win-chance for each root move

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flok
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win-chance for each root move

Post by flok » Fri May 10, 2019 8:06 am

Hi,

I'm looking for a list of win-chances per move in the starting position.
Like, historically playing b2-b4 gives you a 18% win-chance and e2-e4 51% (I made up those numbers).
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Michael Sherwin
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Re: win-chance for each root move

Post by Michael Sherwin » Fri May 10, 2019 8:41 am

Back in the early 70's there was a book titled The blue book of winning chess. Or something very similar. It was a rather large book and gave the winning percentage for all opening moves for the root moves as well as for all the moves of every opening for all positions that had at least 100 games played. I haven't a modern chess games database but don't databases also do that?
I hate if statements. Pawns demand if statements. Therefore I hate pawns.

chrisw
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Re: win-chance for each root move

Post by chrisw » Fri May 10, 2019 9:08 am

flok wrote:
Fri May 10, 2019 8:06 am
Hi,

I'm looking for a list of win-chances per move in the starting position.
Like, historically playing b2-b4 gives you a 18% win-chance and e2-e4 51% (I made up those numbers).
It’s a little problematic because chess has three possible results. 50% could come from 100 draws, which would be 0% win chance and 100% draw chance.
Rebel probably has a PGN analyser for WDL or a PGN database like Skid would tell you

AlvaroBegue
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Re: win-chance for each root move

Post by AlvaroBegue » Fri May 10, 2019 11:32 am


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hgm
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Re: win-chance for each root move

Post by hgm » Fri May 10, 2019 6:30 pm

So 1.Na3 is the best move of all! :lol:

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Re: win-chance for each root move

Post by flok » Fri May 10, 2019 9:04 pm

hgm wrote:
Fri May 10, 2019 6:30 pm
So 1.Na3 is the best move of all! :lol:
I ran a script on 1.5M games and my results look like this:

Code: Select all

move    #       white           draw            black
b1a3    72      48.611111%      5.555556%       45.833333%
f2f3    162     46.913580%      6.172840%       46.913580%
a2a4    160     46.875000%      10.000000%      43.125000%
g2g4    1210    46.694215%      11.983471%      41.322314%
b2b4    8628    44.969866%      17.814094%      37.216041%
d2d4    453523  43.073229%      26.330748%      30.596023%
h2h4    151     43.046358%      11.258278%      45.695364%
e2e4    681058  42.607972%      23.807517%      33.584511%
c2c4    101082  42.343840%      27.350072%      30.306088%
b1c3    4052    41.905232%      22.877591%      35.217177%
g1f3    108024  41.404688%      29.808191%      28.787121%
a2a3    624     40.705128%      17.467949%      41.826923%
b2b3    5960    39.832215%      25.922819%      34.244966%
g2g3    10986   39.568542%      30.183870%      30.247588%
h2h3    167     38.922156%      16.167665%      44.910180%
e2e3    1573    37.507947%      13.986014%      48.506039%
f2f4    9241    37.495942%      22.378530%      40.125528%
d2d3    764     35.994764%      18.848168%      45.157068%
c2c3    367     35.694823%      20.435967%      43.869210%
g1h3    108     32.407407%      12.962963%      54.629630%
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Re: win-chance for each root move

Post by jwes » Sat May 11, 2019 12:11 am

flok wrote:
Fri May 10, 2019 9:04 pm
hgm wrote:
Fri May 10, 2019 6:30 pm
So 1.Na3 is the best move of all! :lol:
I ran a script on 1.5M games and my results look like this:

Code: Select all

move    #       white           draw            black
b1a3    72      48.611111%      5.555556%       45.833333%
f2f3    162     46.913580%      6.172840%       46.913580%
a2a4    160     46.875000%      10.000000%      43.125000%
g2g4    1210    46.694215%      11.983471%      41.322314%
b2b4    8628    44.969866%      17.814094%      37.216041%
d2d4    453523  43.073229%      26.330748%      30.596023%
h2h4    151     43.046358%      11.258278%      45.695364%
e2e4    681058  42.607972%      23.807517%      33.584511%
c2c4    101082  42.343840%      27.350072%      30.306088%
b1c3    4052    41.905232%      22.877591%      35.217177%
g1f3    108024  41.404688%      29.808191%      28.787121%
a2a3    624     40.705128%      17.467949%      41.826923%
b2b3    5960    39.832215%      25.922819%      34.244966%
g2g3    10986   39.568542%      30.183870%      30.247588%
h2h3    167     38.922156%      16.167665%      44.910180%
e2e3    1573    37.507947%      13.986014%      48.506039%
f2f4    9241    37.495942%      22.378530%      40.125528%
d2d3    764     35.994764%      18.848168%      45.157068%
c2c3    367     35.694823%      20.435967%      43.869210%
g1h3    108     32.407407%      12.962963%      54.629630%
I sorted on average points scored by white and got this:

