The 6-player Swiss trap can rear its ugly head when 6 players are paired as a Swiss, and there are either 4 or 5 rounds.
Example (columns are player number, color history, round 1, round 2, round 3):
1 wbw W4 L2 W6
2 bwb W5 W1 W3
3 wbw W6 W4 L2
4 bwb L1 L3 W5
5 wbw L2 L6 L4
6 bwb L3 W5 L1
You will note that round 1 pairings are the normal top half vs bottom half. Round 2 are also the normal pairings, given the round 1 results, with winner vs winner, lowest-ranked winner vs highest-ranked loser, and loser vs loser. Round 3, also normal, pairs the 2-pointers against each other, the 1-pointers against each other, and the 0-pointers against each other.
Now try to pair round 4. You will find there are no pairings at all, even regardless of scores, ratings, or colors. Every pairing attempt involves matching somebody against an opponent he has already played.
How to avoid this trap? Some TDs prefer to use the Crenshaw-Berger tables for a 6-player round-robin, skipping one of the rounds if there are only 4 rounds. But this can get tricky, too.
I prefer to go ahead and pair it as a Swiss, BUT then you need to be careful when you pair round 3. (You can pair rounds 1 and 2 any way you want.)
When you (or the computer) spits out tentative round 3 pairings, just take a close look and see if there is any way at all to pair round 4. If so, go ahead. Round 5 will then work fine, because you would simply pair each player against the one player he has not yet met.
But if there are no round 4 pairings, make some transpositions in the round 3 pairings, and check again to see if there are round 4 pairings.
The following visual method may help a little. After round 2 is paired and the games are being played, draw a regular hexagon, with each vertex representing a player, and each side representing a pairing. In the pairings shown above, you would arrange the vertices in the order 1-4-3-6-5-2-1 going around (say) clockwise. This means, for example, that 4 has played both 1 and 3, etc around the circle, with 2 having also played 1, the hexagon having come full circle.
There are now four possible pairings for round 4:
(a) Pair each player against the player diametrically opposite across the hexagon.
(b) (c) (d) Pair ONE player against the player diametrically opposite across the hexagon, but pair the remaining four players each against an opponent NOT diametrically opposite.
Option (a) is the one that will get you into trouble. Options (b) (c) (d) will all work fine.
That means that you have a 25% chance of screwing up, if you don’t watch what you’re doing.
Bill Smythe