Bug
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re:Chess Tournament Pairing Problem - 2005/11/14 21:50
are several approaches.
One is not to make the colors work too well in the odd-numbered rounds (when only alternation, not equalization, is at stake). An extreme case occurs with 6 players. There, if all the colors alternate in both rounds 2 and 3, then there are NO pairings at all in round 4. I call this the Dennis Keen trap, although TDs both more and less illustrious have fallen into it many times.
With 8 players, if all the colors "work" in rounds 2 and 3, there is only ONE set of pairings which will again make the colors work in round 4, and that is likely to be a highly undesirable bunch of pairings score-wise. Best to let some colors be bad in round 3 -- even transposing to make the colors worse, if necessary.
In general, with fewer than 20 players in an event of 4 rounds or more, I would transpose only to equalize colors, not to alternate them. (This can be accomplished in pairing software by changing the transposition limit for alternation from 80 to 0, while leaving the equalization limit set at 200.)
Tom Doan suggested another idea -- decelerated pairings. In rounds 3-4 of a small tournament (say, fewer than 16 players) of 6 rounds or more, temporarily add 1 point to every player in the BOTTOM half, for pairing purposes.
The classic idea, of course, is suggested in USCF rule 29S, "Using round robin table in a small Swiss". Pair the first round (maybe even the first two rounds) as a Swiss, then look up the Crenshaw-Berger tables in chapter 13, and assign the pairing numbers in such a way that the pairings already made fit into one round (or two rounds) of the table. (Remember, in a round robin the players should be ordered randomly, not by rating.) In subsequent rounds, make the pairing you want on board 1, find that pairing in one round of the table, and make the rest of the pairings from that round of the table. (Assign colors using Swiss rules, though.)
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