In a small tournament – even one not so small so that the number of rounds is barely bigger than the number of players – it is often advisable to make some of the colors NOT work in the early odd-numbered rounds (such as round 3).
Alternating all colors in every round has the effect of dividing the players into two camps, those who started with white and those who started with black, and making inter-camp pairings exclusively, with no intra-camp pairings. Eventually, in a small tournament, there will be a shortage of possible inter-camp pairings, so that intra-camp pairings will become necessary. When this happens, it’s better if it happens in an odd-numbered round, where color alternation is the issue rather than color equalization.
For example, let’s look at your basic 16-player, 4-round “theoretical” tournament (no draws, no upsets, no byes or forfeits):
rd1 rd2 rd3 rd4 colors cumulative
01 W09 W06 W04 W02 wbwb 1,2,3,4
02 W10 W05 W03 L01 bwbw 1,2,3,3
03 W11 W08 L02 W06 wbwb 1,2,2,3
04 W12 W07 L01 W08 bwbw 1,2,2,3
05 W13 L02 W09 W07 wbwb 1,1,2,3
06 W14 L01 W10 L03 bwbw 1,1,2,2
07 W15 L04 W11 L05 wbww 1,1,2,2
08 W16 L03 W12 L04 bwbb 1,1,2,2
09 L01 W14 L05 W13 bwbb 0,1,1,2
10 L02 W13 L06 W12 wbww 0,1,1,2
11 L03 W16 L07 W14 bwbw 0,1,1,2
12 L04 W15 L08 L10 wbwb 0,1,1,1
13 L05 L10 W16 L09 bwbw 0,0,1,1
14 L06 L09 W15 L11 wbwb 0,0,1,1
15 L07 L12 L14 W16 bwbw 0,0,0,1
16 L08 L11 L13 L15 wbwb 0,0,0,0
In the above example, the TD (or pairing program) has made the usual color transpositions in rounds 2 and 3, and all of the colors have “worked” so far. But in round 4, in the 2-point group, there is no reasonable way to avoid bad colors on two of the three boards.
If, instead, transpositions had been made only to equalize (but not merely to alternate) colors, rounds 3 and 4 would have fallen into place naturally:
rd1 rd2 rd3 rd4 colors cumulative
01 W09 W06 W03 W02 wbwb 1,2,3,4
02 W10 W05 W04 L01 bwbw 1,2,3,3
03 W11 W08 L01 W07 wbbw 1,2,2,3
04 W12 W07 L02 W06 bwwb 1,2,2,3
05 W13 L02 W09 W08 wbwb 1,1,2,3
06 W14 L01 W10 L04 bwbw 1,1,2,2
07 W15 L04 W11 L03 wbwb 1,1,2,2
08 W16 L03 W12 L05 bwbw 1,1,2,2
09 L01 W14 L05 W12 bwbw 0,1,1,2
10 L02 W13 L06 W14 wbwb 0,1,1,2
11 L03 W16 L07 W13 bwbw 0,1,1,2
12 L04 W15 L08 L09 wbwb 0,1,1,1
13 L05 L10 W15 L11 bwwb 0,0,1,1
14 L06 L09 W16 L10 wbbw 0,0,1,1
15 L07 L12 L13 W16 bwbw 0,0,0,1
16 L08 L11 L14 L15 wbwb 0,0,0,0
The moral: In a smallish tournament or section, transpose to equalize colors, but not to alternate colors. (In a pairing program, change the alternation limit from 80 to 0, while leaving the equalization limit at 200).
Bill Smythe