[SPOILERS] Woden and ljubljana like boats

[ljubljana]

...i ran a much smaller version on grassland (n=45), and got

36 kills
4 hits for 98 damage
5 hits for 94 damage

what discretized fuckery is this

[ljubljana]

Legions closed things out with a strong run at the end, finishing n=100 on

83 kills
7 hits for 98 damage
10 hits for 94 damage

Still looks like three true outcomes baseball to me, though, quite likely with 80%ish true odds to kill and equal, 10%ish odds for the other two. And yes, it is quite possible I misremembered a 94 damage hit as a 95 damage one last night in the full flower my tiltedness. Combat strength was calculated as

Fleet Caravel: 65 base + 5 alliance + 4 WoR + 3 spy + 5 GA + 7 Embolon + 4 flanking - 2 emergency = 91 CS
Frigate: 45 base + 5 alliance + 6 support = 56 CS

in case anyone wants to triple-check my math... I doubt it's within the purview of lurkers to ask roland how much health is on that ship, even within the privacy of their own thread, but wow am I ever curious as to the answer. I guess I will just have to kill it next turn and find out that way

Not that I have any idea what I will think if I really did do 95 damage...

edit: lol double post

[ljubljana]

No, I was on +35 too. That CS calculation in the last post is from the attack I made in game, on the sim I did legions vs slingers on grassland, presumably just like yours.

Civ6 damage: the twelvefold way - coming soon to a PhD thesis near you...

[ljubljana]

oooone more, to illustrate the resplendent fullness of the Twelvefold Way:



n=92:

Outcome	Count
64	8
66	6
69	6
72	6
74	7
77	6
80	9
82	9
85	5
88	9
90	12
93	9

...everything else, 0

Game Turn, Attacking Civ, DefendingCiv, AttackerObjType, DefenderObjType, Attacker Type, Defender Type, AttackerID, DefenderID, AttackerStr, DefenderStr, AttackerStrMod, DefenderStrMod, AttackerDmg, DefenderDmg
2, 0, 2, 1:1, 6553699:3538997, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 6488162:3604534, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 72
2, 0, 2, 1:1, 6422625:3670071, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 6357088:3735608, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 72
2, 0, 2, 1:1, 6291551:3801145, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 77
2, 0, 2, 1:1, 6226014:3866682, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 69
2, 0, 2, 1:1, 6160477:3932219, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 2, 1:1, 6094940:3997756, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 2, 1:1, 6029403:4063293, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 5963866:4128830, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 2, 1:1, 5898329:4194367, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 2, 1:1, 5832792:4259904, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 5767255:4325441, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 2, 1:1, 5701718:4390978, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 2, 1:1, 5636181:4456515, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 66
2, 0, 2, 1:1, 5570644:4522052, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 2, 1:1, 5505107:4587589, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 2, 1:1, 5439570:4653126, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 2, 1:1, 5374033:4718663, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 2, 1:1, 5308496:4784200, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 74
2, 0, 2, 1:1, 5242959:4849737, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 72
2, 0, 2, 1:1, 5177422:4915274, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 2, 1:1, 5111885:4980811, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 2, 1:1, 5046348:5046348, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 2, 1:1, 4980811:5111885, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 2, 1:1, 4915274:5177422, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 2, 1:1, 4849737:5242959, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 69
2, 0, 2, 1:1, 4784200:5308496, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 74
2, 0, 2, 1:1, 4718663:5374033, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 77
2, 0, 2, 1:1, 4653126:5439570, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 2, 1:1, 4587589:5505107, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 69
2, 0, 2, 1:1, 4522052:5570644, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 4456515:5636181, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 85
2, 0, 2, 1:1, 4390978:5701718, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 4325441:5767255, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 72
2, 0, 2, 1:1, 4259904:5832792, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 4194367:5898329, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 2, 1:1, 4128830:5963866, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 2, 1:1, 3997756:6029403, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 66
2, 0, 2, 1:1, 4063293:6094940, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 3932219:6226014, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 2, 1:1, 3866682:6291551, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 66
2, 0, 2, 1:1, 3801145:6160477, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 2, 1:1, 3735608:6357088, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 2, 1:1, 3670071:6488162, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 77
2, 0, 2, 1:1, 3407923:6422625, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 74
2, 0, 2, 1:1, 3473460:6619236, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 5, 1:1, 6553699:3538997, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 69
2, 0, 5, 1:1, 6488162:3604534, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 5, 1:1, 6422625:3670071, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 77
2, 0, 5, 1:1, 6357088:3735608, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 5, 1:1, 6291551:3801145, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 69
2, 0, 5, 1:1, 6226014:3866682, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 77
2, 0, 5, 1:1, 6160477:3932219, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 66
2, 0, 5, 1:1, 6094940:3997756, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 5, 1:1, 6029403:4063293, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 5, 1:1, 5963866:4128830, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 5, 1:1, 5898329:4194367, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 5, 1:1, 5832792:4259904, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 5, 1:1, 5767255:4325441, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 5, 1:1, 5701718:4390978, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 5, 1:1, 5636181:4456515, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 5, 1:1, 5570644:4522052, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 85
2, 0, 5, 1:1, 5505107:4587589, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 5, 1:1, 5439570:4653126, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 72
2, 0, 5, 1:1, 5374033:4718663, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 5, 1:1, 5308496:4784200, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 5, 1:1, 5242959:4849737, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 5, 1:1, 5177422:4915274, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 5, 1:1, 5111885:4980811, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 93
2, 0, 5, 1:1, 5046348:5046348, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 88
2, 0, 5, 1:1, 4980811:5111885, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 66
2, 0, 5, 1:1, 4915274:5177422, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 74
2, 0, 5, 1:1, 4849737:5242959, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 74
2, 0, 5, 1:1, 4784200:5308496, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 77
2, 0, 5, 1:1, 4718663:5374033, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 74
2, 0, 5, 1:1, 4653126:5439570, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 66
2, 0, 5, 1:1, 4587589:5505107, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 5, 1:1, 4522052:5570644, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 80
2, 0, 5, 1:1, 4456515:5636181, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 85
2, 0, 5, 1:1, 4390978:5701718, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 5, 1:1, 4325441:5767255, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 5, 1:1, 4259904:5832792, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 5, 1:1, 4194367:5898329, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 64
2, 0, 5, 1:1, 4128830:5963866, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 74
2, 0, 5, 1:1, 3997756:6029403, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 72
2, 0, 5, 1:1, 4063293:6094940, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 5, 1:1, 3932219:6160477, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 85
2, 0, 5, 1:1, 3866682:6226014, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 72
2, 0, 5, 1:1, 3801145:6291551, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 82
2, 0, 5, 1:1, 3735608:6357088, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 69
2, 0, 5, 1:1, 3670071:6422625, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 90
2, 0, 5, 1:1, 3342386:6619236, UNIT_BATTLESHIP, UNIT_PIKEMAN, 70, 45, 0, 0, 0, 85

