Openings analysis, seasons 6-16 late stages

About two years ago I did some statistical analysis of the openings that were chosen for the late stages of TCEC. My focus was to try to measure the size of the "TCEC opening space", an undefined and elusive concept. More details can be found in the previous report. I repeat this analysis here with 2.5x more games. I added information about the draw rate (dr) and score (sc) of the openings where:

dr = draw rate (percent) = (number of draws) / (number of games) * 100
sc = score (number between 0 and 1) = average score for white =
  = (number of white wins + 0.5*number of draws) / (number of games)

The games I used for the analysis:

• 1246 games from seasons 6-10, as detailed in the previous report.
• Season 11 premier division - 280 games. The first two RRs in this division were without book and were not used for the analysis.
• Season 11 superfinal - 100 games
• Season 12 premier division - 168 games. Chiron crashed frequently in the division and was disqualified, its games were not used in the analysis.
• Season 12 superfinal - 100 games
• Season 13 premier division - 224 games.
• Season 13 superfinal - 100 games
• Season 14 premier division - 168 games.
• Season 14 superfinal - 100 games
• Season 15 premier division - 168 games.
• Season 15 superfinal - 100 games
• Season 16 premier division - 168 games.
• Season 16 superfinal - 100 games

Total is 3022 games, 1511 game pairs.

The total win statistics are: dr = 68.8%, sc = 0.59

ECO, first letter

 
Entropy =  4.92

ECO, full code

There are 500 different ECO codes. The entropy of the ECO codes in the list is 280.1, covering 390 different codes out of the possible 500. The most frequent ECO codes are

• B90 50 times, dr=62.0%, sc=0.65, Sicilian Najdorf
• B12 38 times, dr=71.1%, sc=0.57, Caro-Kann defense
• B06 36 times, dr=58.3%, sc=0.63, Robatsch (modern) defense
• C11 33 times, dr=66.7%, sc=0.58, French defense
• B01 32 times, dr=81.3%, sc=0.53, Scandinavian defense
• A57 30 times, dr=76.7%, sc=0.62, Benko gambit 

ECO codes with the lowest draw rates and at least 10 games:

• B51 10 times, dr=20.0%, sc=0.70, Sicilian, Canal-Sokolsky attack
• E99 11 times, dr=36.4%, sc=0.45, King's Indian, orthodox, Aronin-Taimanov, main line
• A00 14 times, dr=42.9%, sc=0.64, Polish opening
• C02 20 times, dr=45.0%, sc=0.68, French advance

 ECO codes with the highest draw rates and at least 10 games:

• A25 10 times, dr=100%, sc=0.50, English, Sicilian reversed
• D43 10 times, dr=100%, sc=0.50, QGD semi-Slav
• B89 12 times, dr=91.7%, sc=0.54, Sicilian, Sozin
• A20 18 times, dr=88.9%, sc=0.56, English
• D10 18 times, dr=88.9%, sc=0.56, QGD Slav defense

 ECO codes with the lowest scores and at least 10 games:

• A13 13 times, dr=69.2%, sc=0.42, English
• C34 19 times, dr=78.9%, sc=0.45, King's Gambit accepted
• C33 10 times, dr=70.0%, sc=0.45, King's Gambit accepted
• E99 11 times, dr=36.4%, sc=0.45, King's Indian, orthodox, Aronin-Taimanov, main line
• A36 14 times, dr=78.6%, sc=0.46, English symmetric

 ECO codes with the highest scores and at least 10 games:

• C57 10 times, dr=50.0%, sc=0.75, Two Knights defense
• B78 11 times, dr=54.5%, sc=0.73, Sicilian, dragon, Yugoslav attack
• A16 12 times, dr=58.3%, sc=0.71, English
• A52 10 times, dr=60.0%, sc=0.70, Budapest defense
• B51 10 times, dr=20.0%, sc=0.70, Sicilian, Canal-Sokolsky attack
• B95 10 times, dr=60.0%, sc=0.70, Sicilian Najdorf

Book sequences

If we look at the full book sequences, there are 1452 distinct sequences out of 1511 game pairs, with entropy 1428.4. There are 47 book sequences that appeared in 2 game pairs, 6 book sequences appeared in 3 game pairs.

I truncated the book sequences at fixed lengths to measure the expansion as the length increases. For short lengths I also list the most frequent sequences.

After 2 plys the entropy is only 13.42, a total of 47 sequences for 1506 game pairs. The leading sequences are:

• 1. d4 Nf6, 25.9%, dr=68.6%, sc=0.58
• 1. e4 c5, 18.7%, dr=69.0%, sc=0.60
• 1. e4 e5, 10.9%, dr=70.4%, sc=0.57
• 1. d4 d5, 8.3%, dr=72.0%, sc=0.58
• 1. e4 e6, 6.6%, dr=61.6%, sc=0.63

After 4 plys the entropy is 53.7, a total of 203 sequences for 1503 game pairs. The leading sequences are:

• 1. d4 Nf6 2. c4 e6, 9.7%, dr=72.6%, sc=0.57
• 1. d4 Nf6 2. c4 g6, 8.0%, dr=66.3%, sc=0.58
• 1. e4 c5 2. Nf3 d6, 7.6%, dr=66.2%, sc=0.62
• 1. e4 e5 2. Nf3 Nc6, 7.5%, dr=67.3%, sc=0.59
• 1. e4 e6 2. d4 d5, 5.9%, dr=61.2%, sc=0.64

After 6 plys the entropy is 163.9, a total of 440 sequences for 1487 game pairs. The leading sequences are:

• 1. e4 c5 2. Nf3 d6 3. d4 cxd4, 6.8%, dr=68.8%, sc=0.61
• 1. d4 Nf6 2. c4 g6 3. Nc3 Bg7, 5.7%, dr=64.7%, sc=0.56
• 1. e4 c5 2. Nf3 Nc6 3. d4 cxd4, 3.6%, dr=75.5%, sc=0.57
• 1. e4 e5 2. Nf3 Nc6 3. Bb5 a6, 3.5%, dr=71.1%, sc=0.61
• 1. e4 c5 2. Nf3 e6 3. d4 cxd4, 3.2%, dr=71.9%, sc=0.61
• 1. d4 Nf6 2. c4 e6 3. Nc3 Bb4, 3.0%, dr=70.0%, sc=0.56

After 8 plys the entropy is 313.0, a total of 637 sequences for 1445 game pairs.
After 10 plys the entropy is 492.3, a total of 803 sequences for 1399 game pairs.
After 12 plys the entropy is 729.9, a total of 936 sequences for 1355 game pairs.
After 16 plys the entropy is 1095.7, a total of 1156 sequences for 1252 game pairs.