Here’s an extremely simple example (even simpler than those posted so far):
colors
1 W4 L2 W6 wbw
2 W5 W1 W3 bwb
3 W6 W4 L2 wbw
4 L1 L3 W5 bwb
5 L2 L6 L4 wbw
6 L3 W5 L1 bwb
Here, there were a couple of minor upsets in round 2, otherwise everything went as “planned”, and the round 3 pairings are the only “correct” ones in terms of score. So this is an extremely feasible hypothetical example. Yet, there are no round 4 pairings.
It is a theorem that, in a 6-player Swiss, if all the colors alternate in both rounds 2 and 3, there will be no pairings for round 4.
This is an extreme example of what I call the “camp” effect. If all colors alternate in the early rounds, you have divided the players into two camps, those who started with white and those who started with black, and you have made exclusively inter-camp pairings, no intra-camp pairings. In a small tournament, the inter-camp pairings will soon become extremely scarce, and you will have to make many intra-camp pairings (those where the colors don’t work).
A less extreme example occurs with an 8-player Swiss. In this case, after 3 rounds of perfect colors, there exists only one set of round 4 pairings which continues to alternate colors, and this set is almost certainly ridiculous.
The moral? In a small tournament, make sure some of the colors don’t alternate in round 3. Things will go much better in round 4.
On how many boards should colors fail to alternate? I’d say at least 1/3 of the boards, i.e. 1/6 of the players.
What constitutes a “small” tournament? I’d say up to 20 players or so.
How does one accomplish this with a pairing program? Simply change the transposition limit for alternations from 80 to 0 (but keep the equalization limit at 200). That way, the bad colors will occur primarily in the odd-numbered rounds, where they are less harmful.
Bill Smythe