Copenhagen Openings

[Draganov]

I started analyzing the Copenhagen openings from the games that were played until 2017.
I used this link from this Hagbard's post:

I extracted the first four moves from all games between strong players for the most used variants:
http://aagenielsen.dk/tafl_openings.txt

I took only the Copenhagen games and normalized the moves as they were played from the standard board position (1.h1-h3 instead of 1.k8-i8 for example).
After the notation normalization, I classified the games by their openings. Then, I counted the white's and black's wins and estimated the probability of winning a game in each opening.
I devided the openings in two groups. In the first group I put openings that were initiated by the whites, while the second group consists of openings that were started by the blacks. In this way, it is possible to see which openings are best for blacks and whites.
Here is the list of the openings according my classification:

Millar Gambit Accepted: 1.h1-h3 g5-g2; 2.h3-h2xg2 or 2.h3-g3xg2
Millar Gambit Declined: every move which doesn't take the viking on G2
French Opening: 1.g1-g3 named after the French players Plantagenet, Floki and Ytreza who often played it.
German Opening: 1.h1-h3 d6-d9 named after Schachus and Nath
English Opening: 1.h1-h3 f8-i8 named after Crust and Herjan
Russian Opening: 1.h1-h3 h6-h9 named after Alex Hnefatafl
Italian Opening: 1.h1-h3 f8-c8 named after Mmagari.
American Opening: 1.f2-i2 named after Altti and Cacreal
Canadian Opening: 1.h1-h4 named after Cacreal
Face-to-Face Attack: 1.h1-h3 d6-d3 named like that because the vikings on h3 and d3 are facing each other.
Side Attack: 1.h1-h3 f4-i4 the whites are trying to attack from the side.
Dutch Opening: 1.g1-g2 named after P59xy.
Bulgarian Opening: 1.h1-h3 g5-g4 or (g7-g8, e5-e4, e7-e8, e5-d5, e7-d7, g5-h5 or g7-h7) named after Draganov.
Scandinavian Opening: 1.f2-j2
Norwegian Opening: 1.h1-i1 named after Adam.
Spanish Opening: 1.h1-h3 f4-c4
Polar Gambit: 1.h1-h3 h6-h10 named Polar Gambit because it is so rarely seen that only people who live in Antarctica probably play it.
Hungarian Opening: 1.h1-h3 e7-e9 or (e7-c7, e5-e3, e5-c5, g7-g9, g7-i7, g5-i5 or g5-g3) named after Huzsiati.
Indirect Millar Gambit: 1.h1-h3 e7-b7 or g7-j7 or e7-e10 the idea is that Tim Millar offered a sacrifice not directly to the black opened side but to some of the untouched sides.
Irregular Opening: all other opening moves like 1.f2-k2 or 1.f2-f3 or 1.h1-h5 or 1.g1-g4 or some strange white's responds to 1.h1-h3 like f8-g8 or f8-h8.

Here is the statistical information regarding the winning probability in each opening.

Winning probability for each Copenhagen opening

opening_stats.png (33.45 KiB) Viewed 3343 times

[Draganov]

Let's do some analyses here. As we can see, the blacks started the game with their first move and have limited choices to open the game.
They could play the most frequently used move 1.h1-h3 but it will give the whites plenty of opportunities to decide the opening. If the blacks open the game with 1.h1-h3 they must be well-prepared to face Millar Gambit (then, they will need to decide whether to accept it or decline it) and many other openings like Side Attack, Face-to-Face Attack, English Opening, Russian Opening, Hungarian Opening and so on. Generally the whites could respond to 1.h1-h3 with 13 different openings without mentioning the irregular options. So, a black player who wants to play 1.h1-h3 must be very well-prepared in the opening phase.

That's why the blacks sometimes decide to surprise the white opponent and to play some openings that are less-known. The blacks have 6 ways to determine the opening. Interestingly, 5 of them are really bad for the blacks from a statistical point of view. So, the blacks have practically only 2 reliable choices - to play 1.h1-h3 and give the whites the chance to decide the opening or to play 1.g1-g3 and open the game with the French Opening.

The statistics show that French Opening is probably the best opening for the blacks (at least until 2017). By playing 1.g1-g3 the blacks reduce the white's chance of winning to 61%. If the blacks play 1.h1-h3, they might play against English Opening (67% of white winning), Face-to-Face Attack (66% white winning), Millar Gambit (if Accepted the chance for white winning is 74%, if Declined the chances are 61% but still little bit higher than the 61% of French Opening). So, to avoid the most winning white lines, the blacks could play 1.g1-g3 and initiate the French Opening.

