[PB25-SPOILERS] The Lunacy of the Reign of HAK Continues

[The Black Sword]

I don't know the details of HAK's cities, but the numbers work out, so I assume I'm correct that he makes 32hpt base, which is usually multiplied by 1.75 due to Forge +Bureau for 56hpt.

Are you questioning whether the overflow cap should be the max of (40 or 32) instead of (40 or 56)? The (40 or 56) is correct, you may be thinking that the base hpt is capped by max of (32 or 40/1.75), which obviously gives the same thing, barring some possible rounding difference. I've never seen the game contradict this, and indeed if the cap was max of (40 or 32), then HAK wouldn't have been able to get the 28*1.75=49h overflow he got here.

In practice, this means that it is trivially easy to always get 1t overflow into an item. Overflow cascades are only useful when the items in a cascade have a higher cost than 1t worth of hammers, allowing you to break that 1t limit.

[GermanJoey]

I don't know the details of HAK's cities, but the numbers work out, so I assume I'm correct that he makes 32hpt base, which is usually multiplied by 1.75 due to Forge +Bureau for 56hpt.

Are you questioning whether the overflow cap should be the max of (40 or 32) instead of (40 or 56)? The (40 or 56) is correct, you may be thinking that the base hpt is capped by max of (32 or 40/1.75), which obviously gives the same thing, barring some possible rounding difference. I've never seen the game contradict this, and indeed if the cap was max of (40 or 32), then HAK wouldn't have been able to get the 28*1.75=49h overflow he got here.

In practice, this means that it is trivially easy to always get 1t overflow into an item. Overflow cascades are only useful when the items in a cascade have a higher cost than 1t worth of hammers, allowing you to break that 1t limit.

Ah, I see what you mean. Yes, I had been thinking that base hpt overflow was capped at (32 or 40/1.75), which is actually pretty much the same thing as (40 or 56). Which is it actually, though? If its in terms of base hammers, which is how I've always thought of it, the overflow cap will actually be floor(1.75*(floor(32 or 40/1.75)) = (38 or 56) because 40 isn't evenly divisible by 1.75.

I actually didn't even know the overflow cap could be extended like this! That's pretty neat. I mean, its pretty unusual to blow so far past 1-turning a build for it to matter, even when constructing an overflow-chain, but I can think of a few situations in a past games where I could have made good use of this fact to squeeze out a few more hammers.

[HitAnyKey]

Don't really have much time for planning or simming this morning, so here's just the regular turn stats:

I'll figure out later what to actually have Sleepy build this turn for proper overflow. For those that want to help me understand or help with calculations, here is a screenshot of the city:


It also shows what I have available to build. The Stable is at 58/60 but everything else is not started. Whatever I build this turn, I'll have overflow into the Aqueduct (I think) next turn, so that I can have that being build with a total 200% bonus. I would think/hope that doing so would then give me the greatest overflow for the Taj on the following turn.
So the only real thing that needs to be figured out/understood for this turn is whether I build the Monastery or the Stable. Both are 60H buildings, but one is almost done. If putting this 126 hammers into the Stable (bringing it to 184/60) would cause lost hammers because of some cap, then I guess doing the Monastery is the better option. Especially if Monastery vs Stable will in the end give me the same number of overflow hammers next turn.
Can someone confirm this for me? I might have time to sim it later, but I'm not sure. Other option is putting the 126 hammers this turn into the Colosseum which is 80H, so might allow greater overflow. But because I don't have any hammers in it yet, the end result might be less.

[MindyMcCready]

Overflow cascades are only useful when the items in a cascade have a higher cost than 1t worth of hammers, allowing you to break that 1t limit.

So I'm certainly no micro expert. But that line above + the fact that you're carrying over 28 base hammers means that you're overflowing nearly as much as possible.

I was starting to construct this in excel,...the FLOOR function in excel takes 2 parameters the second being the divisible number. So FLOOR(16,3)=15 in excel since it appears to be acting like TRUNC(16/3)*3.

So GJ,...is the floor in your calculations acting like a truncation? Would using FLOOR(x, 1) give the equivalent?

