Oops, you’re right. There are no two rounds (consecutive or not) in the 6-player Crenshaw-Berger table where all players alternate colors between the two rounds.
OTOH, the tables for 8, 10, 12, … , 24 players all have consecutive rounds where all players alternate. In fact, in every even-numbered round in those larger tables, all players alternate from the previous (odd-numbered) round.
I also note that Messrs. (Mmes.?) Crenshaw and Berger did not use the same algorithm to construct their 6-player table as they did for their larger tables. If they had, their 6-player table would have turned out as follows:
For eight players or more, the only difference between the Crenshaw and Berger tables is the order of the rounds (the rounds are in exactly reverse order in the two tables).
I believe that the construction of the Berger six player table is fully consistent with that of the tables for higher number of players. Isn’t the six player Berger table exactly your table read from bottom to top (that is, reversing the order of the rounds)?
I’m glad we have a historian on board who has finally weighed in.
So, Crenshaw and Berger each had their own sets of tables, which were identical to each other except that the rounds were in reverse order, right?
The treatment in chapter 12 of the 6th edition rulebook only speaks of “these Crenshaw-Berger tables”, without drawing a distinction between the two.
I’ll have to take your word for it, because the 6-player table in the rulebook is another animal entirely, not consistent with either Crenshaw or Berger as you have described them.
Apparently, then, the tables in the rulebook (for 8 players or more) are the Crenshaw versions, which are the exact reverse of the Berger versions. For 6 players, the table I constructed mimicked the rulebook versions of the larger tables, i.e. the Crenshaw versions, which is consistent with your query about my 6-player table being the exact reverse of the Berger 6-player table.
Whew! I hope everybody followed that. Or, at least I hope everybody followed it who still gives a rat’s booty about this whole discussion to begin with.
Berger’s table for a ten person RR has players 1-5 having White against players 10-6 respectively where player 10 stays put while everyone else rotates around a long table. In the second round Player 1 has White (again!) against Player 2 while Player 6 has his second Black against 10. Crenshaw corrected(!?!?) the problem by running the tournament backwards, my solution is to start with Berger but reverse the colors of all games not involving player 10. This link does it both ways: rrpair.php. Player 1 still has White against 10 but 2-5 have Black against 9-6 in mine in the first round.
I’m not entirely sure how I qualify as a “historian.”
I actually believe that “Crenshaw-Berger tables” are the tables in the Official Rules of Chess while “Berger tables” are the tables in the FIDE handbook. I definitely agree the Crenshaw-Berger table for six players is a strange animal that seems to have no rhyme or reason to it.
Interestingly, the Berger tables in the FIDE handbook do not include any instructions for swapping colors in later rounds if there is a withdrawal. I haven’t tried very hard, so I’m not sure whether it is possible to come up with instructions similar to those for the Crenshaw-Berger tables. I also wonder if fixing colors in case of a withdrawal has any influence on why the six player table is as “weird” as it is.
More generally, in the Berger tables for n players:
Only players n/2 and n have perfect color alteration. Players 1 and (n/2 +1) have the same colors in rounds 1 and 2; players 2 and (n/2 + 2) have the same colors in rounds 3 and 4; and so on.
Players 1 through n/2 have white against player n, while players (n/2 + 1) through (n - 1) have black.
For all other games (that is, games not involving player n:
[list][*]If both players’ pairing numers are even or both are odd, the higher numbered player has white.
If one player’s pairing number is even and the other’s is odd, then the lower numbered player has white.
[/*:m][/list:u]
For a double round robin using the Berger tables, the arbiter is instructed to swap the order of the last two rounds of the first half only to avoid giving the same color in three consecutive rounds to two players (players 1 and (n/2 + 1)).
Well, maybe then as an expert in an area I was never sure about.
I am now learning more about these tables than I ever wanted to know.
This is the old scheme that everybody knows, even in “free-for-all” round robins where players just grab each other whenever convenient. “Hi, I’m number 4. What’s your number?” “I’m 10.” “OK, then you have white. Let’s do it.”
You must have decided that the whole round-robin concept, and the last several posts, weren’t complicated enough yet, so you had to add a new wrinkle.
What happens if three players enter late?
What happens if M players enter late, where M is large enough so that there isn’t enough time anymore to make it a round robin, but small enough so that you don’t want to simply convert back to a Swiss because of the various already-played-each-other traps?
<1>You can add any number of players by finding the appropriate entries on the tables.
<2>You start an additional brand new round robin(s).
It works the other direction too. If you have a ten player round robin and three drop out as first round no-shows, that subsequently inform you they won’t be playing (and you can’t substitute somebody else in) then you simply take the games you have, convert to a seven player round robin that matches the colors already played and continue from there (two fewer rounds makes up for the needing to play the one or two unplayed round one games at a later date). If there are multiple possible ways to make the first round fit then make a random selection from them. Don’t do a rebuild like this with FIDE.
Puff, puff.
For <1> you can add two players to the right end and one to the left end, but all of them would have to have really good excuses and anyone already in the tournament could object and shut them out. Letting only one player in if there are an odd number of players should be ok with everyone (that was me about 50 years ago). As for <2>, forget about it.
When in college I was running a team selection tournament as a round robin. Having just learned how the RR worked, I derived the schedule w/o the rule book, but “luckily” had the players rotate the wrong way– after playing round 1 they would play round 9, then 8, etc. At that time the Burger tables started two players with the same color for the first two rounds so everyone would alternate the first two rounds by going backwards. When two players dropped out in the second round, I found a way to do the RR starting with a pair of double colors, reducing the rounds by two and letting the first round opponents of the dropouts play a makeup game.
To inhibit dropouts in a RR, charge the players a refundable escrow fee. If they complete all of the rounds, they get their money back along with any prize earned. The fee has to be large enough to mean something. No excuse, emergency, or imminent Doomsday is accepted for dropping out; the fee reverts to the organizer or to the prize fund. This was done in one event because of potential personal animus between a couple of the players who had a tendency to make scenes and walk out in a huff when they lost a game to a rival. As a result, they behaved like cherubs and the event went off without incident.
There are no two rounds (consecutive or not) in the 6-player Crenshaw-Berger table where all players alternate colors between the two rounds.
