Diagonal Tournament Format test, April 11th - May 14th 2023

Content.
Market Hnefatafl.
Saami Sahkku.
Daldos.
Total Hnefatafl.
Countings.
Conclusion.

Four lines of test:

Market Hnefatafl 9x9 (weak king)
Total Hnefatafl 11x11 (strong king)
Saami Sahkku (race game format 1)
Daldos 14 (race game format 2)

The Market and the Total Hnefatafls follow the description above.

The Sahkku, too.
But a couple of Sahkku tourn. details differ from the standard format:

All players have 4 opponents.
The Sahkku winner is the player with the best tournament performance rating.

Market Hnefatafl 9x9.

13 players: draganov, cromwell, jilles, brave-frog, potapych, dimetr, rosk, jrton80, paul7, skye, mika, themightyglider, hagbard

Step one.
The players are ordered by rating, this test uses the Hist.Hnef. 9x9 sep. rating.

01  1706 Draganov
02  1661 Dimetr
03  1656 Jilles
04  1545 Paul7
05  1453 Potapych
06  1411 Brave-frog
07  1409 Hagbard
08  1398 Skye
09  1387 Jrton80
10  1385 Cromwell
11  1269 Rosk
12  1164 Themightyglider
13  1124 Mika

Step two. Round One.
The players are in three groups, in the first group all have two opponents, second group three opponents, and third group four opponents.
Here the Round One games are

   01 02 03 04 05 06 07 08 09 10 11 12 13
01  -  x        x              
02  x  -  x
03     x  -  x
04        x  -  x
05  x        x  -  x               
06              x  -  x           x   
07                 x  -  x           x  
08                    x  -  x           x
09                       x  -  x  x
10                          x  -     x  x
11                 x        x     -  x  x
12                    x        x  x  -  x
13                       x     x  x  x  -

Step three.
Two players didn't show up.
Two more matches added to replace them.

Step four. Round Two.
Seven players proceed to Round Two.
Set up as a ring in such a way that the "upper half" of players plays against the "lower half"; when possible without repeating any Round One matches.
The players are ordered again by rating:

01  1706 Draganov
02  1656 Jilles
03  1640 Dimetr
04  1545 Paul7
05  1398 Skye
06  1387 Jrton80
07  1164 Themightyglider

Repeating these matches should be avoided: 01-03, 02-03, 02-04, 05-06, 05-07, 06-07.
A solution in this case is:

   01 02 03 04 05 06 07
01  -        x  x              
02     -        x  x
03        -        x  x
04  x        -        x
05  x  x        -
06     x  x        -
07        x  x        -

The setup follows the "first side diagonal", unlike the "center diagonal".
Easy way to find the setup:
"Upper half" is merged with "lower half": 01 05 02 06 03 07 04
The merged row is connected as a ring: 01-05-02-06-03-07-04 plus 04-01

Step five. Round Three.
Four players proceed to Round Three.
Set up as a ring.
The players are ordered again by rating:

01  1706 Draganov
02  1656 Jilles
03  1651 Dimetr
04  1545 Paul7

Two matches have not been played yet and should be part of the set up: 01-02, 03-04.
A solution in this case is:

   01 02 03 04
01  -  x     x
02  x  -  x
03     x  -  x
04  x     x  -

(the ring 01-02-03-04 plus 04-01)

Step six.
There is a winner!
Draganov is last man standing.

Performance Rating also gives this result:

1. draganov 1927
2. paul7 1820
3. dimetr 1808

Saami Sahkku.

9 players: draganov, colophonius, potapych, brave-frog, rosk, jrton80, mika, hagbard, holidayinnes

Step one.
The players are ordered by rating.

01  1616 Holidayinnes
02  1594 Draganov
03  1577 Rosk
04  1498 Hagbard
05  1407 Colophonius
06  1391 Potapych
07  1366 Brave-frog
08  1292 Jrton80
09  < 1292 Mika

Step two. Round One.
All players four opponents.
Here the Round One games are (Race games format 1)

   01 02 03 04 05 06 07 08 09
01  -  x  x              x  x
02  x  -  x  x              x
03  x  x  -  x  x
04     x  x  -  x  x
05        x  x  -  x  x           
06           x  x  -  x  x
07              x  x  -  x  x
08  x              x  x  -  x
09  x  x              x  x  -

Step three.
One player didn't show up.
One more match added to replace him.

