The program was launched on a single computer in 2011. The software is currently running on six intel i7 computers.

ArShah is a logical cluster functioning on a large number of computers. It analyzes, collects and retains the tree of the best moves. For the initial assessment of the position the Stockfish engine is used. ArShah allows the users to analyze any position resulted from the opening position, to play with the program. It can be useful for chess players of highly professional category.

There are 3 types of assessment of a chess position: human, engines and mathematical. If the mathematical assessment of any position can be -1, 0 or 1, then the assessments of human and engines range from -1 to 1 and are changeable. The assessments of modern chess engines reaches to the mathematical assessment closer to the end of the game. In any position the best move is almost the only one. There is a proved theorem - if the chess position is assessed correctly, the assessment of the successive move should be the same. Based on these observations, if we built the tree of the best moves through the assessments of a strong chess engine by bringing the assessment of each next move to the starting position, according to the principle of minimax<=maximin, it will result in the mathematical tree of the best moves. ArShah chess cluster system was created according to that principle.

Increasing the number of computers in ArShah system linearly increases the speed of obtaining the final result and improves the quality of the game. Defeats accelerate the learning process in certain versions. In any version, the incorrectly evaluated position is immediately corrected during the game while passing this version or during the perpetual analysis. In Chess, the number of versions of draws obtained from the starting position using a powerful engine is finite and available in real time. In ArShah system, the time for finding a strong move tends to zero in case of a large number of computers or the growth of data storage. When playing against a strong engine the advantage of ArShah becomes obvious in accordance with the growing number of games. In accordance with the growing number of found versions of a draw the assessment of the moves e4, d4, c4, Nf3 in the opening either will grow to show that the White is winning or must be zero proving the draw in chess. Thus, ArShah can solve the chess problem. Through ArShah system mathematical assessment of game power is received: the strength of a game is in direct proportion to the number of storage positions. In case of the improvement of a userâ€™s interface, creation of a number of functions needed for strong chess players, development of online gaming platform, and the growing number of available positions in the storage, ArShah can become the best chess tool in the world, an unsurpassed chess Encyclopedia.

We are open for cooperation with high quality investors and professionals.

ArShah Team: **grig.arshah@gmail.com**