Current status: 4 most pouplar openings. The whole Queen's Gambit is statistically bad for black. 
List of 3-ply openings, transitions and statistical results
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Jul 28, 2017
0
#2
Jul 28, 2017
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#3
Phoenyx75 wrote:
It also seems that your stats are saying that when white plays 1.e4, black playing 1...c5 is better statistically then 1...e5. Is that what your analysis shows?
Yes, right, the statistical evaluation +0.24 is definitely better for black than +0.44. Also the Sicilian is sharper (for both sides). 
Jul 29, 2017
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#4
Phoenyx75: The formulas are here:
https://www.chess.com/forum/view/chess-openings/statistical-sharpness-and-evaluation
In the case of the Queen's Gambit, W = 35.8%, B = 20.1%. So, sev = W/B - 1 = +0.78. These formulas are convenient since sev is comparable to engine evaluations.
Jul 29, 2017
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#5
The problem with evaluations after a few moves is that human planning and seeing possibilities for tactics and strategies may be easier from a position the computers aren't happy with.
If the formula he used is correct, then it doesn't mean anything.
sev + 1 = ratio of white wins to black wins meaning white takes sev/(sev + 1) of all decisive games. That should probably just be posted.
I do like some sort of number to represent wins, moves, and draws but the problem with this formula is its range goes from infinity for maximum white advantage and -1 for maximum black advantage.
White wins 95% of the time: +18
White wins 5% of the time: - 0.95
If you wan some sort of score consider white's average advantage (or negative for disadvantage) in a 10 game match.
So in this case it is (W - B)*10 giving white an advantage of +1.6
It might be cool to come up with something that takes draws into account though.
Jul 30, 2017
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#7
Lol, Vigor, the great mathematician, is just using a forumula designed to give numbers that look that engine evaluations. Advanced mathematics this multiplying and dividing stuff isn't it. For some reason the parable of the emperor's new clothes comes to mind.
Jul 30, 2017
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#8
TwoMove wrote:
Lol, Vigor, the great mathematician, is just using a forumula designed to give numbers that look that engine evaluations. Advanced mathematics this multiplying and dividing stuff isn't it. For some reason the parable of the emperor's new clothes comes to mind.
Higher mathematics are not necessary in this case.
Jul 30, 2017
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#9
Differentiation2 wrote:
xman720 wrote:
If the formula he used is correct, then it doesn't mean anything.
If black has a higher win percentage, we use 1-sh2/sh1 instead of sh1/sh2-1
Right, otherwise it would be non-symmetric for white and black.
Jul 30, 2017
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#10
xman720 wrote:
It might be cool to come up with something that takes draws into account though.
The draws are taken into account by the sharpness values.
Phoenyx75 wrote:
xman720 wrote:
If the formula he used is correct, then it doesn't mean anything.
sev + 1 = ratio of white wins to black wins meaning white takes sev/(sev + 1) of all decisive games. That should probably just be posted.
If it didn't mean anything, there would be nothing to post :-p. It does mean something, but it would be much easier to understand if it was a shorthand for how often one side wins against the other. To give an example from chesstempo's database (using the 2700+ vs. 2700 filter):
When white plays 1.e4 and black follows with 1...e5, white wins 10.7% more often then black.
When white plays 1.e4 and black follows with 1...c5, white wins 8.5% more often then black.
A shorthand evaluation for these positions could thus be: 1...e5 (W10.7) vs. 1...c5(W8.5)
Incidentally, I tried to see if your formula worked, so I inputed the values that Yigor gave for chesstempo's 2200+ vs. 2200+ Queen's Gambit:
"In the case of the Queen's Gambit, W = 35.8%, B = 20.1%. So, sev = W/B - 1 = +0.78. These formulas are convenient since sev is comparable to engine evaluations."
Using your formula: .78/(.78+1) = .661..., so 66.1% of all decisive games should be won by black.
However, based on my own calculations, that's a bit off. The total decisive games in the above example is 35.8%+20.1%, for a total of 55.9% of the total games played. We can now simply take these number and remove the percentage signs to simplify- 55.9 represents 100% of all decisive games played in this position and of that group, 35.8 represents the games won by white.
So now all we need to do now is divide 35.8 by 55.9 to get .640..., so 64% of games are won by white in this position. Close to 66.1%, but not quite.
I was waiting for someone to correct your math here, but I guess no such luck. sev + 1/sev + 2 is percentage white wins, not black. 1.78/2.78 - 64%, the exact answer. In that post, I considered sev to be without the rather pointless -1 addition at the end, but I supposed while logical that was incorrect.
