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I am not joking when I say I've had the last enemy down to one planet, before, and they were able to sustain a fleet of 800+ ships (hundreds of which were doom stars and titans) on a single star fortress' command points and one planet's income. WHAT!? I had every single planet in the galaxy under my control (tons of planets for income and star bases for CP) and sustaining a fleet of one hundred doom stars for ten turns while I tried to amass a capable invasion force saw me scrapping them by the dozens just to afford the upkeep of the rest. They were able to sustain this 800 ship fleet indefinitely. I proposed an alliance to spam "End Turn" to see how long it would take them to downsize. Hundreds of turns later, no change.
(Before anyone asks how: Stealth Ships. With no way of knowing where I'm attacking or defending, I was cherrypicking their undefended worlds and eventually managed to force them to pool their forces at a single world, before mass-conquering the rest.)
For the record, I've had this scenario occur with four specific factions: Mrrshans, Sakkra, Silicoid, and Klackon, with the Alliance Experiment being with the Sakkra. Any time I'm down to... say, just the Meklar or just the Psilons, they aren't nearly as stupidly infuriatingly BS spamming cheat codes.
That infinite sustain scenario I described seems to happen as low as on Average difficulty. In a Huge system, Average Galaxy age, etc. So it's entirely possible they could have amassed a ton of wealth to sustain it longer - which is why I made an alliance and started spamming end turn to see what would happen. If it was costing me tens of thousands of BC per turn just to upkeep, a much, much smaller force... yeesh.
For starters... let's assume I'm remembering this, correctly: It's 1 CP per size of the ship, meaning a Frigate is 1, a Destroyer is 2, up to a Doom Star at 6, right? Let's be super generous and give them 20 CP due to leaders and officers (only one planet, so it's not like they have tons of battlestations.) They had about 800 ships, about 200 of which were Doom Stars and about 300 of which were titans (rough estimate based on number per row and number of rows). This means they also had about 300 battleships. So let's use 200/300/300 as our reference numbers. Titans take 5 CP, meaning 4 titans alone would leave them with a full 796 ships to pay upkeep for.
200*6 = 1200 for the Doom Stars alone.
296*5 = 1480. (Removing 20 CP worth of titans)
300*4= 1200.
1200+ 1480 + 1200 = 3880 CP over their limit.
10 * 3880 = 38,800 BC per turn just to upkeep.
... that can't be right. I messed my math up somewhere. That's the kind of ship upkeep -I- was paying - and by comparison, my fleet was so small that I couldn't even dent their main force. I was waiting over 20 minutes for my turn when they started to go. Seriously, 800 ships is "Oh god, I wish I could change between Tactical/Automatic combat mid-campaign" worthy.
If It matters, this was in V 1.40 (the Steam Release) and I just recently patched it up to the most recent fan patch, so I don't know if it still happens.
2. If you install 1.50 fan patch, you can easily view what's going on with AI: pressing ALT+X switches you to next player's empire. Works only in single player though and counts as cheat.
3. In any case AI has some discounts on command upkeep depending on difficulty. I don't know the exact numbers, but sure it affects math.
As for impossible, yes. The game cheats, but not in the way you think. The AI has races with a much higher point count, and (as Freysgodi mentioned) a greater tolerance for command point expenditure.
If you have "every planet in the galaxy under your command", sustaining 600 CP in ships should not be difficult at all. Even without hyperspace communications, you can simply set your capped planets to trade goods.
Also, size does not matter, if you've got the tech. Player-built ships in vanilla trump AI built ships 100% of the time, on equal footing. I have a playthrough thread on the forums somewhere, which show a distinct disparity in fleet size, the enemy goes first, and they still get rolled, simply because I built a ship dedicated to one attack type (In this case, beam weapons).
Edit: Here's the image
http://i.imgur.com/PdP5crY.png
As for the gigantic fleets problem, max out phasors. All the mods and add all the beam weapon enhancement dohickeys. Give damage-enhancement and ranged-damage-loss reduction the highest priority. It won't matter how many ships they have. Also, pretty sure energy dampers + the antaran thing that reduces damage 75% makes you invulnerable to weapons damage. Bit of an oversight there. I stopped using that combo a long time ago. Too cheesy.
10 colonies 5 system 64 turn
You don't "have" to customize your race any way you don't prefer. In this video, I played on impossible using "Charismatic" as my only positive pick, with the full gamut of negative picks.
https://www.youtube.com/watch?v=ESdEr-ZiAUU&t=1352s