How many chess games are possible? - Numberphile

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Cites user1583209 · 2017-02 · Chess Stack Exchange · on “What is the number of chess positions for each move?”

You are misusing the word "probability" in your question. 10 to the power 120 is known as the Shannon number and is a lower bound for the game-tree complexity (number of different games of chess). This has nothing to do with probability. Also this number of different games is not the same as the number of possible chess positions (which is estimated as 10^43). If you look at the starting position in chess, each player has 20 possible moves (16 with the pawns and 4 with the knights). So the number of possible games of 1 move (2 plies, i.e. one white move and one black move) would be 20*20 = 400 already. Now the number of possible moves increases initially because your pieces get more space. T

Cites Folling · 2017-08 · Chess Stack Exchange · on “Possible chess positon after X ply?”

I've started to code my own little engine recently and am now working on a perft function which simply sees how many moves there are. Trying to get correct results I searched online for the correct amount of possible positions after e.g. 4 moves. Now according to these sources: [LINK] It should be 197281 possible positions after 4 moves, and I can reach that in my code! But switching a bit around in my code to get some optimization which seemingly shouldn't change anything, I get a different number: 197742 Now I would think that is wrong but I have found different sources again, claiming that is in fact correct: [this video] So, which one is it? 197742 or 197281 possible positions after 4 moves?

Cites Ken Wei · 2017-12 · Chess Stack Exchange · on “Complexity of critical positions”

I'm guessing that by complexity, you mean an estimate for the number of legal positions that aren't 'clearly' lost by some measure (otherwise the answer is exponential, despite the addition of your constraint), as if to build a tablebase that can play through non-trivially lost/won positions (ignoring the technicalities of the missing tablebase problem that would arise...). One estimate of the number of 'sensible' chess games [this video] ; 3^(40*2) ~ 10^40 seems reasonable; however, this answer doesn't work in this setting, because of the way your question is phrased. I claim that our hypothetical 32-man, 'non-trivial' tablebase is composed mostly of positions arising from games that would have

Cites Sujit Bhattacharyya · 2020-03 · Chess Stack Exchange · on “Database of every possible move in chess”

Hey, I am new in this community and I'm from MathStack. Just to share that there are fewer atoms in the Universe than the number of Chess Games possible in a chess match. Try Shannon Number ( [this video] ).

Cites Nathan · 2021-03 · Chess Stack Exchange · on “How many sensible games of chess are there?”

Analytic procedures for estimating the number of possible games of chess typically reason that on each ply, a player has some limited number of sensible options, O , and the average game of chess lasts about p plys. Thus, there are about O^p games of chess. Choosing O =3 and p =80, you get something like 1.5x10^38. This is the strategy taken by Shannon [LINK] and others [this video] . However, such procedures are likely to mis-estimate the true number of sensible games. Chess games are frequently characterized by long sequences of forcing moves, where there is only one option worth considering. Further, the estimated number of options for each ply seems pulled out of thin air. Thus, the true numb