Update

chess.md

@@ -1,6 +1,6 @@
 # Chess
 
-Chess is an old two-player board [game](game.md), perhaps most famous and popular among all board games in history. It is a [complete information](complete_information.md) game that simulates a battle of two armies on a 64x64 board with different battle pieces. Chess has a world-wide competitive community and is considered an intellectual sport but is also a topic of active research (chess is unlikely to be ever solved due to its non-trivial rules combined with enormous state space, Shannon estimated the number of possible games at 10^120) and programming (many chess engines, [AI](ai.md)s and frontends are being actively developed).
+Chess is an old two-player board [game](game.md), perhaps most famous and popular among all board games in history. It is a [complete information](complete_information.md) game that simulates a battle of two armies on a 64x64 board with different battle pieces. Chess has a world-wide competitive community and is considered an intellectual sport but is also a topic of active research (as the estimated number of chess games is bigger than [googol](googol.md), it is unlikely to ever be solved) and [programming](programming.md) (many chess engines, [AI](ai.md)s and frontends are being actively developed).
 
 { There is a nice black and white indie movie called *Computer Chess* about chess programmers of the 1980s, it's pretty good, very oldschool, starring real programmers and chess players, check it out. ~drummyfish }
 
@@ -15,8 +15,6 @@ Chess is an old two-player board [game](game.md), perhaps most famous and popula
 - It is a source of many interesting [mathematical](math.md) and programming challenges.
 - It seems to strike the right balance of simplicity and complexity, it is very simple but not so trivial as to be ever solved in a foreseeable future.
 
-What is the longest possible chess game? It depends on the exact rules and details we set, for example if a 50 move rule applies, a player MAY claim a draw but also doesn't have to -- but if neither player ever claims a draw, a game can be played infinitely -- so we have to address details such as this. Nevertheless the longest possible chess game upon certain rules has been computed by [Tom7](tom7.md) at 17697 half moves in a paper for [SIGBOVIK](sigbovik.md) 2020.
-
 ## Chess In General
 
 Chess evolved from ancient board games in India in about 6th century. Nowadays the game is internationally governed by **FIDE** which has taken the on role of an authority that defines the official rules: FIDE rules are considered to be the standard chess rules. FIDE also organizes tournaments, promotes the game and keeps a list of registered players whose performance it rates with so called Elo system –⁠ based on the performance it also grants titles such as **Grandmaster** (GM, strongest), **Internation Master** (IM, second strongest) or **Candidate Master** (CM).
@@ -53,6 +51,24 @@ Playing strength is not the only possible measure of chess engine quality, of co
 
 { Nanochess is actually pretty strong, in my testing it easily beat [smallchesslib](smallchesslib.md) Q_Q ~drummyfish }
 
+## Stats
+
+Chess stats are pretty [interesting](interesting.md).
+
+**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.
+
+Similarly the number of possible reachable positions is not known exactly, it is estimated to at least 10^40 and 10^50 at most. Numbers of possible positions by plies is 20 after 1, 400 after 2, 5362 after 3, 72078 after 4, 822518 after 5, and 726155461002 after 11.
+
+Shortest possible checkmate is by black on ply number 4 (so called *fool's mate*). As of 2022 the longest known forced checkmate is in 549 moves -- it has been discovered when computing the Lomonosov Tablebases.
+
+Average game of chess lasts 40 moves. Average [branching factor](branching_factor.md) (number of possible moves at a time) is around 33.
+
+White wins about 38% of games, black wins about 34%, the remaining 28% are draws.
+
+What is the **longest possible game**? It depends on the exact rules and details we set, for example if a 50 move rule applies, a player MAY claim a draw but also doesn't have to -- but if neither player ever claims a draw, a game can be played infinitely -- so we have to address details such as this. Nevertheless the longest possible chess game upon certain rules has been computed by [Tom7](tom7.md) at 17697 half moves in a paper for [SIGBOVIK](sigbovik.md) 2020.
+
+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.
+
 ## Variants
 
 Besides similar games such as [shogi](shogi.md) there are many variants of chess, i.e. slight modifications of rules, foremost worth mentioning is for example chess 960. The following is a list of some variants: