After reading this thread I was curious how often morgenish started games last. Considering morgenish has played over 6,000 games on this site, I felt it was worth the time to look at. I looked at all the games played this month. This is the data I compiled. Long post incoming!
First of all, morgenish plays a lot of 2P games and no doubt this was included in the observations. So I separated these. There were two 4P games played this month (and morgenish went first in both!) and the other 49 games were 3P. For simplicity, I treated the 4P games as 3P and compiled the following data:
1st, 2nd, 3rd starting position
Glow: 11, 5, 15
Kingdom Builder: 4, 1, 2
Splendor: 2, 2, 4
Azul: 1, 0, 0
Tokaido: 0, 0, 1
CuBirds: 0, 1, 2
Going first in Glow: 35% (within expectations)
Going second in Glow: 16% (33% expected)
Going third in Glow: 48% (33% expected)
Going first in total: 18/51 = 35% (within expectations)
Going second in total: 9/51 = 18% (33% expected)
Going third in total: 24/51 = 47% (33% expected)
For the sake of completeness, here's the order from most recent to least recent:
last, last, last (3x streak), middle, last, last, last (3x streak), middle, last, middle, first (in a 4p game!), middle, last, first, last, first, first, first (3x streak), last, first, last, last, last (3x streak), middle, middle, first, first, first (3x streak), last, last, last, last (4x streak), first, middle, last, first, first, last, first, middle, first (in a 4p game!), first, first (3x streak), last, middle, last, last, first, last, middle, first, last
As for 2P games, I was only able to look at the last 136 games due to reaching the limit to the amount of replays I can watch. So here's the data on the last 136 head-to-head games:
Azul: 25, 28
Kingdom Builder: 16, 19
CuBirds: 12, 13
Just Desserts: 4, 3
Glow: 5, 7
Patchwork: 0, 4
Percentage of games going first:
Azul: 47% (within expectations)
Kingdom Builder: 46% (within expectations)
CuBirds: 48% (within expectations)
In total: 46% (within expectations)
The sample size is small, I admit, but there's enough to illustrate what's going on. This data explains why morgenish feels like there's some sort of bug that makes it more likely to go last. Especially if 2P games were taken into consideration. It seems the real anomaly is not going second in multiplayer games this month! But I'm sure that will even out within the next few months. Or might have already evened out if previous months had a streak of a lot of times going second.