[SPOILERS] Donovan Zoi and AdrienIer: Slümhund Millionaires!

[AdrienIer]

Short answer to all this.

I think two FW should go to Saint Foy, this city has a criminal number of unimproved tiles and is using coast instead of cottages/workshops. Also we should be making swords while we can, they're very hammer efficient.

About the binary research the question is either 70% for 5t (losing 35gpt for a total of -175g and making 202bpt for 1010 beakers) or 0% for 1t (+172gpt at our current rate) and 100% for 3t (-123gpt and +288bpt). Then whatever maxed research we can get. Which means 172-3*123=-197g and 864 beakers plus a turn at around 70% (maintenance will go down with courthouses I think so it's ok) which is -35gpt and +202bpt. Overall 70% gives us -175g and 1010b and binary -232g and 1066b. It's a trade of 57g for 56b. Shit it's not as great as I thought. But still we have one more market than library so the multiplier is higher for gold and I think we're winning overall.

[Donovan Zoi]

In the matter of The People's Research Commission Vs. Donovan Zoi, we find the defendant Not Guilty.




Not so fast, Mr. Zoi. You still have your crimes in Sainte-Foy to answer for.....

[Dreylin]

The significance of the rounding generally decreases as the game continues. The significance of the Known Tech Bonus generally increases as the game continues.

[GermanJoey]

Donovan, you're wrong. Binary research is as-good or superior (especially for the KTB, as Dreylin and Adrien have said a few times, as well as to maximize what you get from research multipliers like Libraries, Academies, etc) in 99.9% of situations. The only reason I wouldn't run a binary slider is when I don't need an even number of 100% turns to complete a tech (say, I'd only need 3.5 turns or something) and I expect another team to finish research it within the next 1 or 2 turns. In that case, I'd run a shorter slider on the first turn or two in order to maximize the total extra beakers I'd get from the KTB. However, that's just an edge case and the slider is still binary for the remainder. It also requires a lot of math. The only other time I'd do it is if I think I'll get a first-to bonus (like Liberalism, Nationalism, etc), as KTB won't be a facor if I'm the first to a tech and running a partial slider lets you more easily obfuscate your true GNP for your rivals.

[Donovan Zoi]

In this particular case, the math seems to prove inconclusive. Sure, we have 56 extra beakers, but 57g less to put toward binary on the next tech (per Adrien's numbers). Let the record state that I have run binary a majority of the time in this game (and have also yielded to binary for this tech as well), but the gpt costs just seem far too high right now due to lousy maintenance. Once that is resolved, it becomes a moot point because we'll be at 100% more often if we incorporate a Wealth strategy.

Also, when these binary numbers yield a tech in longer time that I can get it straight line (or we run out of money due to the ridiculous gpt at 100%), that's a problem for me. But after reviewing my research overflow simulator, I think I may be sold on this after 5 turns. But I don't think its fair to surmise I have been destroying our game by going the straight line route on occasion when the difference is so minimal.

Lastly, I am sure you have noticed by my turn lengths that I am already a bit too OCD regarding this game. I am more of an instinctual player and if I had to spend too much time on maths I fear I would lose interest in the game fast. But I appreciate the advice and will try to learn from it.

[GermanJoey]

It isn't going to break your game, no, but it does add up. For example, squeezing out just an extra 4bpt on average over for the past 50 turns is half of a classical era tech in total, and the difference could be a lot more than that. The math only seems inconclusive to you because you aren't actually breaking it down in detail in terms of total commerce going in and out. I'd be willing to do that, if you think it would help...

[GermanJoey]

Apologies in advance if this gets a bit mathy, but I think this should clear things up for you. Lets start with a hypothetical scenerio. To start with, lets say you have an empire with no libraries, markets, academies, or anything else. It is T135, you have no gold in the bank or any overflow beakers from the previous tech, and you decide the next tech you want is one that happens to be 1200 beakers. It has 1 prereq. Your empire's total expenses are 200gpt, while your net commerce income is 400 commerce per turn. Nobody else currently knows this tech, and lets also ignore rounding stuff for now in order to keep the numbers nice and even.

