Thursday, December 1, 2016

Future Match Configuration for the World Chess Championship

Gary Kasparov vs. Anatoly Karpov
World Chess Championship 1984

The World Chess Championship has concluded in New York City, NY, USA. The reigning world champion Magnus Carlsen of Norway has defended his crown against challenger Sergey Karjakin of Russia.

The match was to be decided by 12 games, governed by classical time limits (or what might pass as classical today). Players were to have 100 minutes each for the first 40 moves, an additional 50 minutes until move 60, and an additional 15 minutes after that. Plus, they have an additional 30 seconds per move.

These long matches are brutal. Players are under tremendous stress and often lose several pounds throughout a match, just by thinking. Because of the high level of play, draws are common. Draws can also be strategic, though, as a quick one can give both players a much needed break from the stress of the match. In this last World Championship series, 10 of the original 12 games ended in draws.

Because both Carlsen and Karjakin won a single game, their 12-game series ended in a 6-6 tie. After that, the match was settled by a series of speed rounds. Carlsen won.

Between Carlsen and Karjakin, Carlsen's the stronger player by far. Before the match, he was the best player in the world by classical time constraints, best player in the world by speed time constraints, and second best in the world at blitz. In short, this guy is chess incarnate.

It's important to preface what I'm about to say with proper respect for the world's best. Because winning the World Chess Championship with speed game tiebreaks is a bunch of crap.

Apparently, the debate goes back decades, perhaps to the very beginning of the World Chess Championship. At the famous Karpov-Kasparov match in 1984, the first player to win 6 games would be crowned champion, and ties weren't counted. The match went to 58 games and lasted six months. They eventually cancelled it, under much controversy, and allowed Karpov, who was leading in points, to keep the crown.

Such an extreme condition seems unthinkable in today's world where the average Western attention span has been tempered by 30-second commercials, Facebook, and viral Youtube videos. That said, I still prefer it to what just happened between Carlsen and Karjakin.

Classical chess and speed chess aren't the same thing. Speed chess and blitz chess aren't the same thing either. The changes in time controls literally change the game. It's not like adding an extra five minutes to the clock in the NBA. The pieces move the same, but the level of game play changes fantastically.

In fact, there already is a World Rapid Chess Championship and a World Blitz Chess Championship. Can you imagine either of those titles being decided by chess played under classical time controls? No way! It defeats the whole purpose!!

First, FIDE has to resolve to use only classical time controls for a classical time control championship title. It's ridiculous to do otherwise.

Second, I think 12 games is too few. I also think 24 games is too many. However, the need to maneuver within the format has got to be respected. Every little thing means something in these World Chess Championships. The choice of opening, the repetition of moves, the speed at which certain moves are made. More games means more of an open arena for these players to really interact and create some great games.

One simple solution would be to divide the match into fixed sets with artificial end points. The winner would be whoever emerged from a set with a lead in points.

Let's say the match goes to 12 games at first. If a player is winning by game 12, he wins the match. If it's tied, the match continues another 4 games. If a player is winning, he wins the match. If it's tied again, the match continues another 4 games. The match should go like this until 24 games. If it's still tied, the world champion retains his title.

Match sets could be in any configuration. 12-4-4-4 or 12-8-4 or 8-8-8 or 8-8-2-2-2-2. With artificial end points, players will likely push a little harder to try to end the match prematurely.

Third, the way FIDE alternates white and black now is ineffectual. Switching in the middle of set is meaningless. In fact, the way it worked with Carlsen playing white in the first AND last game of the match really benefited Carlsen. For the artificial end points to work, you need to allow both players to be white at the end of a set.

Using Carlsen and Karjakin as an example, let's say a match was divided into 12-4-4-2-2. This would allow for a maximum of 24 classical games and a minimum of 12 classical games. The first 12 would see Carlsen start with white and Karjakin with black in the first game; the last game of the 12 would see Karjakin with white and Carlsen with black. If they remained tied, Karjakin would start the next 4-game set with the white pieces. If they still remained tied after the game 16, Carlsen would start the next 4-game set with the white pieces. Still tied, the next 2-game set would be lead by Karjakin with the white, and finally, if still tied, the last 2-game set would be lead by Carlsen with the white pieces.

This particular set up allows for multiple chances to end the match using ONLY classical time controls. It also incorporates a bit of natural tension to encourage players to avoid draws.

Really, anything is better than what actually happened. No offense, Magnus.

