hnefatafl and the quest for balance

crust
Posts: 127
Joined: Sat Mar 21, 2015 9:29 am

hnefatafl and the quest for balance

Post by crust » Thu Sep 29, 2011 11:17 am

It's a strange thing, if you think about it. We have chosen one of the very few board games which features complete asymmetry, both in the aims of the two players, and in the size of their forces. Then we spend the whole time trying to find the most evenly balanced variation! Well, of course an unbalanced game is not going to be all that much fun to play, nor is one that always ends in a draw. But we persist because it is precisely this asymmetry which makes the Tafl family of games so intriguing.

There's been a lot of discussion on this forum about which version is the most balanced (not all of it as good-humoured as it might have been). We have these statistics to go on:
Fetlar rules: win for white 44 %, black 39 %, draw 17 % (source: Roderich's analysis of our tournament here)
Rachunek or Marseille rules: white 58.26%, black 39.17%, draw 2.56% (source: Brainking.com http://brainking.com/en/GameRules?tp=19 ... !g=5357760 )

This evidence suggests that Fetlar is better balanced in terms of the winning chances of the two players, though Rachunek has far fewer draws.

So, some questions follow. Will our quest for balance in hnefatafl eventually lead to a situation where every game is a draw? Is it worth giving up some of the fairness in order to reduce the number of draws? Or should the "drawishness" of hnefatafl be something we can actually embrace, even celebrate ? (Ok, I admit it, I love draw forts!) Is there some combination of the game variables we haven't tried yet still out there waiting to be found, a game with perfect balance and few draws? Or are we going to have to accept imperfection, and adopt whichever version we like better, based on personal preference?
Last edited by Hagbard on Fri Mar 20, 2015 2:59 pm, edited 3 times in total.

Adam
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Re: hnefatafl and the quest for balance

Post by Adam » Thu Sep 29, 2011 1:49 pm

we should look at all the Fetlar stats, not just tournament, excluding the few draw fort tests, as the brainking stats must include inexperienced players games.

Just to be fair and above board.

crust
Posts: 127
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Re: hnefatafl and the quest for balance

Post by crust » Sat Oct 01, 2011 12:37 am

I agree the tournament may not be a fair sample of games, as all the participants were non-beginners. I'm sure however that the complete catalogue of fetlar games contains some useless stuff too, as many games were test games or incomplete - so some editing may be needed. We might for example rule out games that ended in a time-out, on the grounds that this may well have been caused by a glitch or something else unrelated to the game. Just a thought.

Hagbard
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Re: hnefatafl and the quest for balance

Post by Hagbard » Sat Oct 01, 2011 11:14 am

crust wrote:It's a strange thing, if you think about it. We have chosen one of the very few board games which features complete asymmetry, both in the aims of the two players, and in the size of their forces. Then we spend the whole time trying to find the most evenly balanced variation! Well, of course an unbalanced game is not going to be all that much fun to play, nor is one that always ends in a draw. But we persist because it is precisely this asymmetry which makes the Tafl family of games so intriguing.
Very interesting approach!
crust wrote:We have these statistics to go on:
Fetlar rules: win for white 44 %, black 39 %, draw 17 % (source: Roderich's analysis of our tournament here)
I've done some statistics on he Fetlar games including all games, both with experienced players and beginners.
The full list of Fetlar games 2011-01-05 - 2011-09-08 has 105 real games, i.e. excluding test games and incomplete games.

The count shows:
52 white wins (defenders) = 50%
37 black wins (attackers) = 35%
16 draws = 15%

This result is remarkably close to the statistics from our Fetlar tournament.
Furthermore the count rejects any claim that the attackers should always win by the Fetlar rules! On the contrary, it is the defenders that win much more often!

Hagbard
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Re: hnefatafl and the quest for balance

Post by Hagbard » Thu Nov 03, 2011 2:55 pm

crust wrote: But we persist because it is precisely this asymmetry which makes the Tafl family of games so intriguing.
Asymmetry & balance is a complicated feature of the tafl game. With chess, two extremely inexperienced players and two extremely experienced players can use exactly the same board, pieces and rules and get to the same result: the stronger player wins. With tafl however, it is not so. Beginners might find the one side easier while skilled players with the same board, pieces and rules might contrarily find the opposite side easier. Therefore we in this circle have been more focused on identifying well working rules variants for the skilled players.
crust wrote:Is there some combination of the game variables we haven't tried yet still out there waiting to be found
There have been some test games with these rule combinations:
11x11 board, 2 side king capture, king wins on edge.
9x9 board, 2 side king capture, king wins in corner.
9x9 board, 2 side king capture, king wins on edge.
9x9 board, all pieces move only one square per move.
These test games did not catch enough interest to continue with the variants, but surely there are still combinations waiting to be found.

