@8997
"my figures explain the facts in your example reasonably well" ++ No they do not.
"I could easily fit them exactly" ++ Well do so and let us see.
"observed facts in any of the four of the examples I posted"
++ Are the 4 positions draws? No
Is this a tournament? No
Is this a sufficiently large tournament? No
Is this a sufficiently strong tournament? No
Is this relevant to weakly solving Chess? No
"we have no way of observing them?" ++ We have.
"The value 24 is the expected value given my assumed probability distribution"
++ as there were only 15 decisive games, your assumed probability distribution is wrong
"the actual number of games with 0 blunders must be exactly the expected number from the distribution" ++ Indeed, the task is to explain the observed facts.
"it also produces a proof that chess is a win" ++ No, it does not.
"exactly 83 games with the wrong result and that's not 15 either"
++ So your distribution is wrong.
"Assuming that chess is a win would minimise the differences"
++ No, it is not consistent with the observed facts.
"there are many sequences of 3 that are" ++ But not all are.
"Your proposals are to use SF15 v SF15" ++ No. My proposal to weakly solve Chess is to use SF to calculate until the 7-men endgame table base.
"SF15 is about the strongest player that ever was." ++ ICCF is stronger: human + SF.
Otherwise there would be no ICCF GM: John Doe would be World Champion.
"There were 46 games" ++ There were no games.
There were continuations from 4 irrelevant won positions. There was only 1 entity playing.
"What's the sufficiently large"
++ 136 games and 17 entities like ICCF WC Finals is sufficiently large.
"a Poisson distribution to magically appear?" ++ A Poisson distribution does not 'magically' appear. It is there, but it shows more clearly with a larger sample size.
"They were designed to test the plausibility of a Poisson distribution" ++ Bad design.
"But we've already shown that a Poisson distribution doesn't apply." ++ No, not at all.
"the blunder rates show a marked increase with the number of men from such positions"
++ Most errors should occur with around 26 men, as Chess is most complex then.
"I guess it would be conservatively closer to 10 from the initial position"
++ The initial position has been extensively studied.
"change in the 50 move rule" ++ The 50-moves rule plays no role. The weak solution of Chess reaches a draw without triggering the 50-moves rule. We know that from the perfect games with 0 errors of ICCF WC draws.
"it may have a considerable effect on perfect play"
++ The 50-moves rule has no effect at all on perfect play from the initial position.
Most perfect games are drawn before move 50.
@8995
"[reinserted:You don't expect ]random results from a probability distribution to precisely follow the expected values"
++ I expect the theory to explain observed facts.
Can you stop trying to change the arguments to which you respond by snipping out the bits you don't like please? It's a lot easier for you to use the quote facility than for others to reinsert the omitted bits.
So long as you don't expect random results from a probability distribution to precisely follow the expected values, my figures explain the facts in your example reasonably well. (I could easily fit them exactly in any number of arbitrarily assumed distributions as you do.)
Your theory fails to explain the observed facts in any of the four of the examples I posted. Why would you expect it to correctly predict the facts in the example you posted where we have no way of observing them?
"Your same argument would show Chess is a win." ++ No it does not. There is no consistent way to explain the observed results assuming Chess a win for either white or black.
Yes it does.
Your argument was
(*) "Games with 0 errors: 24" ++ Then Chess is a draw. There were only 15 decisive games.
The value 24 is the expected value given my assumed probability distribution. Your argument holds only if you ignore the bit you snipped out of my post this time. You are assuming that the actual number of games with 0 blunders must be exactly the expected number from the distribution.
If you do that then it also produces a proof that chess is a win, because there would then be exactly 83 games with the wrong result and that's not 15 either.
There is a consistent way to explain the observed results by assuming the actual results in your sample vary from the precise expectations in the distribution. Assuming that chess is a win would minimise the differences in that case, but as I said earlier that can't be taken as a reliable indicator of the theoretical result of chess.
"If you applied your argument to throwing a die and tried it out youl'd reach the conclusion that the numbers 1-6 couldn't be equally probable" ++ No, if the die is not loaded then the results will get closer to 1/6 each the more throws are observed.
If it does not, then the conclusion is the die is loaded and we can calculate how much.
"because that would mean the die should always land on 3½ and it didn't."
++ That is your thinking error, not mine.
Wrong way round as usual. That is your thinking in your proof (*) above. I nowhere use it.
"Any sequence of two real numbers is monotonic." ++ But every sequence of 3 is not.
False actually - there are many sequences of 3 that are. Supremely irrelevant at any rate because you gave a sequence of 2.
"blunder rates @Cobra91 measured"
++ That was not a sufficiently large, sufficiently strong tournament.
Your proposals are to use SF15 v SF15. It was SF15 v SF15. SF15 is about the strongest player that ever was.
There were 46 games. There's little doubt that the blunder rates would be about the same if I repeated the exercise 10 times. What's the "sufficiently large" at which you expect a Poisson distribution to magically appear?
"[reinserted: You may not find it plausible, but it's in accordance with the blunder rates @Cobra91 measured using Syzygy fr]om the example games I posted." ++ All 4 examples are irrelevant to weakly solving Chess.
They were designed to test the plausibility of a Poisson distribution of blunders in chess. Whether they might occur in any particular process for weakly solving chess or your process for weakly not solving chess doesn't appear to be related to that. (They do occur in the Syzygy process for weakly solving most of 7 man chess from an initial position).
"So are you giving up on your Poisson distribution?" ++ No.
How surprising!
"A Poisson distribution is not monotonic except for values near λ=0 which doesn't fit this case."
++ It fits the case as calculated. If the tournament is sufficiently large (136 games) and with a sufficient number of entities competing (17 players), then statistics are applicable.
If the tournament is sufficiently strong like the ICCF WC Finals then λ is close to zero.
A Poisson distribution with λ close to 0 will certainly fit the WDL statistics for the match in question (I should have chosen my wording more carefully). There are an infinite number of other distributions that would also exactly fit.
But we've already shown that a Poisson distribution doesn't apply.
An average blunder rate λ near 0 per game doesn't fit with the average blunder rates in my games. There the mean blunder rate (corresponding to λ) is 2.33.
From running many examples, that appears to be in line with other closely matched ply count 0 positions that can be checked with Syzygy. But the salient point is the blunder rates show a marked increase with the number of men from such positions. I guess it would be conservatively closer to 10 from the initial position.
That applies to SF15 v SF15 games under FIDE competition rules (as you say you plan to use to not solve chess) but the games in your tournament might be expected to have similar attributes. They're effectively SF15 v SF15 and the change in the 50 move rule, while it may have a considerable effect on perfect play. would be mostly opaque to a player at SF15's level.