Not surprising. What does 0.0344426828806207 of a position look like?
Most people are really bad at understanding sh*te.
Chess will never be solved, here's why
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Jun 23, 2024
0
#9623
tygxc wrote:
@12796
You are really bad at understanding.
Positions with 0 promotions to pieces not previously captured: 2.20031610846976E-06
Positions with 1 promotion to a piece not previously captured: 4.38144194423264E-05
Positions with 2 promotions to pieces not previously captured: 0.000420167757003094
Positions with 3 promotions to pieces not previously captured: 0.00255164793821
Positions with 4 promotions to pieces not previously captured: 0.0108970082461421
Positions with 5 promotions to pieces not previously captured: 0.0344426828806207
Positions with 5 promotions to pieces not previously captured:
Positions with 5 promotions to pieces not previously captured:
Those numbers each look much too small.
@12799
"What does 0.0344426828806207 of a position look like?"
++ 0.0344426828806207 of the total number of legal positions, i.e. 3.4%
@12796
"A tree of 10^30 positions might be"
++ We now have a tree. The root is the initial position. After average 39*2 nodes we reach 112 leaves, all certain draws. This tree is pruned out of a denser tree with 10^17 nodes.
chess may never be solved but someone will eat a chess piece
Jun 23, 2024
0
#9628
tygxc wrote:
@12799
"What does 0.0344426828806207 of a position look like?"
++ 0.0344426828806207 of the total number of legal positions, i.e. 3.4%
Which might be what you meant but not what you said.
What you (originally) said was just:
You are really bad at understanding.
Positions with 0 promotions to pieces not previously captured: 2.20031610846976E-06
Positions with 1 promotion to a piece not previously captured: 4.38144194423264E-05
Positions with 2 promotions to pieces not previously captured: 0.000420167757003094
Positions with 3 promotions to pieces not previously captured: 0.00255164793821
Positions with 4 promotions to pieces not previously captured: 0.0108970082461421
Positions with 5 promotions to pieces not previously captured: 0.0344426828806207
Positions with 5 promotions to pieces not previously captured:
Positions with 5 promotions to pieces not previously captured:
@12805
Again, for clarity:
Positions with 0 promotion to a piece not previously captured: 0.0002200316%
Positions with 1 promotion to a piece not previously captured: 0.0043814419%
Positions with 2 promotions to pieces not previously captured: 0.0420167757%
Positions with 3 promotions to pieces not previously captured: 0.2551647938%
Positions with 4 promotions to pieces not previously captured: 1.0897008246%
Positions with 5 promotions to pieces not previously captured: 3.4442682881%
Positions with 6 promotions to pieces not previously captured: 8.2696484148%
Positions with 7 promotions to pieces not previously captured: 15.2398050245%
Positions with 8 promotions to pieces not previously captured: 21.4853176410%
Positions with 9 promotions to pieces not previously captured: 22.6981234558%
Positions with 10 promotions to pieces not previously captured: 17.1030009909%
Positions with 11 promotions to pieces not previously captured: 8.2743742506%
Positions with 12 promotions to pieces not previously captured: 2.0093687063%
Positions with 13 promotions to pieces not previously captured: 0.0840920694%
Positions with 14 promotions to pieces not previously captured: 0.0005166569%
Positions with 15 promotions to pieces not previously captured: 0.0000006340%
Positions with 16 promotions to pieces not previously captured: 0.0000000001%
Total legal positions per Tromp: 100%
Jun 23, 2024
0
#9630
tygxc wrote:
@12796
You are really bad at understanding.
LOL
"if a piece is not in the box you can't promote to it"
++ That is what Gourion counted: his 10^37
So? You need to learn to read. In my previous post I explained that the set of positions without promotion is only relevant to solving chess variants,
This represents 2.20031610846976E-06 of the 10^44 Tromp positions.
That is what happens in the vast majority of master games or ICCF games.
No, actually. Over 1% of master games are not so. And you cannot deduce from this that ANY legal chess positions are not needed for weak solution of the game.
In fact you could not deduce that ANY legal chess positions are not needed for a weak solution of chess if an oracle told you that only 1 in a million optimal chess games has a non-Gourion position (itself an absurd fiction, but one that would be more relevant).
