Число Шеннона

Число́ Ше́ннона — оценочное минимальное количество неповторяющихся шахматных партий, вычисленное в 1950 году американским математиком Клодом Шенноном. Составляет приблизительно 10120. Динамику роста этого числа можно проследить на примере обычной шахматной партии: для первого хода у обеих сторон есть 40 различных вариантов, для второго — ещё 676, для третьего — еще 576. Таким образом, всего на третьем ходу партии существует 40*676*576≈15,5 млн различных вариантов партии. Если исключить откровенно глупые ходы, то это число можно сократить на 10—20 %.

Вычисление числа Шеннона описано в работе «Программирование компьютера для игры в шахматы» (англ. «Programming a Computer for Playing Chess»), опубликованной в марте 1950 года в журнале Philosophical Magazine и ставшей одним из фундаментальных трудов в развитии компьютерных шахмат как дисциплины. В основу вычислений легло предположение о том, что каждая игра длится в среднем 40 ходов и на каждом ходе игрок делает выбор в среднем из 30 вариантов.[1] Для сравнения — количество атомов в наблюдаемой Вселенной составляет по разным оценкам от 1079 до 1081, то есть в 1040 раз меньше числа Шеннона.

Кроме этого, Шеннон высчитал и количество возможных позиций, равняющееся примерно:

Это число, однако, включает также ситуации, исключаемые правилами игры и поэтому недосягаемые в дереве возможных ходов. В настоящее время появился ряд работ, уточняющих[2] или даже опровергающих это число[3].

Примечания

  1. ↑ У больших чисел громкие имена Архивная копия от 28 августа 2010 на Wayback Machine, vokrugsveta.ru  (Дата обращения: 4 сентября 2010).
  2. ↑ Victor Allis[англ.]. Searching for Solutions in Games and Artificial Intelligence (англ.). — Ph.D. Thesis, University of Limburg, Maastricht, The Netherlands, 1994. — ISBN 9090074880. Архивировано 7 марта 2005 года.
  3. ↑ John Tromp. John's Chess Playground (2010). Дата обращения: 4 сентября 2010. Архивировано из оригинала 9 мая 2012 года.

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