Move one loses the game

What is the Best First Move?

Kombilo reports the winning percentage for the results that it finds. Here are the percentages from First Move In The Corner:

• In 13,362 games Black wins 53.5% White wins 43.3.% and 2.2% are undecided (jigo, no result, or unknown).
• In Games where Black plays in one or more empty corners at:
  • Hoshi - B wins 54.7% W wins 44.7% No result 0.6% (precision 1.0%)
  • Komoku - B wins 54.0% W wins 43.4% No result 2.6% (precision 0.6%)
  • Mokuhazushi - B wins 47.4% W wins 42.8% No result 9.8% (precision 3.0%)
  • Takamoku - B wins 47.0% W wins 45.4% No result 7.6% (precision 5.2%)
  • San San - B wins 48.2% W wins 51.3% No result 0.6% (precision 5.4%)
• In Games where White plays in one or more empty corners at:
  • Hoshi - B wins 52.3% W wins 47.1% No result 0.6% (precision 1.0%)
  • Komoku - B wins 53.5% W wins 43.9% No result 2.6% (precision 1.0%)
  • San San - B wins 54.5% W wins 45.1% No result 0.4% (precision 2.5%)
  • Mokuhazushi - B wins 55.7% W wins 37.8% No result 6.5% (precision 3.0%)
  • Takamoku - B wins 59.8% W wins 32.6% No result 7.6% (precision 3.8%)

I found these results quite surprising. I had no expectation that there would be such big differences in the results. Keep in mind that in even games there are four empty corners at the start of the game. Many fuseki combine more than one of the above plays in different open corners. Despite the fact that most games contributing to the results include more than one of the above plays, the figures shown above indicate a pretty clear difference between Black choosing to play hoshi or komoku and choosing to play the other three! Similarly there is a clear difference between White choosing to play hoshi, komoku, or san san and choosing to play the other two.

Personally I found the results not only surprising but disappointing. I enjoy playing mokuhazushi and actually got tied up in this analysis while trying to prepare some statistics on the use of the Taisha joseki. Unfortunately the figures above seem to cast doubt on the use of mokuhazushi, takamoku, and (by Black at least) san san at all - without ever considering minor matters like the choice of joseki.

Just to be very mathematically rigorous, can you give the precision of the calculations? To do it, you just have to take 1/sqrt(N) where N is the number of games.

BobMcGuigan: I think this estimate of error depends on the sample being random which, I think, is unlikely in this case.

Johannes?: If you don't consider it random, what would be your

concept of "precision"?

Bob McGuigan: Unfortunately it is not possible to calculate a "precision" for a sample that is not probability based.

For example, if the number of games in the database is 13,362 then we will see that the fluctuations should be less than 1% which means that the statement that Black wins more than White is reliable. If the numebr of games starting with hoshi is, for example, 6,400 then the expected fluctuation would be 1/0.8 % = 1.125%. If the number of games starting with mokuhazushi is 625 then the expected fluctuation is 4% and so on. This does not deny the conclusions drawn from the averages, but puts some limitations on the reliability of the results.

Johannes?: If you treat the outcome as being biomial distributed, the standard error of your probability estimates would be sqrt(n(N-n)/N) so it would be lower for low than for high probabilities.

Further, it might happen that the root of the problem is only in one of the lines of continuations. For example, looking at my own games I saw that as White I have slightly better results replying with komoku to the opponent's hoshi. But it turned out that looking a step further I saw that if the opponent chooses parallel fuseki then the results don't differ from average, but if the opponent makes a mistake of challenging me to diagonal fuseki, I win with the ratio of 14:4. So, it was not komoku that increased my winning percentage, but rather the fact that I play that komoku in the adjacent and not the opposite corner and even in that case the opponent has to choose the diagonal fuseki. I don't like moyos.