The idea of reversing the formula for white and black is precisely the problem. It doesn't make a lot of sense to make a formula that has to be reversed at\ x= 0 yet has a range to x = -1. This reeks of arbitration. If a formula is switched when white and black wins are equal, they should at least not be continuous at those values. In addition, I was going to yet you discover yourself that the non-symmetry of the formula for white and black makes it contradict itself and inherently meaningless.
It's better to come up with a formula from what it is people want to measure.
The two factors are:
1: What is my chance of winning? (How good is the opening?)
2: What is my chance of drawing? (How sharp is the opening?)
The point of a formula here would be for somebody to pick the opening they like based on how much they are willing to draw compared to how much of a win percentage the opening offers.
IE: supposed there is an opening that wins 50% of the time but never draws
Then supposed there is another opening that draws 100% of the time. Both score the same, but which is preferable? This would be decided ahead of time by the person entering the arguments into the formula.
It seems easy then for the user to make some sort of one dimensional sliding choice. The middle of the slider is 100% good. The right is 100% drawish, and the left is 100% sharp. Sliding it around would change the priority and therefore score of the openings.
On the left, openings would be scored strictly in order of draw percentage from least to most. On the right, openings would be scored strictly in order of draw percentage from most to least. In the middle, openings would be scored strictly by win percentage from highest to lowest.
The formula is this:
On the left, openings are scored for 100% of the win chance plus x% of their loss chance where x is how far along to the left the slider is. On the right, openings are scored for 100% of their win chance plus x% of their draw - win chance where x is how far along to the right the slider is.
This formula seems actually useful for "scoring" openings according to submitted preferences rather than just coming up with numbers that seem like computer evaluations. I would gladly set it up in excel given a database of openings.
Jul 30, 2017
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#12
xman720: U've written the whole roman 
but U haven't understood the formulas. The range is between -∞ (when W=0 %, B≠0 %) and +∞ (when B=0 %, W≠0 %). When W=B, sev=0 (that's why -1 is added to the formulas). When W=2B, sev = +1 and when B=2W, sev =-1 etc.
A function has an input, known as the domain, and the output, known as the range. You say the range can go below -1, so give me an input for sev = w/b - 1 that outputs below -1, keeping in mind that the domain of w is between 0 and 1 and the domain for b is between 0 and 1.
When b = 2w, the output is both -1/2 and -1. This is a contradiction and a problem, and shows that the function doesn't mean anything.
Jul 30, 2017
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#14
xman720 wrote:
A function has an input, known as the domain, and the output, known as the range. You say the range can go below -1, so give me an input for sev = w/b - 1 that outputs below -1, keeping in mind that the domain of w is between 0 and 1 and the domain for b is between 0 and 1.
When b = 2w, the output is both -1/2 and -1. This is a contradiction and a problem, and shows that the function doesn't mean anything.
Differentiation2 has already pointed it out to U. When b≥w, sev = 1-b/w.
Why? Both functions are continuous for infinite domains. The function has to actually have a function to be functional. Your function is terrible and means nothing.
IN that example, sev is also -2/3 because w/b = 1/3 - 1 = -2/3. I understand you can arbitrarily decide to change the function when your function stops working, but you need a reason to do that or you demonstrated that your function doesn't mean anything.
Jul 30, 2017
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#17
xman720 wrote:
Why? Both functions are continuous for infinite domains. The function has to actually have a function to be functional. Your function is terrible and means nothing.
Terrible ?!? LMAO 
It works well anyway.
Jul 30, 2017
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#18
xman720 wrote:
In that example, sev is also -2/3 because w/b = 1/3 - 1 = -2/3. I understand you can arbitrarily decide to change the function when your function stops working, but you need a reason to do that or you demonstrated that your function doesn't mean anything.
Well, I repeat U the last time. The function is
sev = W/B - 1 when W≥B
sev = 1 - B/W when B≥W
If it's not clear to U, U should come back to the primary school.
Jul 31, 2017
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#19
Current status: 6 openings with 100000+ master games. Please notice some rare transitions like Ross Gambit --> King's Knight and Anglo-Scandinavian --> Queen's Gambit. 
Okay, let's pass to 3 plies, 2-ply openings are treated here:
https://www.chess.com/forum/view/general/list-of-all-400-legal-openings-in-2-plies-master-games
I indicate PSCC classification codes, number of master games, engine evaluations, statistical evaluations and the sharpness when sh1 or sh2 <0.5 or >1. Notations: ✔ = 2-ply source, DB = databases, K = 1000, SF = Stockfish 9+.
(to be continued)
Colour notations of moves:
statistically excellent
statistically good
statistically suboptimal
statistically bad