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The game tree size is the total number of possible games that can be played: the number of leaf nodes in the game tree rooted at the game's initial position.. The game tree is typically vastly larger than the state space because the same positions can occur in many games by making moves in a different order (for example, in a tic-tac-toe game with two X and one O on the board, this position ...
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
Some correspondence organizations draw a distinction in their rules between utilizing chess engines which calculate a position in real time and the use of a precomputed database stored on a computer. Use of an endgame tablebase might be permitted in a live game even if engine use is forbidden.
Apart from being a trend strength gauge, ATR serves as an element of position sizing in financial trading. Current ATR value (or a multiple of it) can be used as the size of the potential adverse movement (stop-loss distance) when calculating the trade volume based on trader's risk tolerance. In this case, ATR provides a self-adjusting risk ...
Claude Shannon. The Shannon number, named after the American mathematician Claude Shannon, is a conservative lower bound of the game-tree complexity of chess of 10 120, based on an average of about 10 3 possibilities for a pair of moves consisting of a move for White followed by a move for Black, and a typical game lasting about 40 such pairs of moves.
The total number of possible games can be estimated from the board size in a number of ways, some more rigorous than others. The simplest, a permutation of the board size, (N) L, fails to include illegal captures and positions. Taking N as the board size (19 × 19 = 361) and L as the longest game, N L forms an upper limit. A more accurate limit ...
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PWMs are often represented graphically as sequence logos.. A position weight matrix (PWM), also known as a position-specific weight matrix (PSWM) or position-specific scoring matrix (PSSM), is a commonly used representation of motifs (patterns) in biological sequences.