In the P&N on PBW game, I was in first place for a while, and spent most of the game in second place.
I only really went into combat once, and that was to capture a planet that was pissing off people by causing a whole pile of stalemate combats every turn (since nobody had weapons in the area).
Most of my losses were to damaging warppoints, I think.
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Key things to do:
1) Forge an alliance right away. The trade income will be all you need to prosper, and in return, you can give them access to your ship and base technologies.
2) Von Neumann bases in orbit of allied homeworlds, and in level 4+ nebulae systems.
3) Use the bases to build insane numbers of ships and units in parallel at any location in the galaxy. If you've done the bases right, you should have about 2^5 = 32 bases 10-15 turns after you first visit.
4) Sell your advantages. Somebody needs a quick fleet of 60 cruiser to fend off an enemy? Those Von Neumann bases will let you deliver from almost anywhere with top of the line tech in a few short turns.
One mistake I made in that game was building too many cargo ships.
When you're making that many ships simultaneously, it is very very easy to make more than you need.
I had about 50 large freighters sitting in stock when I had yet to sell the Last of my medium ones. Warships would have been much better, since they have a naturally limited lifetime.
And taking all six P&N racial techs came in very handy
"Maintenance-free, biocrystal-armored, talisman targetting, grav-driven, living warship with Psycho-temporal weaponry. You know you want it!"