Code: Select all

move	#	white	draw	black	av. points
g1f3	108024	0.41404688	0.29808191	0.28787121	0.563087835
d2d4	453523	0.43073229	0.26330748	0.30596023	0.56238603
c2c4	101082	0.4234384	0.27350072	0.30306088	0.56018876
g2g3	10986	0.39568542	0.3018387	0.30247588	0.54660477
e2e4	681058	0.42607972	0.23807517	0.33584511	0.545117305
b2b4	8628	0.44969866	0.17814094	0.37216041	0.53876913
b1c3	4052	0.41905232	0.22877591	0.35217177	0.533440275
b2b3	5960	0.39832215	0.25922819	0.34244966	0.527936245
g2g4	1210	0.46694215	0.11983471	0.41322314	0.526859505
a2a4	160	0.46875		0.1		0.43125		0.51875
b1a3	72	0.48611111	0.05555556	0.45833333	0.51388889
f2f3	162	0.4691358	0.0617284	0.4691358	0.5
a2a3	624	0.40705128	0.17467949	0.41826923	0.494391025
f2f4	9241	0.37495942	0.2237853	0.40125528	0.48685207
h2h4	151	0.43046358	0.11258278	0.45695364	0.48675497
h2h3	167	0.38922156	0.16167665	0.4491018	0.470059885
c2c3	367	0.35694823	0.20435967	0.4386921	0.459128065
d2d3	764	0.35994764	0.18848168	0.45157068	0.45418848
e2e3	1573	0.37507947	0.13986014	0.48506039	0.44500954
g1h3	108	0.32407407	0.12962963	0.5462963	0.388888885

flok
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Re: win-chance for each root move

Post by flok » Sat May 11, 2019 1:04 am

jwes wrote:
Sat May 11, 2019 12:11 am
flok wrote:
Fri May 10, 2019 9:04 pm
hgm wrote:
Fri May 10, 2019 6:30 pm
Conclusion: we cannot conclude anything as every attempt gives different results?
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Henk
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Re: win-chance for each root move

Post by Henk » Sat May 11, 2019 8:12 am

At least number of games should be equal. Maybe also ELO of players should be about equal.
And what if they play a move with the wrong plan.

I can imagine there are moves underestimated. For instance in 1800 nobody played Sicilian. Why would that be different in 2019.

Maybe only engines should be used that are developed starting from zero chess knowledge. Otherwise you don't get objective results.

But there is a problem that every engine using knowledge which was a result of a local optimal. So again subjective results.
Maybe one should also use a large set of different engines.

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Ajedrecista
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Re: win-chance for each root move

Post by Ajedrecista » Sat May 11, 2019 9:10 am

Hello:
jwes wrote:
Sat May 11, 2019 12:11 am
flok wrote:
Fri May 10, 2019 9:04 pm
hgm wrote:
Fri May 10, 2019 6:30 pm
So 1.Na3 is the best move of all! :lol:
I ran a script on 1.5M games and my results look like this:

Code: Select all

move    #       white           draw            black
b1a3    72      48.611111%      5.555556%       45.833333%
f2f3    162     46.913580%      6.172840%       46.913580%
a2a4    160     46.875000%      10.000000%      43.125000%
g2g4    1210    46.694215%      11.983471%      41.322314%
b2b4    8628    44.969866%      17.814094%      37.216041%
d2d4    453523  43.073229%      26.330748%      30.596023%
h2h4    151     43.046358%      11.258278%      45.695364%
e2e4    681058  42.607972%      23.807517%      33.584511%
c2c4    101082  42.343840%      27.350072%      30.306088%
b1c3    4052    41.905232%      22.877591%      35.217177%
g1f3    108024  41.404688%      29.808191%      28.787121%
a2a3    624     40.705128%      17.467949%      41.826923%
b2b3    5960    39.832215%      25.922819%      34.244966%
g2g3    10986   39.568542%      30.183870%      30.247588%
h2h3    167     38.922156%      16.167665%      44.910180%
e2e3    1573    37.507947%      13.986014%      48.506039%
f2f4    9241    37.495942%      22.378530%      40.125528%
d2d3    764     35.994764%      18.848168%      45.157068%
c2c3    367     35.694823%      20.435967%      43.869210%
g1h3    108     32.407407%      12.962963%      54.629630%
I sorted on average points scored by white and got this:

