Every time you pair players for the first time the number of first-time pairings increases by 1 for each player. So no it doesn't necessarily minimize, actually it doesn't ever minimize, nor maximize. All you can do is arrange players to maximize first-time pairings in the current round.

For that I suggest a computer program to run combinations, or for small tournaments just keep a league table and use it for the next tournament as well, blocking out pairs which have already been done and then limiting yourself to choosing pairs from what is available.

In theory there's no way to get around the fact that each time you pair someone the number of previous pairings increases by one; no matter how you try to arrange the players, eventually there will exist players who have a previous number of first time pairings equal to the number of players in the tournament, and then there's just nothing you can do. Well there's one thing. If you seed players with a large number of pairings against players with a low number of previous pairings in the first round, that makes it more likely the players who have a large number of previous pairings will get knocked out. That's about all you can do I'd guess, once you start running into large numbers of players with more than 7 previous pairings.

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Since the pairing in question is knock-out, any pairings that are added during the knock-out are irrelevant, since that pairing can never happen again anyway, as one of the players has been knocked out. That means that only the prior pairings from the McMahon phase (rounds 1-7) are relevant.

As Joaz has shown theoretically, and several programs have since shown experimentally, it is possible to minimize the chance of repeat pairings in the next round by optimizing the pairing for the current round.



For general pairing, there are plenty program. This thread is very specifically about an 8 player knock-out after 7 rounds McMahon at the European Go Congress.



The pairing does not involve the whole tournament, only the top 8 Europeans, who have played part of their previous pairings against players outside the top 8 (or against non-European players).