if desired), and an open tour, where the knight can end wherever it pleases.
The mathematician discovers that as long as m, n≥5, then an open tour is possible on an m x n board; if additionally at least one of m, n is even, then a closed tour is possible as well. Perhaps most closely related to the game of chess, both an open tour and a closed tour are possible on the 8 x 8 chessboard.Being naturally curious, the mathematician also wishes to know how many valid knight tours exist on a n x n, square chessboard. To figure this out, the mathematician must rely on the computer scientist.
The Computer Scientist:
The computer scientist wishes to develop a clever yet reliable algorithm to complete a knight’s tour on an n x n board; brute force methods will not be appropriate for larger sized boards. The computer scientist develops heuristics, implements binary decision algorithms, and optimizes machine learning methods to more efficiently find solutions.
Fortunately for the computer scientist, the problem of finding a successful knight tour is linear in time complexity. This means, roughly, that the amount of time required to solve the puzzle is proportional to the number of squares on the board. Because of this, solutions to the knight’s tour on an n x n board can be found for extremely large values of n.
But even if finding solutions to the knight’s tour puzzle is a problem whose time complexity is linear in nature, finding the exact number of open knight’s tours on an arbitrary n x n board remains a difficult question. The number of knight’s tours on an 8 x 8 board, however, has been calculated to be 19,591,828,170,979,904 as discovered by Alex Chernov in 2003.
Whew, that was intense, and we’ve barely scratched the surface. The mathematics and computer science behind chess is indeed a vast topic that one could study for years upon years — just look at the Chess and Mathematics course taught by Harvard professor of mathematics and chess master Noam Elkies. More colleges should offer this class; come on, it’d be fun!
Chess Puzzles from the Chess for Unity 3rd Saturday Tournaments
Editors’ note: We selected interesting puzzles from the games of our 3rd Saturday Tournaments. We hope that you enjoy solving them!
Puzzle 1 edited by FM Arthur Xu
Black to move and win. Don’t be afraid that your queen is being attacked!