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without analysis there's no reason to play.

Wednesday, October 05, 2005

Chess Puzzle Goodness

When I first came back to playing Chess this year after a brief binge of playing Go, I was disappointed that there seemed to be no good chess equivalent to GoProblems.com There seemed to be no good repository of easily accessible Chess puzzles. Well, now that I've found the Chess Tactics Server, my disappointment is over.

In addition to being a great source of tactical problems, this Chess puzzle server has a number of innovative features that appeal to my inner geek.

Firstly, all registered users have a rating. This is cool. User statistics and graphs are available which track this rating, user activity, and performance over the last 200 puzzles. This allows users to observe their progress over time, and may provide an incentive towards improvement. Here is my set of stats.

Initially, one might wonder how a rating can be calculated from chess puzzle solving performance. Ideally, this would take into account the time taken to solve the puzzles, the correctness of the solution, and the difficulty of the puzzles solved. The Chess Tactics Server team have solved this problem with an innovative puzzle rating system. The puzzles themselves have ratings which function in the same way as user ratings. When a player "loses" against a puzzle, the player's rating decreases, and the puzzle's rating increases. Vice versa if the player correctly solves the puzzle. This accounts for the difficulty of the puzzle and correctness of the solution.

The best thing is that time is also accounted for using a time regime. If a puzzle is solved within 3 seconds, the result is 1:0 - a clear win for the player. After 3 seconds, the result decreases linearly with 1/2:1/2 (a draw) at 10 seconds. After 10 seconds, the decrease of the result is proportional to exp(-x).

Somewhat suprisingly, this complex but simple rating system works really well. The problems that appear are randomly selected depending on the player's rating. This means that most of the puzzles that a player is given to solve will have a rating similar to the player. The larger the rating difference between the player and the puzzle, the smaller the frequency of being given such a puzzle. So in general, puzzles will be neither too hard nor too easy, yet there will still be the occasional challenge or walk-over thrown in.

Another advantage of this system is that since the ratings of puzzles are floated and not fixed, there are no issues with puzzle authors having to artificially quantify the difficulty of a puzzle. In fact the system works so well, that puzzles are automatically generated and validated via the BetaX chess engine.

It is obvious that some really smart people put a lot of thought into this, and equally obvious that their endeavors have resulted in a great product.

So go ahead and puzzle on! Personally, I'll be catching up on some sleep lost playing on the Chess Tactics Server until 2:00 am last night. *Yawns*


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