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### Awkward numbers at tournaments

Posted: Sat Jun 04, 2016 2:31 pm
In our early Skat tournaments we assumed that we can only run a round if the number of players is a multiple of either 3 or 4. This meant that on occasions the organiser has needed to sit out to make the numbers right. In a tournament in early 2012 we had the very awkward number of 11 so two players sat out.

Our earliest tournaments were all Synchron, and all our Synchron tournaments have had a multiple of 3 or 4 in each round. In 2009 we ran our first non-Synchron tournament (hands dealt at each table separately), and in the first two such tournaments we occasionally asked a 4-player table to play 24 boards while other tables played only 18. In 2011 we introduced the "floater" which allows a mixture of 3- and 4-player tables. (So far we have only used this to enable 10 active players, but the method would work for 7, 11 or larger awkward numbers.)

We have so far been unable to run a Synchron tournament with a mixture of table sizes because of various assumptions we make about each round of a tournament:

(a) all players must play the same number of boards;
(b) in Synchron each player is ranked against one player at each of the other tables, and a fixed number of matchpoints is shared among the players in any seat.

(a) is important in non-Synchron tournaments since most scores are positive and it is unfair to allow some players more chance to get these scores than others. In Synchron it is less important since one is really playing for "diff" (the deviation from the average score in one's seat) and the average of this is zero.

(b) seems obvious, but it is possible to run a tournament which violates it and is workable. In the following discussion I shall assume we have seven players, though the idea can be extended to 10, 11 or more.

The scheme is simple. Four players sit at table 1 and three at table 2. Each table plays 12 boards, starting with board 1 on table 1 and board 7 on table 2. The boards are played strictly in order, with the dealer moving one place to the left after each board. (The colours of the packs will be appropriate at only one of the tables, so the other table must take care that the correct player deals.)

At the end of the round each player will have been compared three times with each of the players at the other table, so a player's "diff" is obtained by comparing with a composite opponent rather than a single other player. The matchpoints could be calculated by simply ordering the "diffs", but this would exaggerate the effect of one big board, and I suggest simply awarding 2 points for a positive "diff", 1 for zero and 0 for negative. This means that the total number of points awarded will vary: it will usually be 6 or 8 but could be anything from 2 to 12.

The standard scoresheets can be used while playing. Working out the scores is more intricate than in standard tournaments but it is manageable with a spreadsheet.

Seven rounds are needed to give all players the same number of boards, and that is why I suggest only 12 boards per round. If we don't mind a slightly unbalanced tournament we can play fewer rounds with more boards — I suggest a multiple of 4 rather than 3 so that everyone at each table plays the same number. (Doing this is best if it is likely that an eighth player will arrive late.)

With ten or eleven players the matchpointing would be done by the same method as above for each of the three pairs of tables. Each player gets two scores which are then added together. Ten players could equalise the boards per player by having five rounds of 12 or 16. With eleven we would have to have slightly different numbers of boards per player, since time does not allow for eleven rounds.

Patrick