If a promotion to a piece not previously captured happens in a master or ICCF game, then to a queen.
If an underpromotion happens in a master or ICCF game, then the piece already is in the box.
That is why 10^38 is a better starting position than either 10^44 or 10^37.
If repeating the same mistakes is a valid form of reasoning you are doing great.
Otherwise, you should learn how to read, so that you can find from earlier posts that:
- The set of positions without promotions is woefully inadequate for solving chess. (Exactly like your skillset).
- That "usually" is not a valid step in reasoning.
- That 1 in a million legal chess positions is of the order of 10^38 positions, so any arguments based on "1 in a million" events (extrapolated unreliably from master chess) not being likely and thus to be ignored is kind of stupid (as well as invalid).
Jun 23, 2024
0
#9631
playerafar wrote:
MEGACHE3SE wrote:
playerafar wrote:
Hey shig - tygxc doesn't have to shut up.
What are you doing here?
tbf it would be highly beneficial to all parties involved if tygxc DID shut up.
MEGA - have you noticed that nobody ever agrees with tygxc?
...
Not quite true. @tygxc does sometimes (but not always).
@12807
Again:
Promotions happen in chess games, and neither the Gourion paper nor the file with 10,000 sample positions without promotions to pieces not previously captured exclude those:
they exclude only promotions to pieces not previously captured.
Promotions to pieces not previously captured happen occasionally in master games or ICCF games, but when they happen, then promotions are to a queen.
Underpromotions happen occasionally in master games or ICCF games,
but when they happen, the piece promoted to is already captured.
Underpromotions to pieces not previously captured do not happen in master games or ICCF games, so should not be counted when talking about optimal play by both sides as relevant to weakly solving Chess.
If the Laws of Chess were changed so you could only promote to either a queen,
or a piece previously captured, then all master games and ICCF games would stay the same,
with the same moves and the same outcome.
So the count should be as if the Laws of Chess were thus changed.
Jun 23, 2024
0
#9633
Again, repeated stupid claims is not a valid form of reasoning.
You take tiny samples of not provably optimal play and generalise to a set that is almost incomprehensibly bigger. The number of ICCF positions in particular is MINISCULE! But even the master database (containing play that is up to 1400 points weaker than optimal) only contains around a billion positions. Even ignoring the absurdity of suggesting these are optimal, it's only about 10^37 as many as the set of all legal positions, and perhaps 10^20 times smaller than a proof tree for chess.
@12810
"repeated stupid claims" ++ My assertions are true and valid.
Please show one master game with an underpromotion to a piece not previously captured.
@12810
"10^20 times smaller than a proof tree for chess"
++ Where does that come from?
Schaeffer had a 10^7 proof tree and a 10^14 search tree for 5*10^20 legal Checkers positions.
Jun 23, 2024
0
#9636
Optimissed wrote:
Elroch wrote:
If repeating the same mistakes is a valid form of reasoning you are doing great.
Otherwise, you should learn how to read, so that you can find from earlier posts that:
- The set of positions without promotions is woefully inadequate for solving chess. (Exactly like your skillset).
- That "usually" is not a valid step in reasoning.
- That 1 in a million legal chess positions is of the order of 10^40 positions, so any arguments based on "1 in a million" events (extrapolated unreliably from master chess!) not being likely is kind of stupid.
So far as I can see, Elroch, you're repeating the same mistakes. Firstly, your belief that Zermelo's theorem can be used to prove that chess can be represented mathematically is a childish mistake.
Every knowledgeable person agrees that chess not only can be, but is, represented digitally, thus mathematically. No-one needs to prove it, and no-one uses Zermelo's theorem to do so.
Your problem is that you don't know what a mathematical representation is.
The idea that mathematical induction can be used to map a solution of the simplest linearly solveable games to chess is a childish error. They are mutually incommensurable and therefore the mathematical induction becomes philosophical induction. You are unintelligent not to understand that. Used in that sense, Zermelo's Theorem is bogus.
Here you are exhibiting narcissism by claiming better understanding not only than Zermelo but than everyone who has worked in or studied the field since, while simultaneously revealing your lack of understanding. It's not even as if Zermelo's theorem is difficult - first year undergraduates would have no problem.
