I noticed game 237 late on the evening it was posted, and I thought I would load the save and maybe play the first few turns. Of course, a few "just one more turn"s later and I had already blitzed out around 70 moves on auto-pilot, which is probably not conducive to a quick finish time. The game is going alright, but I don't think I will be troubling any hall of fame entries with this one.
I started by moving onto the silver, to grab the north banana for the capital. I went monument - worker - shrine, and was lucky to still get first pantheon (religious idols). Later on I would get even more lucky in my faith game by getting two big faith ruins (60 faith each), getting me a nice and early religion (tithe, religious community). I noticed that my starting island only had two reasonable city spots, so I went Pottery - Sailing - Optics. That made for quite a slow start, however, especially since my fourth city was quite late because of barbarians on the west island.
One thing I wanted to try in this game was to demand tribute from city states using triremes. I had read a player's account of an older GoTM prince water map (I believe 161, Germany) that you can tribute using only two triremes. It kind of worked for me. I built two and purchased another, and managed to tribute three city states. I also built another warrior to clear the barb camp on the west island. All that military makes for a comfortable game, but perhaps it costs some tempo when you are going for a quick science victory. Despite all those triremes, I still got my cargo ships going very late - and that is often a deciding factor in how well an island game is going.
On prince, there is always at least the temptation to go for Great Library, and especially for a science-victory game it's good if you can get it without sacrificing too much in the early game. However, it already went on turn 57, by which time I had barely researched writing. I have had this experience before on water maps, that the wonders seem to go earlier than I was expecting from the difficulty level. Perhaps it is because the AI has nothing better to do than to spam wonders: no neighbors to pester, no barb camps to clear, indeed, no cities to settle. Fortunately I did not lose any hammers, but I did have to postpone my NC, which was already late for a science game, because Portugal was building Oracle around turn 90. Ideally in a prince game, you can complete Oracle the turn you enter Renaissance to immediately pick Rationalism. Perhaps in this case, I should simply have ignored Oracle.
In the turn 100 screenshot below, I am finally building my NC, but I'm also building another settler. I had spotted the south island quite late, but it had some decent resources and a luxury, so I thought: why not. My first expand Osaka is currently building Colossus. I would also have liked to get Hanging Gardens in that city, since it has no fresh water of its own, but you can see in the bottom right of the screen that Pocatello just constructed it.