For break-even research, that works out like this:

Code:

(400 income - 200 expenses) = 200 base beakers per turn, which coincides to a 50% slider, 200*1.2 = 240 beakers per turn with the prereq bonus.
240*5 turns = 1200 beakers exactly, completing on EOT T139 with no gold in the bank.

For binary research, it works out like this:

Code:

save gold for 2 turns, then turn on research to 100%, then do the last turn at 50%:
(2*400 + 200)*1.2 = 1200 beakers exactly, also completing on T139 with no gold in the bank.

In this scenerio, you are right - there is no difference. However, let's look at two others cases. In the first, lets say your capital, which produces 100 of your 400 total commerce, finishes a library 3 turns into the tech. This isn't enough to change the slider at all, so you'll still leave it at 5 turns at 50%. However, you now end up with 45 overflow beakers that go into your next tech!

Code:

2*1.2*0.5*(300 + 100) + 3*1.2*0.5*(300 + 1.25*100) = 1245 beakers.

In contrst, the binary case looks like this; because we save gold for the last 2 turns the library is under construction, we get more value out of it within this 5 turn window:

Code:

2*1.2*(300 + 1.25*100) + 1.2*0.5*(300 + 1.25*100) = 1275 beakers!

That's an extra 30 overflow beakers compared to the break-even case, for free!

Next, lets imagine that two other teams get our tech during this 5 turn period. The first team gets it after two turns, while the second team gets it after 3. The breakeven case is like this:

Code:

1.2*0.5*(300 + 100) + (1.2+0.04)*0.5*(300 + 100) + 3*(1.2+0.08)*0.5*(300 + 1.25*100) = 1304 beakers, a total of 104 overflow.

While binary works out like this:

Code:

2*(1.2+0.04)*(300+100*1.25) + (1.2+0.04*2)*0.5*(300+100*1.25) = 1360 beakers, a total of 160 overflow!

Remember, in both cases we end up with the exact same gold in the bank, zero, and thus the extra beakers generated by doing binary research are pure profit.

Interestingly, because we're now generating more overflow than we need, we can transmute some beakers to gold, if that's what we wish. In the break-even case, we can set the slider to 40% for the last turn to end up with 49 overflow beakers and 40 gold instead of 104 overflow beakers. Likewise, in the binary case, we can actually set the slider to just 30% on the last turn, to end up with just 17 overflow beakers and 80 gold saved instead of 160 overflow beakers. I hope that helps you see that gold and beakers are different forms of the same thing (commerce) and are transmutable into each other.

Now, the nice thing about binary research is that you don't actually have to calculate this kinda crap every turn or even at all, you just need to delay researching a tech until the last minute because that's always guaranteed to be as-good or better than the break-even approach. Waiting until the last minute to turn on research also lets you change your target tech at the last minute too, which is a very nice strategic benefit.

[Donovan Zoi]

Looks good Joey and thanks for that.

Incidentally, after our 3rd turn of CS research at 100%, there will only be a fraction left. Enough to possibly go down to 20% next turn and add 115 more gold to the 17 we'd have left (so yeah, 132g crushes the 53g I was boasting about). Or spend some of the 17g at 60% and get a good head start on our next tech. This is pretty much what I expected, so I am onboard now.

[Donovan Zoi]

OK, quick recap

- Set Salmon Falls to all 5 specialists. We can have a Golden Age in 6 turns, which should nearly coincide with our getting Engineering.

- Sainte-Foy has 2 new Workshops. I'll be sending the mainland workers back to Frontenac now to farm the neglected Cottage in Carillion in order to irrigate Frontenac's wheat.

- We will have a stack of 9 WEs and growing just outside of Harrapan. Krill has moved all the Impis out so only 2 Longbows, 2 Axes and one other unit remain. So It would be great if we could capture it (and the MoM) by the halfway point of our GA. Though I still see merit in blazing through a lesser defended Creole though but MoM benefit may be too good to pass up.

- With a GA coming, I think we should wait to switch to Caste/Bureau until that time. It will keep others wondering what tech we got too. GA workshops will yield 4 hammers so it may be worth getting out of Slavery.

[AdrienIer]

MoM is only worth something if we conquer it before the GA starts. It might even be worth delaying the GA until the turn we take it.