The Mysterious Math of Chess: Probabilities and Possibilities

  • Context: Undergrad 
  • Thread starter Thread starter cepheid
  • Start date Start date
  • Tags Tags
    Chess Probabilities
Click For Summary

Discussion Overview

The discussion centers around the mathematical complexities and probabilities associated with chess moves and games. Participants explore the implications of claims regarding the number of possible chess moves compared to the number of atoms in the universe, as well as the estimation of acceptable games based on various rules and strategies.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the interpretation of "total number of possible chess moves," suggesting it may refer to the number of different chess games rather than individual moves.
  • Another participant notes that the number of games is finite due to rules like the 3-move repetition and the 50-move rule, indicating a lack of connection to probability theory.
  • A participant mentions the complexity of chess, referencing the estimated number of legal positions and game-tree complexity, citing Claude Shannon's calculations.
  • Some participants discuss the concept of acceptable games and the challenges in estimating their number, with one suggesting the use of genetic algorithms for this purpose.
  • There is a proposal that the number of ways to play chess could be infinite, as checkmate scenarios are not included in the count of possible moves.
  • Another participant draws a comparison between the number of combinations in chess and the number of distinct atoms in the universe, suggesting that the potential configurations of the universe could vastly exceed physical counts.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the original claim regarding chess moves and the implications of game complexity. There is no consensus on the estimation of acceptable games or the relationship between chess moves and atomic configurations.

Contextual Notes

Participants highlight limitations in defining "acceptable games" and the assumptions underlying the estimation of possible moves and configurations. The discussion reflects varying interpretations of rules and mathematical principles without resolving these ambiguities.

cepheid
Staff Emeritus
Science Advisor
Gold Member
Messages
5,197
Reaction score
38
Today my little cousin (age 10) showed me a line from his book (The Usborne Guide to Playing Chess, or something like that) that claimed that the total number of possible chess moves is greater than the total number of atoms in the known universe! I don't remember the exact wording, so I guess we'll never know exactly what they meant by "total number of possible chess moves". Still, it seems crazy to me! It's a question of probability right? How many permuations are possible for x number of chess pieces on a board with y number of squares, given that each piece is governed by a certain set of rules. Can anyone shed some light on this?
 
Physics news on Phys.org
I wonder if it was saying that the number of different chess games is greater than the number of atoms in the universe? The number of games is finite because of things like the 3-move repetition rule and the 50-move rule that comes into play when no pawns are advanced and no material is captured. I don't see any obvious link to probability theory.
 
That sounds possible, and it makes more sense.
 
A set theorem thing. Take the same number of atoms that are not restricted in degrees of freedom and you get many more possible outcomes.
 
Well as I know as a chess player, we have a lot of technics of playing, each with lots of possible ending that are always growing by the play of "the experts" of this game.
It means that we just accept a moving as a part of game, if there are reasons of "being a good possibility". If not, you will be checkmated very soon! and it is not an acceptable "game".
As you know, we have 10 princibles of starting in chess, that reasons in about 50(or more) technics of playing.
Also in every day of chess life, we see a lot of new "games" by the experts. So it seems that we haven't arrived to the limits of this game yet!
But I haven't seen any any estimations about the number of "acceptable games".
It should be a hard work!
Have any idea?!
 
Last edited:
The Wikipedia article about chess mentions some of the things that are discussed in this thread. This is a part of that article:

The number of legal positions in chess is estimated to be between 10^43 and 10^50, with a game-tree complexity of approximately 10^123. The game-tree complexity of chess was first calculated by Claude Shannon (father of information theory) as 10^120, a number now known as the "Shannon number". Typically an average position has thirty to forty possible moves, but there may be as few as zero (in the case of checkmate or stalemate) or as many as 218.
 
yes the acceptable game that would ingnore a lot of moves, but ! but if say the possible of ways play chess could be infinite since checkmate or not is not include.d

alternative atom have they basic principle rules, and can limit to a n possible of ways
 
Of course you are comparing the number of combinations to the number of physical things. If you take every atom in the universe as individual and distinct and you can swap any two atoms around as a single move then given you can make as many moves as you want how many possible set ups of the universe do you think would be possible?

Answer, a lot more than the number of anything physical we know about.
 
Another question!:
Can anyone introduse a neat way to estimate the number of acceptable games?
S
uppose that we can just accept the games with more than 50 moves (for each player) that has enough logistic reasons.
We can do it by a "genetic algorithm"!
Anyone expert in it?!
 

Similar threads

Undergrad How many possible plays in first 10 moves of a game of Chess?
  • · Replies 22 ·
Replies
22
Views
15K
Is chess fundamentally harder to "effectively" solve than Go?
  • · Replies 29 ·
Replies
29
Views
5K
How Do Players Cheat in Chess?
  • · Replies 42 ·
2
Replies
42
Views
5K
Undergrad Probability to get a certain number or less by throwing two 6-faced die
  • · Replies 6 ·
Replies
6
Views
3K
High School Baccarat math and beating the edge
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Ways to put n balls in m boxes such that exactly k boxes are empty?
  • · Replies 29 ·
Replies
29
Views
8K
Undergrad Does Dark Energy drive up Entropy?
  • · Replies 7 ·
Replies
7
Views
2K
Challenge Math Challenge Thread (October 2023)
  • · Replies 25 ·
Replies
25
Views
5K
What is the complexity of possible chess game combinations?
  • · Replies 10 ·
Replies
10
Views
4K
Probability of Pairings in Chess Game
  • · Replies 3 ·
Replies
3
Views
10K