As for the Berserk Hnefatafl suggestion, alas no serious test games have yet been played to find out if the rules are hopeless or if they really might work. I await in suspense this to be sorted out.

Hagbard
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Re: hnefatafl and the quest for balance

Post by Hagbard » Mon Jan 30, 2012 3:47 pm

Roderich wrote:(20 Aug 2011) Hi Adam, here's a first contribution from me. I've analized 54 shetland-fetlar-games from Aage's Homepage (including the tournament games) to find out if this variant is well balanced.

Result: The shetland variant is indeed surprisingly well-balanced.
We've got 39% wins for black, 17% draws and 44% wins for white.
I've done a new calculation of the Fetlar Hnefatafl 11x11 balance based on the by now rather large statistical material collected from our games here.

If the calculation is limited to only cover the latest year (365 days), 292 Fetlar Hnefatafl 11x11 games were completed by 195 different players.

The calculation is further limited to fairly experienced players by these rules:
A player is included only if
- he has completed tafl games against at least 3 different opponents.
A Fetlar Hnefatafl 11x11 game is included only if
- the couple of players has completed a full match, i.e. each player has played against the other as both defender and attacker.
- when the same couple of players has done several games, only the latest one is included.

This method leaves 36 games completed by 11 different players:
Adam Hagbard 0-1, Adam crust 0-1, Adam Roderich 0.5-0.5, Adam Jonas 0.5-0.5, Adam Hugues 1-0, Roderich Hagbard 1-0, Roderich crust 0-1, Roderich remi 1-0, Roderich Adam 0-1, Roderich Jonas 1-0, crust Hagbard 0.5-0.5, crust Pedro 1-0, crust MaC 1-0, crust Roderich 0-1, crust Jonas 1-0, crust Adam 0-1, crust chuck ward 1-0, Jonas Hagbard 0-1, Jonas crust 0-1, Jonas Roderich 1-0, Jonas Adam 0.5-0.5, Hugues Hagbard 1-0, Hugues Adam 0-1, Evans chuck ward 0-1, Pedro crust 1-0, Hagbard Hugues 1-0, Hagbard crust 1-0, Hagbard Roderich 0.5-0.5, Hagbard Jonas 1-0, Hagbard Adam 0-1, Hagbard chuck ward 1-0, remi Roderich 0-1, MaC crust 0.5-0.5, chuck ward Hagbard 0-1, chuck ward crust 0-1, chuck ward Evans 1-0

The count shows for Fetlar Hnefatafl 11x11:
16 white wins (defenders) = 44%
14 black wins (attackers) = 39%
6 draws = 17%


- the same result as Roderich's analysis above!

crust
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Re: hnefatafl and the quest for balance

Post by crust » Mon Jan 30, 2012 5:38 pm

That's brilliant - we may (occasionally) have our concerns over draws etc, but on the subject of balance, I think Fetlar has passed the test with flying colours. I'll take the liberty if you don't mind of forwarding your post to Peter Kelly. Thanks Hagbard for your work on this, and Roderich too.

On another note I am trying out ard ri and brandubh on dragonheelslair, and finding both of them horribly unbalanced in favour of black. Haven't quite made up my mind about what they call "hnefatafl A" (king escapes to the edge), but I suspect it may be slightly unbalanced also in favour of black.

Hagbard
Posts: 406
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Re: hnefatafl and the quest for balance

Post by Hagbard » Wed Jun 27, 2012 11:29 pm

From the rules elements:

Board size 9x9 / 11x11
King wins on edge / corner
King captured from 4 sides / 2 sides / unarmed
(initial orderings of pieces are not changed)

in how many ways can these elements be combined and give balanced game variants?

We know from experience that
the 9x9 board is easier for white than 11x11 (shorter distance from throne to edge or corner)
edge win is easier for white than corner win
king captured from 2 sides is of course easier for white than an unarmed king, and captured from 4 sides is even easier.

We know from experience that the rule combination 9x9 board, edge win, king unarmed is balanced (Sea Battle tafl and Rachunek).
This is the easiest possible board for the king, and it follows that all other rule combinations with the king unarmed are too hard for white and therefore unbalanced.

We know from experience that the rule combination 11x11 board, corner win, king captured from 4 sides is balanced (Hnefatafl 11x11, Fetlar and Copenhagen).
This is the hardest possible board for the king, and it follows that all other rule combinations with the king captured from 4 sides are too easy for white and therefore unbalanced.

