Hi,
In a McMahon tournament of, say, 70 players and 5 rounds, how should the McMahon bar be set up if we want to fairly award the three best players ?

I'd start with the idea of having 6 players above the bar. If they'd all meet each other, they would be all fairly ranked.

However since they will be paired together in the first round, they won't play each other in the second round, as the winners of the n-1 group will meet the loosers of the top group.
I don't know what to do... If it have any relevance, there is a favorite: the winner of the two last editions of the tournament is 7 dan, and nobody else is ranked better than 4 dan.

Thanks for any input.

http://britgo.org/organisers/handbook/tournament4.html

I'd say have at least 8. We usually have 8 for a 3 round McMahon with 30-50 players in the UK, though Geoff Kaniuk (the author of GoDraw and probably that document) tends to think we sometimes have too many if you have some 2k in there with a 4d as that's basically a no-chance match.

Thanks for the link. I found this information, but it is only relevant if we want to fairly decide one winner. Shouldn't things be different if we consider the top three winners ?

I guess that setting the bar higher will decrease the luck factor in the attribution of the second and third prize, that is unavoidable with only 5 rounds for 70 players. On the other hand, it will be more unfair for those who could pretend to get to the 2nd and 3rd place, but would then start below the bar.

If you are interested in 2nd and 3rd place, wouldn't that mean increasing not decreasing the number of players above the bar versus those recommendations?

That's exactly what I am wondering.
On one hand, it seems fair for the new players included. Is that what you mean ?
On the other hand, doesn't it increase the probability to have ties ? And then prize attribution based mostly on luck... It's a complicated math problem for me.

Ideally, everyone with a reasonable chance of winning is in the open group, and everyone else is set below them. You probably want to have at least as many people in the open section as you have rounds, but you also don't want to flood it with players who may win by beating everyone else at their rank but not having many games with stronger players because of the distribution of ranks in the bar.

You might be better off by looking at the highest ranked player and placing the bar a certain number of ranks below them, so if your strongest player is 6d, maybe the bar is set to 4d and above. Once you start getting farther apart, the games become more and more of a foregone conclusion, which isn't that much fun for anyone.

That said, if you have as in your example one 7d and the rest of the group at 4d or below, it may be best to consider a slightly different format that McMahon, which with even games will basically reward the 7d player with first place for showing up. Perhaps a top group that at 4d and above is considered in the bar for the purposes of placing in the tournament, but which still plays at handicap against the 7d until they win up to that level. I gather this is why you want to collect enough data for good 2nd and 3rd place winners, but you may as well declare them winners of the 2nd group rather than the open group if you want to stick with McMahon with that big a gap, and have an open group of 1.

Thanks for your suggestions, Uberdude and skydyr.

I don't think that I'll mess with handicaps at a 7 dan level. But people in the federation seem to have the same preference as you : the more people in the top group, the better (as long as it doesn't introduce an odd repartition, as skydyr recall).

So I'll try to be on the 12 players side rather than on the 6 one.

12 players in the top group looks reasonable. With 70 players I assume that there isn't any big gap in the strength distribution just below the top.