Sunday, November 27, 2016

The Allure of KENKEN

This is KENKEN, a puzzle that piggybacked on Sudoku's popularity over a decade ago. I personally fizzled out on Sudoku pretty early on when I heard about editors merely deleting some of the numbers off the opening Sudoku puzzles to make them harder (never mind that the puzzles had been designed to be solved through logic alone). Disillusioned with a puzzle that could so easily be tampered with, I turned to KENKEN.

KENKEN, like Sudoku, requires the same numbers to be entered into every horizontal row and vertical column. In this particular puzzle, because the grid is 6x6, every row and column require the numbers 1 through 6 exactly once each.

What makes KENKEN different is that it incorporates basic math. Every bold shape (usually a rectangle or square, though sometimes a funky looking piece) has either a number alone or a number and an arithmetic symbol. The squares that have single numbers have no puzzle attached and can be filled in, as below:

After these giveaways, a solver must look to the other bold shapes, or cages, to solve the puzzle. Most cages have a number and symbol which is the clue to that cage's numbers. For example, the long rectangle next to the 1 in the upper left corner has "30 x" in it. That means the three numbers in that cage, when multiplied, equal 30. Two sets of numbers makes this true: 6, 5, 1 and 5, 3, 2. Since 1 is represented in that row, the set 6, 5, 1 is eliminated, leaving the other. However, the solver doesn't know what order to put those numbers in, so the puzzling continues. 

Like Sudoku, you have to sort out exactly what you can logically deduce from the information given, fill in a square or two, then repeat. Do this enough times, and you solve the puzzle.

The reason I linked to this particular puzzle is because it beautifully illustrated what I like about KENKEN. Even though these examples are time-stamped within a few minutes of starting, I actually had to spend nearly half an hour to make my first move!

I first went around the grid, trying to learn what I could. After figuring out part of the "30 x" cage, I knew the upper right corner had the numbers 6, 4 because they were the last two numbers for the row AND the equation made sense (6 - 4 = 2). But I still couldn't write anything. I moved on wondering about all the "2 ÷"s and feeling a little hopeless about them because they could all be solved with 2, 1 or 4, 2 or 6, 3. They represented too many variables to sort out. I looked at the "10 +" and the other "10 +". The second one can be problematic because it wraps around a corner, just like the "15 +" below. Because of this wraparound, they obey slightly different rules. These corner cages can have the same number in them so long as those numbers don't fall in the same row or column. In fact, several of my first KENKEN puzzles were ruined because I didn't understand this fact. The corner "10 +" could be 3, 4, 3, as long as the 3s didn't touch. Anyway, I looked at all these potential avenues for breaking into the puzzle, and though I collected bits of information, it wasn't enough to write anything down.

Finally, I had a breakthrough.

One thing I had overlooked was that certain cages COULDN'T have certain numbers in them. For example, all of the "2 ÷"s could never have a 5 in them. Once I figured this out, then I was able to bounce to the row with the 4 in it. Since it had two cages with "2 ÷", I knew that the 5 had to be in the "3 -" cage. This meant that the two numbers were 5, 2 (because 5 - 2 = 3), though I didn't know the order. That in turn meant that the rest of the row had to be filled in with 1, 3, 6. Only two of these numbers (6, 3) could fit into the far right "2 ÷" cage and make sense in an equation.

So after all of that, I knew definitively that the 1 had to go in the yellow square below. My first written square after the freebies!

Yes, that one square took me about half an hour. If I did these puzzles more regularly, I'm sure I would have found it quicker, but I'm out of practice. After the 1, I could fill in the square below it with 2 since that's the only equation that can work (2 ÷ 1 = 2).

Then it was back to the drawing board. Once again, you have to analyze the cages and figure out what information is there. With the "15 +" cage, I knew that it had to have a 6 in it. No combination of numbers adds up to 15 without a 6. But where did the 6 go?

If you'll recall, the top right cage has a 6 in it, and the cage to the right of the 4 has a 6 in it, so the 6s in both of those columns are spoken for, so to speak. You don't know which square they belong to, but you can black out those columns. And for our purposes, that's enough information!

With one square left in the "15 +" cage, we know definitely that the 6 goes in the yellow square below:

This is your introduction to KENKEN. I love it and I hope you enjoyed your introduction to it. How it fits in this blog is perhaps somewhat puzzling, but I leave it to you to figure it out. Any ideas?