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@ -184,9 +184,9 @@ Chess stats are pretty [interesting](interesting.md). Thanks a lot e.g. to Liche
{ Some chess world records are here: https://timkr.home.xs4all.nl/records/records.htm. ~drummyfish }
**Number of possible games** is not known exactly, Shannon estimated it at 10^120 (lower bound, known as *Shannon number*). Number of possible games by plies played is 20 after 1, 400 after 2, 8902 after 3, 197281 after 4, 4865609 after 5, and 2015099950053364471960 after 15.
**Number of possible games** is not known exactly, Shannon estimated it at 10^120 (lower bound, known as *Shannon number*). Number of possible games by plies played is 20 after 1, 400 after 2, 8902 after 3, 197281 after 4, 4865609 after 5, and 2015099950053364471960 after 15 ([OEIS A048987](https://oeis.org/A048987)).
Similarly the **number of possibly reachable positions** (position for which so called *proof game* exists) is not known exactly, some upper estimates have been made, lower bounds are much harder to set. The estimates are placed around 10^40 or 10^50 at most. [Here](https://tromp.github.io/chess/chess.html) is a site that gives a proven upper estimate of 45193640626062205213735739171550309047984050718 (2^155), also providing a more precise one of 7728772977965919677164873487685453137329736522 (~10^45.888, ~2^152) which was however proven with a program that's a bit obscure and less trustworthy. Numbers of possible positions by plies are 20 after 1, 400 after 2, 5362 after 3, 72078 after 4, 822518 after 5, and 726155461002 after 11.
Similarly the **number of possibly reachable positions** (position for which so called *proof game* exists) is not known exactly, some upper estimates have been made, lower bounds are much harder to set. The estimates are placed around 10^40 or 10^50 at most. [Here](https://tromp.github.io/chess/chess.html) is a site that gives a proven upper estimate of 45193640626062205213735739171550309047984050718 (2^155), also providing a more precise one of 7728772977965919677164873487685453137329736522 (~10^45.888, ~2^152) which was however proven with a program that's a bit obscure and less trustworthy. Numbers of possible positions by plies are 20 after 1, 400 after 2, 5362 after 3, 72078 after 4, 822518 after 5, and 726155461002 after 11 ([OEIS A083276](https://oeis.org/A083276)).
**Shortest possible checkmate** is by black on ply number 4 (so called *fool's mate*); in fact there are 8 different games that can end like this. As of 2022 the **longest known forced checkmate** is in 549 moves -- it has been discovered when computing the Lomonosov Tablebases. EDIT: now it seems there is one in 584 moves. Please note this: there most likely exist much longer forced mates, these are just the KNOWN ones. Consider e.g. that if black blunders a queen in the opening, the game is very likely a theoretical win for white since then, i.e. a forced mate, and with perfect play black can probably resist for very long. However such situations are too complex to explore fully.
@ -394,7 +394,9 @@ Again, Lichess only analyzed the first 150 moves and here it marked practically
What is **the rarest move**? Some [YouTube](youtube.md) video tried to investigate this with the help of Lichess database. Things that immediately come to mind like en passant checkmates and checkmates by promoting to a knight are rare but not insanely rare. A crazily rare kind of move, which only appeared ONCE in the whole database, was a doubly disambiguatated (i.e. with the necessary specification of both rank and file of the bishop) checkmate by a bishop (specifically Bf1g2#, occurring in a 2022 game) -- this is rare because to need a double disambiguation for a bishop move it is necessary to underpromote two pawns to a bishop and then place them correctly. Yet rarer moves, which NEVER appeared in the database, were a doubly disambiguated knight checkmate with capture and doubly disambiguated bishop checkmate with capture, latter of which was judged less likely and therefore probably the rarest move ever.
Anyway, you can try to derive your own stats, there are huge free game databases such as the Lichess [CC0](cc0.md) database of billions of games from their server.
The maximum number of **black and white queen pairs placed on an empty board so that none is attacked** is 12 (that is 12 white queens and 12 black ones). This number as a [function](function.md) of board size is the [OEIS sequence A250000](https://oeis.org/A250000) and starts like this: 0, 0, 1, 2, 4, 5, 7, 9, 12, 14, 17, 21, 24, 28, 32, ...
Anyway, you can try to derive your own stats, there are huge free game databases such as the Lichess [CC0](cc0.md) database of billions of games from their server, as well as powerful [free software](free_software.md) engines allowing you to arrange and automatically play out hundreds of thousands of games. Why not take the chance?
{ TODO: Derive stats about the best move, i.e. for example "best move is usually by queen by three squares" or something like that. Could this actually help the play somehow? Maybe could be used for move ordering in alpha-beta. ~drummyfish }