mr LK wrote: "evidence is so overwhelming that chess is a draw"
yep, in a current Iccf tourn at master level where i participate all games are
becoming a draw (2/3 finished and all draws0, and thats with participants rating 'only'
between 2300 and 2400 (but with comp use allowed). And not even all book moves were
boring/solid, i encountered some interesting opening moves in a few games, in one game
clearly a suboptimal line by Black in the French but then even with an advantage of 0.3 I now
can't convert it to a win (in a bishop/pawn endgame. In the current ICCF word championship
the late world champ GM Dronov passed away but for the rest all games are draws.
And yes for correspondence chess it -still- would be interesting to see how
some rules could be modified to reduce the draw problem (other option would
be similar methods as used in TCEC, e.g unbalanced openings or some lousy
openings with both sides to play the same opening (the latter not present
in the current tournament system.
Whereas a general deduction is unlikely, one of the most convincing evidence
imo is coming from the chinese database (confirming what i found earlier);
rules of chess are complicated but nevertheless graph theory may later
give some deeper insights in the game if some academic researchers would
continue to work on that (i recall some work done years ago). There probably
are other games or systems more interesting for the application of graph theory.
https://www.perplexity.ai/search/how-ha ... dBrvVUyQ#0
and this is what chatgpt4 has to say :
### Integrating Network Theory with Deductive Arguments to Explore Chess as a Draw
Using network theory along with deductive reasoning can create a robust framework to analyze whether chess might theoretically end in a draw. Here’s how these two methodologies can be conjoined:
#### 1. **Premises Based on Network Theory**
- **Nodes and Edges**: Considering each chess position as a node and each legal move as an edge, the game of chess can be visualized as a vast network or graph.
- **Finite Network**: Despite the complexity, the chess network is finite, as there are a limited number of possible positions and moves.
- **Recurrent Positions**: Some positions recur, indicating cycles in the network.
#### 2. **Deductive Reasoning from Network Analysis**
- **Starting Assumption**: If chess is a perfect information game with finite possibilities, then theoretically, an optimal play defined path should exist (as per Zermelo's Theorem).
- **Cyclic Paths Analysis**: Deductively, if you can prove that all starting positions either lead to cycles that include previously acknowledged drawn positions or directly result in such positions, then the game can be deduced to be a draw.
#### 3. **Exploring Connectivity for Drawn Networks**
- **Drawn Configuration Identification**: Begin with known drawn positions and states (e.g., insufficient material, perpetual checks). These are like "terminal nodes" in terms of game theory which do not lead to wins.
- **Backward Induction**: Start from these terminal drawn positions and explore backward through the game’s network to see if all paths inevitably lead to one of these positions.
#### 4. **Game Reductions and Simplification**
- **Reductive Deductions**: By applying reductive strategies (simplifying the game to known drawn positions and their reachability), one maps out paths from typical game starting points to these end-states.
- **Choke Points in Network**: Identify critical nodes (positions) that frequently transition to or sustain drawn games. Overwhelming connectivity to drawn nodes could underpin a deductive proof.
#### 5. **Further Deductive Inferences**
- **If there exists at least one non-drawn ascent path**: The entire premise can be challenged. Hence, one needs to deductively prove that every path has its end in a draw under optimal play.
- **Complete game survey**: Deductively, one might argue that given a comprehensive enough analysis or simulation, all play variations can be reduced to outcomes that predominantly link to draw nodes under optimal strategies.
#### 6. **Practical and Theoretical Limits**
- **Ideal Assumptions**: This approach assumes optimal play, which is more theoretical and not often practical.
- **Computational Constraints**: Even with strong deductive arguments and network mapping, the real-world computation and validation of these deductive pathways over the vast chess network pose significant challenges.
### Conclusion
Proving chess is a draw using network theory combined with deductive reasoning presents an intellectually stimulating but formidable challenge. Theoretically, if every game path can be linked to a cycle involving network nodes representing known draw positions, and no new winning strategies emerge from the analysis, the game could be deductively argued as drawn under optimal play. This, however, remains an overarching theoretical exercise, constrained by practical computational capabilities and the infinitude of real-game variables and strategies.
My comment: some interesting insights here in the above, whereby i do not agree with the 'infinitured of
real-game variables and strategies' After all chess is a finite game and draw eg. by 3 pos repetition is a draw,
in fact chatgpt4 in the conclusion seems to contradict itself regarding it stated earlier.
Whether this method would be easier then selective (alfa/beta type) number crunching in checkers
(or Othello) style of course remains a question.
PS as for mr Sanders (?) maybe i overreacted a little, he just asked for a scientific 'explanation' not a proof
(in fact i tried to make a last edit, but this then was refused, a time out, ah well no big deal).
There is a Lewis F Sanders btw, Fide rated 1840 or so. As for explanation(s) that chess is draw, 'scientific' or
not 'fsanders' may not have seen all earlier discussions, there was a thread 'is there a project to solve chess'
with a lot of yes/no arguments about what a real proof should be, and then this thread with also some
arguments from my experience. We have scientific explanations that the earth isn't flat, general relativity
to explain gravity And yep, we there also is a Chinese database showing that in chess White can
not find a fundamental opening advantage from the opening stage, which maybe isn't a
'scientific' explanation but nevertheless imo a significant empirical finding. If i fly in one direction
from London and then after many hours endup in London again, having viewed some curved horizons,
it still maybe doesn't qualify as a 'scientific' explanation that the earth isn't flat (unless many scientists
would do it and write a paper, i suppose). In a similar way inspecting the Chinese database means almost
by deductive reasoning that White can not find a forced win (with other engines e.g Torch
or whatever the tree again would be slightly different but with new analysis the drawish nature
(and thus imo the draw result) would again be confirmed. And for those not believing this there's
my 10 k$ challenge; if i would be rich i would offer a million, no big deal.
So good luck again, and now instead of number crunching you can also try to use network
theory to prove in chess there is a forced win for White (thus having solved the game).
tip: don't try 1.g4 for such a purpose