So admitting that I don't know what FLOOR is doing it still seems to me that:
-you have 28H (base) in overflow on a 35H base so you've got very little room to improve that.
-A settler is your highest hammer cost item however it will probably eat the overflow.
-My truncated, non-floored, untested calculation suggests that you'll have 23 base hammers overflow if you build a Colosseum. This is down from your current 28.
-I understand that a Wealth build will preserve the overflow,...capped overflow?

I *think* that the following might be possible.

T154 - complete settler. 1T with minimum 10(?) overflow
T155 - Put 80H or whatever into next settler.
T156 - Complete settler with maybe 40 base hammers in overflow.


Topic: Civic switch as soon as possible.
-I tested last night to make sure that Merc DOES NOT kill trade routes (LOL,...we're doing that). Confirmed.
-So every waterside size 1 city with make something like 6-9 commerce from trade + 6 gpt or +6 beakers per turn. 23 cities x 6 gpt = 138 gpt + modifiers.

-Back of the envelope, bureaucracy is probably giving us +15 commerce (+25%) and less than 20 hpt. Every size 6 draft is like turning 30 food into a 70H unit and that can happen 3X per turn for at least 5-6/10 turns. So Nationhood > bureau in hammers and commerce.
-I'm not sure how maintenance cost work in the mod (Nationalism used to be low cost) but unless they're really, really high we should make the switch as soon as possible.
-So switching out means that we're not as likely to land the wonder without bureau:
-You're losing overflow on the stables. You shouldn't lose overflow when you switch out of bureau.

Counter point:
-MC may underestimate your chances or the seriousness of your attempt at Taj.
-MC is likely in bureau,...is his capital as hammer-heavy as ours is? If not, then you have an advantage there. His next best city doesn't look like it would have advantages over our capital I think.

This overflow exercise is useful,...but you should also evaluate MC's chances to beat you to it before we base our game around this.

[MindyMcCready]

So a quick post on HAK's behalf.

It looks like we're going all-in for TAJ. We're delaying our switch to Merc + Nationhood in favour of staying in bureau with a T159 switch to slavery and an enormous T161 7-pop whip to our capital. If we miss it, we're going to be in a world of civics hurt since we're relying on landing Taj to switch back.

MC is building Taj in his Moai city. He'll lose a lot of hammers when he comes out of GA. He's also not getting the bureau bonus. Our guesstimate shows MC landing Taj on T163. We think that we will be able to whip it on T161.

HAK's simming this out still so stay tuned. I don't think that either of us are quite sure what this means for our island invasion plan quite yet.

[GermanJoey]

Overflow cascades are only useful when the items in a cascade have a higher cost than 1t worth of hammers, allowing you to break that 1t limit.

So I'm certainly no micro expert. But that line above + the fact that you're carrying over 28 base hammers means that you're overflowing nearly as much as possible.

I was starting to construct this in excel,...the FLOOR function in excel takes 2 parameters the second being the divisible number. So FLOOR(16,3)=15 in excel since it appears to be acting like TRUNC(16/3)*3.

So GJ,...is the floor in your calculations acting like a truncation? Would using FLOOR(x, 1) give the equivalent?

So admitting that I don't know what FLOOR is doing it still seems to me that:
-you have 28H (base) in overflow on a 35H base so you've got very little room to improve that.
-A settler is your highest hammer cost item however it will probably eat the overflow.
-My truncated, non-floored, untested calculation suggests that you'll have 23 base hammers overflow if you build a Colosseum. This is down from your current 28.
-I understand that a Wealth build will preserve the overflow,...capped overflow?