HolIgor

I added the "precision" above calculated at 1/sqrt(number of corners played as listed on First Move in the Corner). I have no idea if this is what should be used, though. The point is that winning percentage is calculated by looking at the results of games but each game contains four different corners. I am too lazy to find the number of games for each line (at least right now :-) Do mathmaticians have different ways to assess this situation? DaveSigaty

It would be interesting to group the players by strength and recalculate statistics for each group!

mat

Agreed. I have calculated Go Seigen, Kitani, Sakata, Cho Chikun, Yi Ch'ang-ho, and Cho Hun-hyeon so far and will post them here shortly - Black and White have to be calculated separately for individuals so I already have 12 tables of results :-( The differences are interesting but tend to reflect what we would expect from their various styles, I think. Dave

Individual Players' Results

Go Seigen

373 Games as Black
                   Corners    B wins  W wins  Other*
Overall              1,449     77.5%   19.5%   3.0%
Go's Choices Playing Black
Komoku         Black   469     81.0%   16.4%   2.6%
Hoshi          Black   294     80.6%   17.0%   2.4%
Mokuhazushi    Black    23     65.2%   26.1%   8.7%
San San        Black    39     59.0%   41.0%   0.0%
Takamoku       Black    14     57.1%   42.9%   0.0%
His Opponents' Choices Playing White
San San        White    21     66.7%   33.3%   0.0%
Komoku         White   306     72.9%   23.9%   3.2%
Hoshi          White   132     78.8%   20.5%   0.7%
Mokuhazushi    White    80     77.5%   16.3%   6.2%
Takamoku       White    51     92.2%    7.8%   0.0%

469 Games as White
Overall              1,785     39.2%   55.7%   5.1%
His Opponents' Choices Playing Black
Takamoku       Black    62     43.5%   50.0%   6.5%
Komoku         Black   521     41.3%   54.5%   4.2%
San San        Black    24     37.5%   58.3%   4.2%
Hoshi          Black   273     37.0%   57.1%   5.9%
Mokuhazushi    Black    50     36.0%   56.0%   8.0%
Go's Choices Playing White
Mokuhazushi    White    16     12.5%   87.5%   0.0%
Komoku         White   517     37.1%   59.2%   3.7%
Hoshi          White   201     36.8%   53.7%   9.5%
San San        White    55     50.9%   47.3%   1.8%
Takamoku       White    48     56.3%   35.4%   8.3%

• "Other" includes various results that are not wins for either Black or White: jigo, unfinished, result unknown, etc.

Anonymous: Are these statistics that meaningful? Maybe the only conclusion to draw is "The weaker player should choose non-standard moves." That by itself may account for the difference.

Fhayashi: Huh? The only conclusion is Hoshi and Komoku (and as white, San San) seem to be the best opening play, unless you're Go Seigen, in which case you should be playing Mokuhazushi more often as white...

Harpreet: It's likely to be more complicated than this. There are very different numbers for how many times each move has been tried. 4-4 and 3-4 may really be better or it may just be that they are understood more because they have been played more.

Andrew Grant: Something that never gets mentioned in these statistical analyses is - how many of these games were played with komi? (And what value of komi?) It should be clear that in the pre-komi era Black would have a better winning percentage regardless of which move he chose in the opening. Unless you can separate the no-komi games from the rest your stats are inevitably going to be misleading.

DaveSigaty: This is not strictly correct although it is certainly something to keep in mind. In the pre-komi era most games are with the nominally weaker player on Black. This offsets the first move advantage to some extent I expect. Without redoing the whole thing the winning percentage for first move on komoku up through 1939 (1940 seems like a reasonable proxy for the adoption of komi from scanning the games) was 54.6% and since 1940 was 53.3%. The figures are not exactly comparable to those above since they are from a different edition of GoGoD CD.

RafaelCaetano: I find the results and conclusions above quite unconvincing. For instance, Black wins only 47.4% of the games when he plays mokuhazushi (a.k.a "the 3-5 point"). But then, 9.8% of the Black mokuhazushi games are "undecided"! So maybe 47.4% is not so low. If you discard the "undecided" games, then Black wins 52.5% of the games.

By the way, it's misleading to refer to jigo and unknown results as "no result", as this term already has a specific meaning in Japanese rules.