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Anyhow, the production of rare variants is very random. Best bet is to start construction and then cancel it. You get all of your materials back, but lose money. This is the fastest way for trying to force a rare.
My impression about "rarity luck" is that the game sets the odds when you boot it up. If you aren't getting rares, try quitting and booting the game again.
Thus, you can calculate backward from previously known times to a decent approx of what to look for with Marlene.
In my previous game I got rare variants several times (for large galleons) in the span of a few minutes, The only perceptible difference between my 2 playthroughs was the addition of the DLC in my newest playthrough.
After trying again today, with Sabin Stargem's suggestions, I managed to get both the Spanish variant in Seville and shortly after the Victory in Plymouth. It took me about 20-ish minutes for each. I strongly suspect that Sabin Stargem's idea about rarity luck is genuine.
Thanks for the assistance folks. It is much appreciated.
1) You can only get rare ship if you use blueprint construction(or the chance is nigh negligible as I never managed to get a rare in my loads of attempts)
I doubt this is the case since I assume you knew that... but who knows.
2) If you simply try to RELOAD the save file - it won't work. You need to fully quit the game and attempt construction again.
Otherwise you will keep getting same ship. So if you were supposed to get rare ship and saved BEFORE you invested resources - you will still always keep getting construction time of the rare ship.
Basically it is semi RNG, some part of the RNG is preseeded when you try to launch the game.
The reloading mechanism is as simple as that.
Beyond that your RNG from my experience is ~5-15% with tech 1000 and ~15 shipbuilding(not sure if shipbuilding matters beyond certain amount)
Might depend on ship type since some types constantly had slightly better chances from my tests.
2) Reloading the save file works perfectly fine as long as you save before you started building the ship. I literally just confirmed this was the case earlier today. There was no need to quit the game and relaunch during each attempt to get a rare variant.
Even during my first attempt that prompted my creating this post, I was getting different ships every time (each regular ship had different bonuses). I just wasn't getting any rare variants. Thankfully, as I stated earlier, Sabin Stargem's idea about rarity luck and reloading the game to change it seems to be true.
Clipper and Ship of Line build time are both 28 days
Tea Clipper is 31 days, they are unneeded product anyway...
Ariel and Cutty Sark are 39 days.
Purple SoTL build time are all 37 days.
And yeah, save before build ship work fine, you don't need to quit game like some rumors suggested.