Programmer Puzzle: Encoding a chess board state throughout a game

Question

Not strictly a question, more of a puzzle...

Over the years, I\'ve been involved in a few technical interviews of new employees. Other than asking the standard \"do you

Answer 1

In the base case of the initial board plus subsequent moves, consider the following.

Use a chess program to assign probabilities to all possible moves. For example, 40% for e2-e4 20% for d2-d4, and so on. If some moves are legal but not considered by that program, give them some low probability. Use arithmetic coding to save which choice was taken, which will be some number between 0 and 0.4 for the first move, 0.4 and 0.6 for the second, and so on.

Do the same for the other side. For example, if there is a 50% chance of e7-e5 as the response to e2-e4 then the encoded number will be between 0 and 0.2. Repeat until the game is done. The result is a potentially very small range. Find the binary fraction with the smallest base which fits in that range. That's arithmetic coding.

This is better than Huffman because it can be thought of as fractional bit encoding (plus some at the end of the game to round up to a whole bit).

The result should be more compact than Huffman, and there are no special cases for promotion, en passant, the 50 rule move, and other details because they are handled by the chess evaluation program.

To replay, again use the chess program to evaluate the board and assign all probabilities to each move. Use the arithmetic encoded value to determine which move was actually played. Repeat until done.

If your chess program is good enough, you can get better compression with a two-state encoder, where the probabilities are defined based on moves for both black and white. In the most extreme case of some 200+ states, this encodes the entire set of all possible chess games, and is therefore not feasible.

This is pretty much a different way of saying what Darius already wrote, only with a bit of example of how arithmetic coding might work, and a real example of using an existing chess program to help evaluate the probability of the next move(s).