I tend to avoid playing second. There isn’t any strategic advantage to playing second vs playing third or fourth: I don’t get much of a chance to learn from others on an unfamiliar game, and I don’t have enough information to settle on a strategy on a familiar game when I’m playing second.
Playing third is my second least-favourite choice. It’s only sometimes better than playing first: it does give me some information that might be valuable if the placings are tight, but it’s not as valuable as fourth.
Playing fourth gives me the most information, but also puts the most pressure on me. For games I understand well and where there are several choices of strategy depending on my scoring deficit, fourth is my preferred choice simply because it allows me to minimise risk, despite the pressure. I can adjust strategy depending on the scoring gap I need to close.
On games where there is not much of a choice of strategies (such as Flash Gordon, where ball time pretty much relates linearly to score because there are few “monster shots”), I often choose first. That’s because knowing what score the other players have achieved doesn’t give me much of a strategic advantage, but coming last when I’m behind just puts pressure on me. I might as well play first and do as well as I can. If that isn’t enough, it’s unlikely that playing last would have made much of a difference.
So, in order of preference for me:
Familiar game with strategic choices: 4th, 3rd, 1st, 2nd.
Familiar game without strategic choices: 1st, 4th, 3rd, 2nd.
Unfamiliar game: 4th, 3rd, 1st, 2nd.
This last one is possibly irrational; if I don’t know the game, preferring first over second may well be wrong because any information I can glean by watching my opponents play is potentially valuable. I guess I just don’t like second…