Code: Select all

move	#	white	draw	black	av. points
g1f3	108024	0.41404688	0.29808191	0.28787121	0.563087835
d2d4	453523	0.43073229	0.26330748	0.30596023	0.56238603
c2c4	101082	0.4234384	0.27350072	0.30306088	0.56018876
g2g3	10986	0.39568542	0.3018387	0.30247588	0.54660477
e2e4	681058	0.42607972	0.23807517	0.33584511	0.545117305
b2b4	8628	0.44969866	0.17814094	0.37216041	0.53876913
b1c3	4052	0.41905232	0.22877591	0.35217177	0.533440275
b2b3	5960	0.39832215	0.25922819	0.34244966	0.527936245
g2g4	1210	0.46694215	0.11983471	0.41322314	0.526859505
a2a4	160	0.46875		0.1		0.43125		0.51875
b1a3	72	0.48611111	0.05555556	0.45833333	0.51388889
f2f3	162	0.4691358	0.0617284	0.4691358	0.5
a2a3	624	0.40705128	0.17467949	0.41826923	0.494391025
f2f4	9241	0.37495942	0.2237853	0.40125528	0.48685207
h2h4	151	0.43046358	0.11258278	0.45695364	0.48675497
h2h3	167	0.38922156	0.16167665	0.4491018	0.470059885
c2c3	367	0.35694823	0.20435967	0.4386921	0.459128065
d2d3	764	0.35994764	0.18848168	0.45157068	0.45418848
e2e3	1573	0.37507947	0.13986014	0.48506039	0.44500954
g1h3	108	0.32407407	0.12962963	0.5462963	0.388888885
I would like to add the lower bound of the Wilson score interval to take into account the effect of low number of games for some initial moves. The following table is sorted by this lower bound with 95% confidence (z ~ 1.95996398 in Excel):

Code: Select all

Move     Games    White (W)     Draw (D)      Black (B)     W + D/2       L.B.W.S.I.
------------------------------------------------------------------------------------
d2d4    453523    0.43073229    0.26330748    0.30596023    0.56238603    0.56094169
g1f3    108024    0.41404688    0.29808191    0.28787121    0.56308784    0.56012781
c2c4    101082    0.42343840    0.27350072    0.30306088    0.56018876    0.55712660
e2e4    681058    0.42607972    0.23807517    0.33584511    0.54511731    0.54393442
g2g3     10986    0.39568542    0.30183870    0.30247588    0.54660477    0.53728108
b2b4      8628    0.44969866    0.17814094    0.37216041    0.53876913    0.52823571
b1c3      4052    0.41905232    0.22877591    0.35217177    0.53344028    0.51805518
b2b3      5960    0.39832215    0.25922819    0.34244966    0.52793625    0.51524825
g2g4      1210    0.46694215    0.11983471    0.41322314    0.52685951    0.49868710
f2f4      9241    0.37495942    0.22378530    0.40125528    0.48685207    0.47666885
a2a3       624    0.40705128    0.17467949    0.41826923    0.49439103    0.45531731
a2a4       160    0.46875000    0.10000000    0.43125000    0.51875000    0.44180222
f2f3       162    0.46913580    0.06172840    0.46913580    0.50000000    0.42390230
e2e3      1573    0.37507947    0.13986014    0.48506039    0.44500954    0.42061405
d2d3       764    0.35994764    0.18848168    0.45157068    0.45418848    0.41919998
c2c3       367    0.35694823    0.20435967    0.43869210    0.45912807    0.40883098
h2h4       151    0.43046358    0.11258278    0.45695364    0.48675497    0.40835618
b1a3        72    0.48611111    0.05555556    0.45833333    0.51388889    0.40069755
h2h3       167    0.38922156    0.16167665    0.44910180    0.47005989    0.39588875
g1h3       108    0.32407407    0.12962963    0.54629630    0.38888889    0.30227648
This ranking of the initial moves makes more sense IMHO. I hope no typos.

I already applied the lower bound of the Wilson score interval in this thread from 2016:

Opening book from a statistical point of view

Regards from Spain.

Ajedrecista.

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