How many unique games of chess can be played?? A quadrillion, maybe a googol (10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000) well it's more than that. A close estimation of the number was found in 1950 by the, "father of information theory", Claude Shannon. He estimated the lower bound on the game-tree complexity of chess to be about 10¹²⁰. In his paper "Programming a Computer for Playing Chess " he explains:

With chess it is possible, in principle, to play a perfect game or construct a machine to do so as follows: One considers in a given position all possible moves, then all moves for the opponent, etc., to the end of the game (in each variation). The end must occur, by the rules of the games after a finite number of moves (remembering the 50 move drawing rule).Each of these variations ends in win, loss or draw. By working backward from the end one can determine whether there is a forced win, the position is a draw or is lost. It is easy to show, however, even with the high computing speed available in electronic calculators this computation is impractical. In typical chess positions there will be of the order of 30 legal moves. The number holds fairly constant until the game is nearly finished as shown [...] by De Groot, who averaged the number of legal moves in a large number of master games. Thus a move for White and then one for Black gives about 10³ possibilities. A typical game lasts about 40 moves to resignation of one party. This is conservative for our calculation since the machine would calculate out to checkmate, not resignation. However, even at this figure there will be 10¹²⁰ variations to be calculated from the initial position. A machine operating at the rate of one variation per micro-second would require over 10⁹⁰ years to calculate the first move!

Later Dutch computer scientist Victor Allis estimated it to be closer to 10¹²³

This is a huge number. For comparison note that some have estimated that the total number of atoms in the observable universe is somewhere around 10⁷⁹to 10⁸¹

The Gaussian Eliminators

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