Yeah, the floor acts a truncation. There's three places a truncation can happen. The first is when the total overflow hammers are capped after a build completes, which is what TBS and I were talking about. The second place is when your production modifier gets divided out; so, e.g., if you had 10 total overflow hammers but a 25% production modifier, you get floor(10/(1+0.25)) = floor(8.8) = 8 "raw" hammers of overflow, which is the same as if you had 10 total overflow hammers. Finally, the third place is when the hammers get applied to your new build; this 8 then gets multiplied again by your forge, giving you floor(8*1.25) = 10 hammers into your next build, or floor(8*(1+0.25+0.50)) = 14 hammers if you were putting it into a wonder w/ marble hooked. However, for the last calculation note that its your *total* hammers that get multiplied by the modifier, so the truncation can happen differently. For example, if you had 7 raw overflow hammers in a city with a forge that got 13 base hpt, you'd actually get floor(1.25*(7+13)) = 25 hammers for your output.

I believe FLOOR(x, 1) is the right Excel expression, yeah.

[GermanJoey]

Don't really have much time for planning or simming this morning, so here's just the regular turn stats:

I'll figure out later what to actually have Sleepy build this turn for proper overflow. For those that want to help me understand or help with calculations, here is a screenshot of the city:


It also shows what I have available to build. The Stable is at 58/60 but everything else is not started. Whatever I build this turn, I'll have overflow into the Aqueduct (I think) next turn, so that I can have that being build with a total 200% bonus. I would think/hope that doing so would then give me the greatest overflow for the Taj on the following turn.
So the only real thing that needs to be figured out/understood for this turn is whether I build the Monastery or the Stable. Both are 60H buildings, but one is almost done. If putting this 126 hammers into the Stable (bringing it to 184/60) would cause lost hammers because of some cap, then I guess doing the Monastery is the better option. Especially if Monastery vs Stable will in the end give me the same number of overflow hammers next turn.
Can someone confirm this for me? I might have time to sim it later, but I'm not sure. Other option is putting the 126 hammers this turn into the Colosseum which is 80H, so might allow greater overflow. But because I don't have any hammers in it yet, the end result might be less.

I can't tell you what to build and how to order your chain to avoid wasting hammers, sorry. I can help you understand how it works, or how it works with various kinds of builds... I encourage you to try to sim it out if the equations we've been posting don't make sense.

[Dreylin]

I believe FLOOR(x, 1) is the right Excel expression, yeah.

Personally I use ROUNDDOWN( "function" ,0) ; don't think I've ever used FLOOR, but I probably should.

[HitAnyKey]

So.....since the turn was still available due to Gavagai not being able to play last night I had a thought to see if it's even possible to get Nationalism this turn so that we can start Taj a turn sooner....



So for this turn, basically everything is on hold so that we can start it next turn. This is another do-or-die situation, since doing this will delay every other build by a turn. If this doesn't pay off, it'll hurt us quite a bit.

[HitAnyKey]

Just completed a SIM using the tiles as they are now (even working the cottages) as our worst case scenario. Basically a scenario where on T159 (last turn of our GA) we do all the civic swaps, including going from Bureau to Nationalism. This also doesn't included the extra workshop that will be completed in 4 turns.
In this SIM, on T161 we have 559H invested into the Taj, and it allows me to do a 7pop whip, which jumps it to 709. The remaining tiles can be maxed out to get me an additional 52H for a final result of completing Taj T162 at 761/700H. So if I'm correct, even if Commodore also completes Taj on T162, he would need to have his T161 bringing it to more than 761H to beat me, right?

In a little bit I'll run another SIM using methods of possibly starving the city for a couple turns to get more hammers earlier on to see if there is a way to whip it 1 turn sooner. The first option I will use is that of not switching out of Bureau on the last turn of our GA. Just means we would have to wait 5 more turns (in the next GA) to be able to start drafting...which will be well into any war if Gavagai decides to attack me once the Peace Treaty ends.

EDIT: New SIM run and it's better. T160 we can do a 5pop whip, completing the Taj with 771/700H. I think I did it all correctly in the sim, and it does depend a bit on when that Workshop does actually finish, since without logging back into the game right now I believe it finishes on T158. This also all goes to hell if even a minor thing happens that screws up the getting of Nationalism this turn. Since as you can see from the screenshot, it is using every penny of my treasury to only just barely get the tech. So if we somehow lose even 1 GPT at the turn flip, this won't work. Just like how Commodore missed his own getting Nationalism by a turn because of Elkad's war declaration.