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win-chance for each root move
Posted: Fri May 10, 2019 10:06 am
by flok
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).
Re: win-chance for each root move
Posted: Fri May 10, 2019 10:41 am
by Michael Sherwin
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?
Re: win-chance for each root move
Posted: Fri May 10, 2019 11:08 am
by chrisw
flok wrote: ↑Fri May 10, 2019 10:06 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
Re: win-chance for each root move
Posted: Fri May 10, 2019 1:32 pm
by AlvaroBegue
Re: win-chance for each root move
Posted: Fri May 10, 2019 8:30 pm
by hgm
So 1.Na3 is the best move of all!
Re: win-chance for each root move
Posted: Fri May 10, 2019 11:04 pm
by flok
hgm wrote: ↑Fri May 10, 2019 8:30 pm
So 1.Na3 is the best move of all!
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%
Re: win-chance for each root move
Posted: Sat May 11, 2019 2:11 am
by jwes
flok wrote: ↑Fri May 10, 2019 11:04 pm
hgm wrote: ↑Fri May 10, 2019 8:30 pm
So 1.Na3 is the best move of all!
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
Re: win-chance for each root move
Posted: Sat May 11, 2019 3:04 am
by flok
jwes wrote: ↑Sat May 11, 2019 2:11 am
flok wrote: ↑Fri May 10, 2019 11:04 pm
hgm wrote: ↑Fri May 10, 2019 8:30 pm
Conclusion: we cannot conclude anything as every attempt gives different results?
Re: win-chance for each root move
Posted: Sat May 11, 2019 10:12 am
by Henk
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.
Re: win-chance for each root move
Posted: Sat May 11, 2019 11:10 am
by Ajedrecista
Hello:
jwes wrote: ↑Sat May 11, 2019 2:11 am
flok wrote: ↑Fri May 10, 2019 11:04 pm
hgm wrote: ↑Fri May 10, 2019 8:30 pm
So 1.Na3 is the best move of all!
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.