Free The Immortal Game by David Shenk Page A

moves.

    Each Knight is restricted to two possible first moves. 2 x 2 = 4 moves.
    (The Rooks, Bishops, King, and Queen are all blocked and have no chance of moving on the first move.)
    Black has the same twenty possible moves with his first response.
    But with chess, the number of legal moves is only a small part of the equation. Because while there are only forty possible first moves per pair of players, there are actually
400
possible board positions inherent in those moves. That’s because for every one of White’s twenty moves, Black’s response can lead to twenty separate positions. If White moves his Pawn to a3: Black can move Pawn to a6, or Pawn to a5, or Pawn to b6, or Pawn to b5, or Pawn to c6, or Pawn to c5, or Pawn to d6, or Pawn to d5, or Pawn to e6, or Pawn to e5, or Pawn to f6, or Pawn to f5, or Pawn to g6, or Pawn to g5, or Pawn to h6, or Pawn to h5, or Knight to a6, or Knight to c6, or Knight to f6, or Knight to h6.
    If White moves his Pawn to a4, Black can move Pawn to a6 or Pawn to a5…
    If White moves his Pawn to b3, Black can move Pawn to a6 or Pawn to a5…
    —and so on up to 400 distinct positions. To the outsider, the distinctions among all of these early board positions may seem negligible, but the seasoned chess player knows from hard-won (or rather hard-
lost
) experience that every such variation is critically distinct, that the dynamics of the game depend entirely on the exact position of the pieces. Just as an infinitesimal change in the interaction of H 2 O molecules will change their structure from water to ice, the movement of any Pawn just one square forward can drastically alter the course of a hard-fought chess game.
    Think of it as chess chemistry: each player moving just once can yield any one of 400 distinct chess “molecules,” each with its own special properties.
    In the second move, the number of possible chess molecules shoots up almost past belief: for every one of those 400 positions, there are as many as 27 options that each player has for a second move. It’s not quite so simple a calculation as with the first move, but the total number of distinct board positions after the second complete move (two moves per player) is—you’ll have to trust the number crunchers on this—71,852. After just two moves each, the power of geometric progression is already bearing down hard on both players. Already, it is nearly impossible for any human to track all the possible chess molecules.
    After three moves each, the players have settled on one of approximately nine million possible board positions.
    Four moves each raises it to more than 315 billion.
    The game has barely started and already we’re into the hundreds of billions of game sets. From there, it’s not so difficult to imagine how easily the number of discrete board positions spirals into the stratosphere as the game winds on. The total number of unique chess games is not literally an infinite number, but in practical terms, the difference is indistinguishable. It is truly beyond comprehension—“barely thinkable,” as one expert puts it—and beyond human or machine capacity to play through them all. The estimated total, in scientific notation, is 10 120 .
    With all the zeros laid out, that’s
1,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000, 000,000,000
games.
    (In conversational English, it is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion games.)
    By way of comparison, the total number of electrons in the universe is, as best as physicists can determine, 10 79 . A chessboard, bizarre as it sounds, is pregnant with vastly more possibility.
    Thus the unsettling term
near-infinite
is not inappropriate. Of course there’s no such thing in the literal sense (perhaps a physicist or mathematician will correct me on this point), but in subjective human reality, the