Secondly, you actually claimed (twice!) that you could write a program to represent chess mathematically. If you could do that, then you should do it since it would make you world famous. But it was another invention or pretence.
No it wouldn't, because it's no big deal.
Every program that generates a tablebase represents a subset of chess mathematically and generates a strong solution of every position in the tablebase.
Very little change would be needed to make it generate a 32-piece tablebase (it would just be impractical to run and store the output, a strong solution of every chess position). It's not representing chess that is the barrier to solving chess, it is the size of the computation.
The really amusing thing was that you claimed to be supported by intellectual heavyweights such as playerafar, Dio, BigChessplayer, Rattigan and others. How can they possibly lend weight to anyone's arguments? You seem to have no conception as to how ridiculous that is!
They have failed to meet the ultimate criterion of quality - boosting your ego?
You haven't satisfied me that chess can be represented mathematically and your arguments fall apart because of that, since you criticise inductive reasoning in tygxc while taking great pains to unsuccessfully hide the fact that you rely on it yourself. You have no-one with any credentials to back you up and indeed, anyone with credentials isn't going to be seen dead supporting you. What a shame.
I would always prefer to enlighten. Let's try. Do you accept that tictactoe can be represented mathematically? How about checkers? Other games that have been rigorously solved?
Jun 23, 2024
0
#9637
tygxc wrote:
@12810
"repeated stupid claims" ++ My assertions are true and valid.
Please show one master game with an underpromotion to a piece not previously captured.
You seem to have forgotten. I posted this one for you near the start of the thread.
Jun 23, 2024
0
#9638
@Optimissed, here is access to a mathematical representation of all chess positions with 7 or fewer pieces on the board:
And here is a paper about a mathematical representation of checkers to prove its game theoretic value.
https://www.researchgate.net/publication/231216842_Checkers_Is_Solved
Jun 23, 2024
0
#9639
Elroch wrote:
@Optimissed, here is access to a mathematical representation of all chess positions with 7 or fewer pieces on the board:
No it's not.
These positions, for example, are not represented.
Jun 23, 2024
0
#9640
Optimissed wrote:
Sorry, Rattigan, I'm not answering you. You don't have the credentials to make my trouble worthwhile. Neither does Elroch, for that matter. I like intelligent, honest people.
Well many thanks for that. It's bad enough when you answer something I ask you. Starting to answer me when I didn't ask you anything in the first place would be very tedious.
@12796
You are really bad at understanding.
Positions with 0 promotions to pieces not previously captured: 2.20031610846976E-06
Positions with 1 promotion to a piece not previously captured: 4.38144194423264E-05
Positions with 2 promotions to pieces not previously captured: 0.000420167757003094
Positions with 3 promotions to pieces not previously captured: 0.00255164793821
Positions with 4 promotions to pieces not previously captured: 0.0108970082461421
Positions with 5 promotions to pieces not previously captured: 0.0344426828806207
Positions with 6 promotions to pieces not previously captured: 0.0826964841478584
Positions with 7 promotions to pieces not previously captured: 0.152398050244733
Positions with 8 promotions to pieces not previously captured: 0.214853176409515
Positions with 9 promotions to pieces not previously captured: 0.226981234558182
Positions with 10 promotions to pieces not previously captured: 0.171030009908595
Positions with 11 promotions to pieces not previously captured: 0.0827437425059972
Positions with 12 promotions to pieces not previously captured: 0.0200936870633122
Positions with 13 promotions to pieces not previously captured: 0.000840920694087676
Positions with 14 promotions to pieces not previously captured: 5.16656932855929E-06
Positions with 15 promotions to pieces not previously captured: 6.3395210957599E-09
Positions with 16 promotions to pieces not previously captured: 1.34259045827625E-12
Total Tromp positions : 1
"if a piece is not in the box you can't promote to it"
++ That is what Gourion counted: his 10^37.
This represents 2.20031610846976E-06 of the 10^44 Tromp positions.
That is what happens in the vast majority of master games or ICCF games.
If a promotion to a piece not previously captured happens in a master or ICCF game, then to a queen.
If an underpromotion happens in a master or ICCF game, then the piece already is in the box.
That is why 10^38 is a better starting position than either 10^44 or 10^37.