Step four. Round Two. Final.
Two players proceed to Round Two.
Losses are cleared.
Since there are only two players, two matches are started.

Losses counted simply by lost games:
Potapych: 0.5, Holidayinnes: 1, Colophonius: 2, Hagbard: 2, Jrton80: 2, Draganov: 2, Rosk: 2.5, Brave-frog: 3.
By counting surviving game pieces:
Potapych: 1, Holidayinnes: 1, Colophonius: 2, Hagbard: 2, Jrton80: 2, Draganov: 2, Rosk: 2, Brave-frog: 3.
By comparing game lengths:
Potapych: 1, Holidayinnes: 1, Colophonius: 2, Hagbard: 2, Jrton80: 2, Draganov: 2, Rosk: 2, Brave-frog: 3.

By all three counting methods, Holidayinnes and Potapych proceed to Round 2.
So, the simplest method 1 gives the same result as the other two methods.

Step five.
There is a winner!
Holidayinnes won all four games in the Final.
Counting losses it's 0-2.
Counting surviving pieces it's 21-0.

Performance Rating also gives this result:

1. holidayinnes 1829
2. potapych 1674
3. hagbard 1666

Daldos.

12 players: floki, Draganov, rosk, Tengrikut, jilles, Potapych, brave-frog, JanK, Hagbard, xerxes, holidayinnes, Colophonius.

Step one.
The players are ordered by rating.

01  1588 jilles
02  1581 holidayinnes
03  1569 Potapych
04  1548 brave-frog
05  1514 xerxes
06  1512 rosk
07  1511 Tengrikut
08  1471 Hagbard
09  1466 Draganov
10  1449 floki
11  1426 Colophonius
12  < 1426 JanK

Step two. Round One.

Simulator runs show that a Round One with 2 opponents for all players, eliminates only 1-3 players; so the next Round Two would be like doing Round One over again.
So, to eliminate more players and progress the tournament, Round 1 has still 4 opponents but set up in a different way.
Losses are accumulated.

All players four opponents.
Set up as a ring in such a way that the "upper half" of players plays against the "lower half" (Race games format 2)

   01 02 03 04 05 06 07 08 09 10 11 12
01  -                 x  x        x  x
02     -              x  x  x        x
03        -           x  x  x  x
04           -           x  x  x  x
05              -           x  x  x  x
06                 -  x        x  x  x
07  x  x  x        x  -
08  x  x  x  x           -
09     x  x  x  x           -
10        x  x  x  x           -
11  x        x  x  x              -
12  x  x        x  x                 -

Easy way to find the setup:
"Upper half" is merged with "lower half": 01 07 02 08 03 09 04 10 05 11 06 12
The merged row is connected as a ring: 01-07-02-08-03-09-04-10-05-11-06-12 plus 12-01
These are all the matches of distance 1.
Adding all the matches of distance 3: 01-08, 07-03, 02-09, 08-04, 03-10, 09-05, 04-11, 10-06, 05-12 plus 11-01, 06-07, 12-02

Step three.
One player left the tournament (timed out more than half of his games) and is removed.
Two more matches added to replace him.

Step four. Round Two. Final.
Two players proceed to Round Two.
Since there are only two players, two matches are started.

The "ring" 01-02 plus 02-01

Step five.
There is a winner!
Jilles is last man standing.

Performance Rating also gives this result:

1. jilles 1859
2. xerxes 1781
3. rosk 1662

Total Hnefatafl 11x11.

6 players: draganov, jrton80, potapych, mika, staticmatic, brave-frog

Since there are only 6 players, a double Round Robin is tested.

Step one. Round One.
First Round Robin.

Step two.
One player didn't show up.
He's removed from the tournament.

Step three. Round Two.
Second Round Robin.

Step four.
One player left the tournament (timed out all his Round 2 games).
His games are ignored.

Step five.
There is a winner!
Draganov won both rounds.

            r1  r2  sum
Draganov     6   6  12
Potapych     3   3   6
Jrton80      3   3   6
Brave-frog   0   0   0

Performance Rating also gives this result:

1. draganov 1867
2. Potapych 1641
3. jrton80 1621

In this test with six players, each of the two Round Robins gave the same result as the sum.
So in this test one Round Robin would have sufficed.

Countings.

Conclusion.

The tests worked.
No winners were very unexpected, and all winners also had the highest performance ratings.
The Daldos tournament with "Race games format 2" showed that it is possible to accumulate the losses also in a race game tournament.