Miscellaneous topics
High Score:
There is a brain-dead way to increase your score indefinitely. You need only give systems to a non-repulsive enemy, and capture them back, over and over. The only non-trivial detail lies in making sure you don't exceed 32,767 points, since negative scores don't register on the high score list. So much for score.
High Population:
Growing a high population is a slightly less boring way to increase your score. Locally advantageous strategies include:
A less trivial step is to destroy all planets which are toxic, medium, small, or tiny. The key here is to give systems containing such planets to a computer opponent, and then attack using a fleet equipped with a stellar converter. As long as you leave one inhabitable planet in the system, you can use it to build artificial planets out of the destroyed planets. You may even want to arrange for the computer to attack your home planet, so you can grow the planets in the home system (This has a low probability of working). You can also exploit a planet capacity bug, and fit up to 53 population in a huge terran planet by shipping in tolerant population, such as androids.
Fast Game
It is possible to win a game in three turns (3500.3) if conditions are appropriate. Settings should be: small advanced universe with 2 players. Your race should be creative, telepathic, and transdimensional, and the picture should be Elerian, to minimize the possibility of a telepathic opponent. The strategy is simple: send your ships out to the enemy worlds at once, dividing your forces so that you can still defeat the resident defenses without losses. This is certainly not guaranteed to work, since you cannot get to some of the opponent's worlds in three turns if the stars are not properly aligned. Astrology works. Heh.
Phasing Cloak
If you have Phasing Cloak technology and your opponent doesn't, you have a distinct advantage, especially if you also have Time Warp Facilitator. However, if both you and your opponent have phasing cloak, you will need to play carefully to win.
I will assume battle takes place with ship initiative on. Phasing cloaks disable themselves at the end of the 10th turn of engagement, so whoever has the highest ship initiative gets to fire first on the eleventh. You will not want to use time warp facilitators, as those cause you to decloak in half the time, automatically making you a sitting duck. Since ship initiative is 10*mobility + ship offense, you want a good computer and an experienced crew on your ships, and you want empty space along with augmented engines. If you have a racial beam offense advantage or a good leader, you should have little trouble starting first, but otherwise, you will want to partially empty your ships. However, you will want your ships to have enough firepower to annihilate the opposition. In particular, you will want to use your highest-initiative ships to kill those opposing ships with highest initiative, so that your lower-initiative ships (if you have them) can be the next to fire. This requires a careful balance depending on your expectation of the enemy's ships defenses: near the endgame, a single fully loaded ship can destroy several opponents, even if they are heavily armored, so in order to approach the optimal one-to-one kill ratio, you will need to fill your ships with very few weapons and hope the enemy doesn't slightly outdo you.
I'll write more later.