To the best of my knowledge it's pure coincidence. However, more than one
player in a game does increase drops and drop classes/amounts, if I am not
mistaken.

Hmmm, maybe somebody with some actual knowledge could answer this.

A little of each :)

Mickey

In a solo game Nilly has a 1:12.66 chance of dropping a Key of Destruction.
In general, more players in the game give you a better chance of a drop. For
example, a party of 8 all killing Nilly together has a 1:8.81 of getting a
Key.

The technical specifics about it:
There is something called 'effective players'. This is partied players who
are in the same area (about 2 screens distance) at the time of the kill.
Partied players not in the same area, unpartied players and additional
players from the SP command '/players x' count as 1/2 of an effective
player. For drop purposes fractions of effective players are dropped. When
running act bosses, in order to reduce their 'no drop' chance to zero (to
guarantee they drop their maximum number of items) you need 3 'effective
players'.

So in your case above, the additional player in the game didn't change the
drop chances at all, you just had a lucky streak. And overall, you got more
Keys than average. Three keys usually take 38 runs.

Regards-
Mark

Bongo-Fury

JR