Game of Chess and the Knights Tour

Other than science, Isaac Newton and Albert Einstein had one more thing in common. They both loved chess. It is not just scientists however, who saw chess as more than just a game.

In an interview, two-time Oscar-nominated actor, Will Smith, revealed, “….The elements and concepts of life are so perfectly illustrated on a chessboard. The ability to accurately assess your position is the key to chess, which I also think is the key to life.” Indeed, chess helps us to assess our position from a deeper understanding of life.

Game of chess is about planning, strategizing, and dealing with winning and losing. It’s about an understanding of the lessons we learn from our choices, decisions, mistakes, and failures. To win a game of chess, players need to have a plan or two up their sleeves, ready for any unforeseeable circumstances. Most don’t want to live life like shooting in the dark.

A game of chess can teach us how to turn the tides in our favor—through careful planning and quick thinking. Chess teaches you to have a plan B and a plan C. Chess teaches strategy and this creates thinking about two or three moves in advance instead of focusing only on what the next move of your chess piece will be.

In 64 squares of a chessboard, every piece, except the pawn, can move backward. Stepping back is an integral part of the game. By retreating, a player can find new ways to move forward and sometimes even confuse the opponent. In life, as well, it is okay to step back once in a while. In this process, we often see the bigger picture.

Some university campuses realize the importance of chess and have giant chess boards and pieces. When I was on the campus of Asian Institute of Technology in Bangkok during my doctoral research, I remember we had a giant chessboard right next to the library. But I never saw anyone play!

Chess teaches patience because your opponent in fact contributes to your knowledge. More you play and more you lose you hone new skills and insights. Chess teaches you to think like your opponent. I have learnt a lot in my life through my peers and competitors.

Chess is a great board game for parents and grandparents to play with their children and grandchildren. This is a game when you can share and teach strategies, learn from mistakes and be with each other in a quiet, thoughtful way. My father in law Capt Apte (read my blog)  used to play with my son a game of chess every other day. I could sense that my son was able to absorb experience and strategies of a pilot with 35 years of flying, implicitly and so unspoken.

We have a little granddaughter now and I am anxiously waiting when will she grow up and start playing with me a game of chess.

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Anyone who has played chess knows that no two games are alike. The thirty-two pieces and 64 squares ensure practically infinite permutations and combinations of games. And so is the case with our lives. Each person’s life is so completely different, so you, me and all of us play completely different games. Each time you play the game of chess, it is a new experience.

Chess teaches you to be decisive and take risks. In this process, chess teaches you to make sacrifices. In this context, perhaps the most underrated chess piece is the pawn. Pawns can be instrumental in your endgame strategy, so one should avoid sacrificing your pawn chess pieces in the early state of the game. You must treat your pawns with respect as the Irish saying goes, “When the game of chess over, the pawn and the king go back to the same box”. I love this saying.

Remember that every pawn has a dream of “reincarnation” i.e. to be the one who occupies the position when the pawn reaches the other end on the ”enemy” side. So to me pawns are like young interns and research assistants in the organization, who provide exceptional support in the difficult times and have a dream to become just like their mentors.

Every chess piece – King, Queen, Bishop, Rook, Knight, Pawn – has certain strengths – and weaknesses. Chess is therefore a great game for those who manage people of different kinds and win despite the “differences” between the team members. In fact, differences or limitations of the team are strategically used by the chess player (or team leader) for the advantage. Sometimes, I try to identify people in my company and imagine what role they play e.g. Queen, Bishop, Rook, Knight or Pawn.

Game of chess in the Greek times 

The knight is the only piece that doesn’t move in a straight line; instead, the knight is entitled to “L” based 8 possible positions. This feature has made knight a special piece of interest as it can throw surprises. One of the celebrated subjects regarding the knight is the “knight tour.” Knight’s tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. Although the objective of the puzzle appears simple, completing this task is quite complicated. It’s a complex mathematical puzzle that has endured more than 1000 years and has been a subject of advanced mathematics and heuristics algorithms.

While I was an undergraduate student at IIT Bombay, Professor D B Phatak of the Department of Computer Science gave us the knight tour problem to solve and generate the tour using ACE (Auto code for Engineers) language. I remember in “solving” this problem, we had to think about situation two steps ahead i.e. make scenarios. The first step consisted of  imagining the 8 L possible (or available) positions for the knight on the 64 square chess. Then for every available place, we had to estimate the possible available positions.

The difficulty was the decision. I thought that this part was straightforward  – i.e. the knight should certainly opt for the position that had maximum available future options. I wrote the algorithm in ACE, and it failed miserably. It was late night, and I was scratching my head as any other decision would simply beat the logic of life.

It then occurred to me that why not I try an extreme option (that appeared both irrational and risky) that the knight should move to the place that had the least available future options. I changed the code and lo behold – it worked. The knight under this strange policy completed the tour over 64 squares by visiting each square exactly once! This “irrational” algorithm was against the fundamentals of a standard greedy heuristics that looked at maximum future options.

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The revised algorithm taught me a new lesson in life. It essentially said that when faced with a list of things to be completed, start with the less attractive options first, and save the best until the end.

I don’t know how much I could follow this lesson in my own life.

Other day, I was thinking about what welcome gift should I give to the new “joinees” at my company EMC.

I decided to order game of chess as my welcome gift (and then ask them to figure out the knight’s tour)

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This blog draws some text from the article by  Andrew Hercules “15 Important Life Lessons From Chess: How Chess Is Related To Real Life Situations” . Gratefully acknowledged