From this, I think it's reasonable to conjecture that every combat has exactly 12 possible outcomes, distributed roughly evenly about its expected value. There are ups and downs in the frequency distribution, but not more than what you'd expect from chance, and I think it's highly likely that all 12 outcomes are equally probable.

That means that, in every combat, your odds to kill are always an exact multiple of 1/12! Among other things, that implies that some CS points are more important that others with respect to one-shot kill odds - going from +30 to +37 takes your odds from 6/12 to 12/12 but involves crossing 7 CS point boundaries, so somewhere in that range, there exists a CS point increase that doesn't help your chances at all!

That range also goes to show you why +25CS is such a terribly inefficient place to be in terms of striking power. It's a guaranteed two-shot by a huge margin, but with a 0/12 chance to one-shot - these units are functionally no better than ones with, like, a 50 to 74 range, assuming you're fighting only one kind of enemy unit type. This is a good illustration of the general theory behind not always combining your units into corps - if your units are in two-shot range before and after combining, you've lost effective kill power, and even if you boost a unit from two-shot into one-shot range, you've only broken even. Corps are good for concentrating power in a restricted area and reusing promotions, not for every application in generic circumstances. Which is good game design, really

The RNG, on the other hand...  I'm reminded of nothing so much as Sullla's Final Fantasy V Berserker report, where the same strings of damage numbers kept appearing in deterministic boss battles due to the finite nature of the 256-seed RNG. But this RNG doesn't have 256 seeds...it has 12 seeds! Is that old-school or what?