Left are the combinations with the king captured from 2 sides.
Because 11x11 board, corner win, king captured from 4 sides is balanced, it follows that 11x11 board, corner win, king captured from 2 sides is too hard for white and therefore unbalanced (Scandinavian Museums' Hnefatafl), and experience confirms this.

Because 9x9 board, edge win, king unarmed is balanced, it follows that 9x9 board, edge win, king captured from 2 sides should be expected to be too easy for white (Cartier tafl),

Left are now two combinations with the king captured from 2 sides.
9x9 board, corner win, king captured from 2 sides (could be called Scandinavian Museums 9x9). Actually earlier test games suggested that this variant might be balanced.
11x11 board, edge win, king captured from 2 sides (could be called Scandinavian Museums Edge 11x11).

So these four are the only possible balanced rules combinations from the above rules elements:
9x9 board, edge win, king unarmed (Sea Battle tafl and Rachunek). Known to be balanced.
11x11 board, corner win, king captured from 4 sides (Hnefatafl 11x11, Fetlar and Copenhagen). Known to be balanced.
9x9 board, corner win, king captured from 2 sides (Scandinavian Museums 9x9). Probably balanced.
11x11 board, edge win, king captured from 2 sides (Scandinavian Museums Edge 11x11). Not enough experience.

Hagbard
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Re: Balanced 9x9 and 11x11 tafl variants

Post by Hagbard » Thu Jul 05, 2012 5:15 pm

Adam wrote:Could we see the black vs white statistics gathered thus far from the website on these variants on this thread?
Counting one year back and counting all full matches (for each game A against B there must be a game B against A). Timeout-games ignored.

Hnefatafl 11x11 (40 games, 17 players)
19 white wins, 20 black wins, 1 draws.

Fetlar Hnefatafl 11x11 (90 games, 21 players)
48 white wins, 28 black wins, 14 draws.

"Old" Copenhagen Hnefatafl 11x11, the tournament rules (70 games, 11 players)
37 white wins, 32 black wins, 1 draws.

Berserk Hnefatafl 11x11 (82 games, 12 players)
46 white wins, 30 black wins, 6 draws.

Rachunek tafl 9x9 (18 games, 5 players)
13 white wins, 3 black wins, 2 draws.

Sea battle tafl 9x9 (38 games, 5 players)
22 white wins, 12 black wins, 4 draws.

Too few games: New Copenhagen Hnefatafl 11x11, Scand. museums Hnefatafl 11x11, Scand. museums Hnefatafl edge 11x11, Scand. museums Hnefatafl 9x9, Cartier tablut 9x9, Swedish tablut 9x9, Ashton tablut 9x9, Unarmed king tafl 9x9.


"Strong players' statistics"
Interestingly the balances change when the same counting is done including only players rated well above the average 1500:

Fetlar Hnefatafl 11x11 (52 games, 6 players)
28 white wins, 17 black wins, 7 draws

"Old" Copenhagen Hnefatafl 11x11 (46 games, 7 players)
22 white wins, 23 black wins, 1 draw

Berserk Hnefatafl 11x11 (50 games, 7 players)
25 white wins, 22 black wins, 3 draws

Rachunek tafl 9x9 (10 games, 2 players)
6 white wins, 3 black wins, 1 draw

Sea battle tafl 9x9 (36 games, 4 players)
21 white wins, 11 black wins, 4 draws

This way of counting is more helpful for judging whether a rules set could qualify for tournaments.

crust
Posts: 127
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Re: Balanced 9x9 and 11x11 tafl variants

Post by crust » Thu Jul 26, 2012 10:51 pm

Hagbard wrote:Strong players' statistics:
Fetlar Hnefatafl 11x11 (52 games, 6 players)28 white wins, 17 black wins, 7 draws
"Old" Copenhagen Hnefatafl 11x11 (46 games, 7 players)22 white wins, 23 black wins, 1 draw
Rachunek tafl 9x9 (10 games, 2 players)6 white wins, 3 black wins, 1 draw
Sea battle tafl 9x9 (36 games, 4 players)21 white wins, 11 black wins, 4 draws
Very interesting statistics and summary - great work Hagbard.

Quite surprising results. It strikes me that Fetlar is maybe a bit less balanced than we thought... even experienced players are finding white has an easier time than black. "Old" Copenhagen rules are a definite improvement. I think we should continue working on copenhagen rules, depriving white of the centre fort draw and the perpetual check draw are both good changes.

Also Rachunek and Sea Battle are much more weighted towards white than I expected. So banning perpetual check in those versions or counting repetitive check as a black win would help a bit.

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