# FIDE vs naive vs delete1-Buchholz (Danger, Math)

• FIDE-Buchholz BF: the one that is used in "official" tournaments and defined in the FIDE rules, somewhat complicated. Considers bye, forfeit and other not played games.
• Naive Buchholz BN: Sum of the opponents points.
• Delete-1 Buchholz BD: Naive, plus deleting pointwise worst opponent

I just played a tournament, where my competition ended up equal in points, so Buchholz had to decide. Cross table suggested I was in front whoppingly: 4.5 BP. We both played against two different players who played only 5 (me) resp. 2 (him) rounds. Delete for fairness - I'm still 2.5 BP in front. Official table: A tiny 0.5 BP.

Seeing patterns everywhere, since 5-2=3 can't play a role here, let's generalize: A and B played maximally against one C and D having not played all games, C=D is allowed. Assume C and D are deleted by BD. Then for the Buchholz differences of A and B the following holds for my case:

BD=(BN+BF)/2, i.e, the official Buchholz doubles the effect of the delete-1 one.

Is this correct in general?