Let's see why the blacks should be afraid of entering into English Opening, Face-to-Face Attack or Millar Gambit? The main opening of Adam (former world champ) is English Opening. In 2015 he won the world championship by using English Opening in 11 of his 12 games with the whites. Crust mainly played Millar Gambit, which was named after him. He won the world championship twice and was one of the strongest players ever. Casshern, who is arguably the greatest player of all time, uses Face-to-Face Attack as his main weapon.
Moreover, this opening lines were played so often and the game archive is full of game examples for them. So, even a low-rated player could study these openings and see how these three great players were playing with the whites.

Who played French Opening? This opening was the first choice of Plantagenet. He won the world championhsip in 2017 by using mainly French Opening when playing with the blacks. Moreover, Plantagenet is probably the strongest player with the black pieces (except maybe Casshern). So, if such a strong black player is rellying on French Opening, we also must give it a try.

[Draganov]

Another remarkable thing to mention is that Indirect Millar Gambit is significantly worse choice for the whites than the standard Millar Gambit. When I was studying the Indirect Millar Gambit, I saw that the strongest players usually accepted it without any fear. However, the strongest players usually declined the standard Millar Gambit.
We can see from the statistics that the best situation for the whites is when they offer Millar Gambit and the blacks accept it. So, Millar Gambit Accepted is crushing the blacks with 74% winning chances for the whites.

However, is offering Millar Gambit the best choice for the whites as a response to 1.h1-h3? What if the blacks decide to decline the gambit and enter into Millar Gambit Declined? Then, the white chances will be reduced to 61%. So, the whites have two better options than offering Millar Gambit. They can respond to 1.h1-h3 with English Opening or Face-to-Face Attack and keeping their winning chances higher than 65%.

Let's see another point. Are Russian, Hungarian and Bulgarian openings that bad for the whites? These three openings were usually played by unexperienced players that didn't understand their main ideas. Nowadays, I won many remarkable games with the Bulgarian Opening, Alex Hnefatafl won many games with Russian Opening (including a game against Casshern) and SebastianMucke effectively used Hungarian Opening.

The same situation we can see with Canadian Opening in which Cacreal achieved great results (even a victory over Casshern). Before 2017 the strongest player who frequently used Canadian Opening was Unterwichtel whose maximum reached rating was 1567.
However, in general, I think there are certainly some better openings for both colors but these less-known and statistically less-effective openings deserve more studying.

My future plans are to analyze the best responses for both colors in each of these openings. I also would like to study the main ideas behind each opening. I hope that my work will be beneficial for the whole tafl community and will help all of the players to improve and explore the tafl game in a deeper way.

[Draganov]

Here are the statistics for Millar Gambit Accepted and Millar Gambit Declined:

Millar_Gambit.png (23.71 KiB) Viewed 3285 times

Let's do some analyses here. As we can see, in Millar Gambit Accepted there are only two ways for the blacks to accept the sacrificed viking.
Statistically both choices are bad for the blacks.
The first one I named it Adam Variant (1.h1-h3 g5-g2; 2.h3-h2xg2). In my opinion, this variant is more common nowadays. One of the first players to use it was Adam. However, the blacks cannot equalize with this move and the whites have 77% winning chances.

The other way to accept the Millar Gambit is by playing the move that was used by Altti (1.h1-h3 g5-g2; 2.h3-g3xg2). It is now considered little bit unorthodox way to accept the gambit but statistically it gives the blacks little bit more chances to survive (the whites have 73% winning chances).


If we go to Millar Gambit Declined, we will have more options to do that.
The move 2.f2-c2 (proposed by Adam) is the best option for the blacks. It reduces the white's chances to only 55%. The position is practically equal with chances on both sides.

Kratzer and Crust's way to decline the gambit are statistically in favour of the whites.
Here I would like to mention the idea of Casshern (2.k5-i5) which I think is very interesting and worth to be better tested. Casshern played 3 times this variant and won twice (against Plantagenet and Nath) and lost once (against Plantagenet). Plantagenet also tried this variant against OdinHimself and lost the game with the blacks. So, the balance is 50:50 (2 wins for the whites and 2 for the blacks) but it is remarkable that so strong players like Casshern and Plantagenet considered this variant worth to be tried.