About the Keizer system

Read this article in Italian here.

The Keizer system is well known in the Netherlands and in Belgium, but is still hardly known in the rest of the world. This is pitiful because it is a very nice competition system in many circumstances, especially for club competitions.

The system was developed in the late fifties by the chairman of a chess club in Hengelo (Holland). His name was Keizer (which is the Dutch word for “Emperor”) and the system has been named after him later. He found for his club that is was very annoying that players who appeared on the club very well might not be able to play, as there opponent did not show up. Round robin competitions suffer from this problem. There are a fixed number of rounds. Everyone has to play everyone else. If someone’s opponent doesn’t show up then he can’t play. If more opponents don’t show up then a number of players may not be able to play. They are forced to play blitz games or so. Another well-known problem of Round Robin competitions is that very uninteresting games may be scheduled. Usually a game between a 1900 rating player and a 1400 rated opponent is not really interesting.

Swiss pairing systems can be used to work around these problems but they have some problems as well. Usually you are not allowed to play the same opponent twice (although no-one will really stop you from doing so). Furthermore Swiss is complex to pair and the scoring has some drawbacks.  They tend to be pretty leveling. Someone can play bad in a number of rounds, can recover against a number of weak opponents en with a sprint in the final rounds he can finish on a nice position anyway. Especially when the number of rounds is high (more than 10) then this is an important drawback of Swiss.

So Keizer came up with a system which handles these problems well – or at least better. Important ideas behind Keizer are:

  • Not everyone will play anyone else during the tournament. Maybe because the number of participants exceed (by far) the number of playing rounds. Or because this results in more interesting games.
  • Everyone will be able in each playing round, except one if the number of available players is odd.
  • A win against a strong opponent scores more than a win against a weak opponent.
  • Multiple plays between two players may be allowed.
  • Every play is supposed to be between two nearly equally strong players.

Every player in a Keizer competition will have a value. The highest value goes to the top ranked player; the second highest value goes to the second ranked player, and so on. Usually the value of the top ranked player is approximately three times the value of the lowest ranked player. Each next player has a value one less than the previous one. For instance: If a competition has 35 players then a nice value would be 50 for the top ranked player. The bottom ranked player would consequently have a value of 16.

A player who beats an opponent will score the value of this opponent. A player who draws someone else gets half of the value of the opponent. A player who loses gets 0 points.

Pairing of a Keizer competition basically is very simple. The top ranked available player is paired to the second ranked available player. The third ranked player is paired to the forth, and so on. However, many clubs prefer to have a number of exceptions on this. For instance when two players have met in some round then they should not meet again in the next X rounds. Also it may be required that players should not play with the same color more than two times in a row; or that the color balance of any player may not exceed +2 or -2. But these are variations which are not really endorsed by the original Keizer system. Just many clubs prefer to apply them.

Color allocation is done in a way that the color preference of the player with a color balance most distant to zero is granted. If two players have the same color balance then the player who has played the most successive games with the same color will now play with the other color. If this criterion ties too then the history is checked. Where a change in color sequence occurs there the colors will be opposite to the color allocation of that round. If this also ties then various color allocation rules may be used: this is not fixed in Keizer.

Absences don’t always score 0 points in Keizer. If an absence should score 0 then the absent player would drop a lot on the ranking and would probably meet a much weaker player in the next. This is not nice for both of them. Therefore absences are usually rewarded with 1/3 of the players own value. Sometimes players can not play because they are occupied on behalf of the club. For instance: they have to play with a club team against another club. Then 1/3 of the player’s value would be a small reward for their effort. Usually they will be rewarded with 2/3 of their own value. In some cases clubs prefer to take into account the result of a club match. Then the opponent players are rewarded a virtual value, and the result of the club players is multiplied with these virtual values, depending of winning, drawing or losing. Usually the virtual value of the top board is higher than the virtual value of the lower boards.

The values of the players are recalculated after each round. Then the total score is recalculated from scratch. Suppose John beat Jim in one of the first rounds. Jim had a value of 50 so John received 50 points. But in the next rounds Jim plays poor and the drops in the ranking. His value has now become 40. Then in the ranking the result of John earlier will no longer be 50 points but 40 instead. The idea behind is that Jim appears not to be as strong as assumed earlier, and the performance of John is not as great as was assumed earlier. Therefore Johns score is corrected after all. If Jim recovers and after some more rounds his value has become 45, then Johns score for his earlier win against Jim will become 45 at that point; etcetera.

For calculating the ranking the scores of each round are added. In addition to that, each player gets a “bonus” of one time his own value. Then the player with the highest score is ranked first.

Below is a small example, taken from the document Keizer wrote about his system. The initial ranking is:

1.  Johnson      50
2.  Petersen     49
3.  Baker        48
4.  Butcher      47
5.  Carter       46
6.  Harrison     45
7.  Smith        44
8.  Higgins      43
9.  White        42
10. Brown        41

Results of the first round:

Johnson    Petersen     1-0
Baker      Butcher      ½-½
Carter     Harrison     0-1
Smith      Higgins      ½-½
White      Brown        0-1

Ranking after round 1:

1.  Johnson      50+49=99
2.  Harrison     45+46=91
3.  Brown        41+42=83
4.  Baker        48+23½=71½
5.  Butcher      47+24=71
6.  Smith        44+21½=65½
7.  Higgins      43+22=65
8.  Petersen     49+0=49
9.  Carter       46+0=46
10. White        42+0=42

The pairing for the second round would be:

Harrison   Johnson      1-0
Brown      Baker        1-0
Butcher    Smith        ½-½
Higgins    Petersen     0-1
Carter     White        ½-½

Now for the ranking the values are related to the ranking after the previous round. So Petersen’s value no longer is 49 but it is 43, which is the value for the eighth position. This means that Johnson’s win in the first round no longer scores 49 points but only 43.

1.  Harrison     49+42+50=141
2.  Brown        48+41+47=136
3.  Johnson      50+43+0=93
4.  Butcher      46+23½+22½=92
5.  Smith        45+22+23=90
6.  Petersen     43+0+44=87
7.  Baker        47+23+0=70
8.  Higgins      44+22½+0=66½
9.  Carter       42+0+20½=62½
10. White        41+0+21=62

For the ranking of the next round, Harrison’s value will be 50, and White’s value will be 41. Etcetera.