3-ply position graph


I'm trying to imagine the finite graph of all positions in chess. Due to the sheer number of possible positions, it is impossible with current technology to build an exhaustive database. Such a database would require more than 100 zetabytes of storage.

But even if we can't store the positions exhaustively, would it be possible to count winning lines for each side? That is, can the number of arrows going to Draw, to Black Won, and to White Won be determined mathematically? And if so, would White have more winning arrows than Black?

  • So your question is: when considering all possible "final positions" in chess, what is the white win / draw / black win ratio? – Rauan Sagit Mar 28 '14 at 11:15
  • Yes. More interestingly, is there balance? Whites make their step firsts, is it equal? Probably, it is not possible, but, better than ratio, precise numbers. – Anomalous Awe Mar 28 '14 at 11:44
  • I think the total number of "drawing positions" is probably close to the total number of non-checkmate positions, since intuitively it seems like you should be able to engineer a line that ends in a draw by threefold repetition at the vast majority of possible positions. – Henry Keiter Mar 28 '14 at 15:38
  • An interesting problem for a computer program would be what is the total number of final checkmate positions for a given set of pieces. – user11382 Jul 23 '17 at 22:58

Theoretically, we don't know, because we can't calculate it yet. Chess is not solved as an universal and general problem and we don't know that if two gods play chess in an infinite manner, which color wins or maybe it's just a draw.

Statistically, you can gather data from chess databases in websites, tournaments and computer tools to have an estimation. For example see this online databases.

  • Probably, correct should be "We can't calculate, yet". – Anomalous Awe Mar 28 '14 at 12:19

The answer to this question is most probably highly influenced by the style of play (i.e. perfect play, grandmaster-level, intermediate level, junk-play, or pure-random moves).

In high-quality play between chess engines (grandmaster level) I believe the ratio is about 35% (White wins), 41% (Draw), and 24% (Black wins). This is based on referenced information from Wikipedia.

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