(of course, it almost certainly has plenty of seeds in reality as I could find no discernable pattern in the sequences of results...but I admit that I also didn't really look that hard )

edit: As far as I can tell, this was first discovered by icon41gimp over at CFC - they have 13 posts there, 12 of which were from 2005, and the 13th is this one. I believe that their proposal of randint([24, 36)) * e^(D/25) is essentially the correct formula, though its exact predictions are still slightly high relative to the above data. Major props to you, icon, wherever you may roam 

[ljubljana]

oh yeah, definitely good on seeds, idk what Civ6 uses for backend but any language worth anything at least has RSA or something behind its builtin random library. I am just amused that this game uses all those thousands of bits of randomness to simulate...four bits of randomness

As much as I am curious where the n is such that going from n to n+1 in CS doesn't actually help you get kills, that may be beyond my simming patience at this point. Maybe once the turn rolls around I'll do that to distract me from williams' 8347295 privateers...

edit: As for roland, let's not worry about asking them - I don't want to give the impression of trying to get information relevant to the gamestate, even if it is meaningless (which it actually would not be if I had a quad or galley in this fleet). I will simply kill the offending frigate next turn and then report back on the 6 damage I did in so doing

[ljubljana]

Happy anniversary, everyone

Corollary to this, the most recent turn in which we were not in a war to the death with someone was turn 125. That turn was played on May 10, almost 7 months ago...

I didn't mention this at the time, but I had an entire romantic relationship that began the day we took Writing on the Wall and ended while we were sieging down Open Government. I got a master's degree during the t147 pause, moved cross-country on t154, changed jobs on t172...

[Woden]

What is surprising and a little sad, six months ago (June 8th) we were on Turn 145. We have played 40 turns in 6 months.

Edit: And apparently you live a whole life in that time.

[ljubljana]

I was going to make a snarky post in the tech thread about going for the record, but...I double-checked and apparently PBEM18 was only 11 months and 2ish weeks... But if you measure by turn count, we are still some 80 turns behind. On the bright side, we are on pace to catch up before 2023...

We must have REALLY freaked out roland if they are taking 2 days to pass the turn, though

edit: I also have noticed with no small amount of consternation that we are rapidly gaining on suboptimal/Bruindane's post count. We were 20 pages behind a week or so ago, now it's down to 12(!)

[Woden]

Turn 185-Vikings start
Quickly loading the game to take a look but will probably not play for a few hours. Here is what the Battle of Australia looks like....
   

Looks like they took the ironclad bait and left most of your ships alone. Good, you should be able to do maximum damage. I will kill the only caravel next to my lone ironclad or I can go after the  fleet caravel and injury him enough so you can finish it off with a frigate. Overall, I think it best to attack the southern ships and try to form a line to minimize damage if there are more ships in the north. No more ships south of the southern most frigate and the northern most caravel has another ship behind it. Alternatively, I could kill the Australian privateer and give them a target for anything in the north. I do have another frigate coming out of Fort Miln next turn and my fleet in the southern ocean will have pillaged everything I can and will start moving up here. Your fleet surviving to take out the bulk of the ships might be worth an ironclad. 

Over by your core...
   

Russia seems to be shifting south around Linear B. That city will be hard to crack but he might bypass it for Linear A or be looking for my fleet...oh, please be looking for my fleet, please!

Down by Geneva...
   

All is quiet, a little too quite. A lone privateer between Freyra and Geneva that will die from both cities' attack but nothing else. I am wondering if I am wrong with a pack of privateers or he saw my ironclads and is why he is moving his northern fleet south thinking I only have a few ships in the area, or is he trying to distract us from something and trying to draw our ships somewhere. IDK, I am going to have to think about this. For one thing, I do need to protect my frigates with Refining finishing next turn. I also should think about protecting the IZ at Loki. They do provide science when pillaged. Maybe I will form a line of ironclads diagonally off of the encampment at Loki and move some of my frigates up to you city north of Loki. Then, unless his ships are already up there, he won't be able to sail around my ironclads. I will also stage a line over by Official Visit where I will have 4 other frigates.

Edit: Or I kill the privateer near Freya with the ironclad fresh out of Freya and see if there is a fleet of ships around.

[ljubljana]

Interesting, they took 2 frigate fleets (including a 4-promoted one) but mostly left my caravels alone. That’s a good move and will slow us down a lot in cracking their cities...however yeah their fleet is very badly exposed now. Might need to take some bad frigate merges after this is all over, but ultimately not a terrible outcome unless there are more Russian privateers behind those two.

I would kill the caravel w your clad and leave the privateer, we will want at least one of your ships alive down here for pillages + city captures if we manage to finish off the fleet.