Another pairings question

[Smythe_Dakota]

@wbport

… [ The trap ] could be avoided with a swiss guided round-robin. Select pairing numbers which will give traditional swiss pairings in the first round then select the round from the RR table that pairs the most number of perfect scores.

For a 6-player tournament, that’s overkill. Rounds 1 and 2 can be paired any way you want. When you pair round 3, simply make sure there exists a set of round 4 pairings.

If you prefer a visual demonstration, simply draw a regular (equal-sided, equi-angular) hexagon. Place the players at the vertices in such a way that each player is adjacent (along the perimeter) to the two players he has already played in rounds 1-2.

For example, in the case I presented:

(1) 1.0 W4 L2
(2) 2.0 W5 W1
(3) 2.0 W6 W4
(4) 0.0 L1 L3
(5) 0.0 L2 L6
(6) 1.0 L3 W5

– you could arrange the players on the hexagon in the order 1,4,3,6,5,2 (clockwise around the perimeter).

To pair round 3, simply draw a line (chord) between each player and one of the other players he has not yet played. There are four ways to do this:

(a) Pair each player against the player diametrically opposite (i.e. draw the three diamaters).

(b) (c) (d) Pair one player against the player diametrically opposite (i.e. draw one diameter). Make non-diameter pairings for the remaining four players, by drawing the two non-diameter chords perpendicular to the diameter already drawn.

There is only one way to do (a). There are three ways to do (b) (c) (d), depending on which diameter you started with.

Of these four possible pairings, only (a) falls into the trap.

Bill Smythe

[Smythe_Dakota]

Even in a somewhat larger tournament, it is still not a good idea to make the colors work too well.

In an 8-player 4-round tournament, for example, if all the colors work perfectly in the first three rounds, there will be only one set of pairings in round 4 which will continue the perfect color streak. And that set will probably be peculiar, such as pairing a 3-0 against an 0-3.

In a tournament with fewer than, say, 20 players, I prefer to transpose only in order to equalize colors, never merely to alternate colors. In the pairing programs you can change the transposition limit for alternation from 80 points to 0, while leaving the limit for equalization at 200.

Bill Smythe

[Harold_S]

Not true. With 6 players, the trap occurs with equal likelihood in either a 4- or a 5-round event. In fact, if you can pair round 4, you can automatically pair round 5 – just pair each player against the one player he hasn’t already played.

Perhaps you meant that the trap can occur only in an even-numbered round. That’s true for 6 players, I’m not sure about more.

The reason it doesn’t happen in a 5 round Swiss with 6 players is because it wouldn’t (or shouldn’t) be paired as a Swiss. It would be paired as a round robin! A director who would try to pair it as a Swiss is looking for trouble.

[Smythe_Dakota]

@Harold S.

… A director who would try to pair [ a 6-player 5-round event ] as a Swiss is looking for trouble.

Trouble which can be easily avoided just by being careful in round 3. As I said, using a round-robin table is overkill in this case. I prefer to keep the brain cells alive by forcing myself to think while pairing.

Bill Smythe