Binary research - a worked example from a real game (part 1)

[RJM]

A thread on expansion rate has been somewhat hi jacked by a discussion of binary research. I have opened this thread to widen the audience and give a worked example from a real game.

This is from a recent game of mine (played at Emperor)

0% research generates 15 gold which will allow 5 turns at 100%
Break even is at 80% while 1@0% +5@100% is an average of 83.3%. This presumably gives a slight advantage to binary research.

To avoid complications, the starting position has been adjusted to prevent a library being completed and to prevent any city growth.

Binary research generates 111 (21->132) while break-even research gives 108 (21->129)

I was expecting a gain of 1 Not sure where the other 2 came from.

(to be continued)

 

[RJM]

City growth should not be an issue so repeat allowing growth. As expected, both binary and break-even research reach the same totals.

Now let's allow the library to complete. Break-even research generates 114 (21-135). Binary research generates 119 (21->140). In both cases the could be increased by running two scientists - 132 for break-even, 139 for binary.

Finally, what happens if we whip the library? Break-even gives 136 ; binary gives 151 .

Virtually none of these figures turned out to be what I was expecting. There are clearly some factors I don't know about. I conclude that binary research usually has a small benefit. The only downside I'm aware of is where it delays discovery of a key tech such as currency.

 

[Soirana]

Binary research generates 111 (21->132) while break-even research gives 108 (21->129)

I was expecting a gain of 1 Not sure where the other 2 came from.

(to be continued)

Need to break up if you wan to get it.

Binary gets 1 free beaker at zero than 22 per turn 5x22+1 -- 111

Steady goes at 18 per turn 18x6 108 --- 108

The main thing is you very rarely get amount of beakers in tech which is equal to beakers you generate. actual gain is larger - you now requisite modifier. In this case
100% slightly looses due to pretech modifier as diferential between 100% and 80% does not kick extra beaker due to modifier [actual gains are 18 and 22 while game shows 14 and 18... not really sure how 14beakers generate 4 extra in tech but I as never good in hidden mods]
[Edit2: oh, well figured 14+1hidden multiplied by 1.2 is exactly 18
18+1 hidden is however however falls one beaker short of getting extra +1 from 1.2 modifier [end 22.8 loosing .8 beaker to rounding]
so actual case is rather generous for steady path ]
Now let see there differential comes from -
at 80% you loose 1 gold/beaker per turn due to rounding. that is +6. You get one turn less of +4 beakers due to modifier [prereq and other mods give ]
So that is total +2 beakers, not sure there does last beaker, right that is actually that free beaker at zero slider, cause I think it is one +4 per turn I already calculated as benefit to steady path.

So actual math is
binary +6 to rounding savings +1 on zero turn +20 [5x4] on 100% turns
steady +24 [6x4] from hidden modifiers
total --- +6+1+20-24 = +3 to binary. Case solved

Edit: need to test things but I could imagine some scenario - early overexpansion with low total beaker total and slider at 30-40% while having like two prereq for writing where losses from turns without having prerq mods would overcome rounding issues and steady would come ahead. Well, maybe not too realistic afterall.

 

[admtanaka]

All that math is giving me a headache. Strict "binary research" it's too much micromanagement for me. I tend to play so absentmindedly I'm likely to erode the benefit by forgetting to turn research back on!

My simple rules:

1. Turn off research while building a library in the capital
2. Turn off research when unsure what to research next (alpha v aesthetics, etc); restart when the decision is clear.

 

[RJM]

All that math is giving me a headache. Strict "binary research" it's too much micromanagement for me. I tend to play so absentmindedly I'm likely to erode the benefit by forgetting to turn research back on!

My simple rules:

1. Turn off research while building a library in the capital
2. Turn off research when unsure what to research next (alpha v aesthetics, etc); restart when the decision is clear.

I agree that the level of micro-management becomes excessive. I don't mind in the early game when there's not much else going on, but I tend to stop after about turn 100. Fortunately the benefit is fairly small by then.

BTW, you don't lose the benefit by forgetting to turn research back on; you just dfer it a bit longer.

 

[barbertje]

You can something to rounding in 3 places.

1. The total amount of commerce that your cities produce gets multiplied with the slider and the result is rounded down to a whole number

2. The total amount of research that your cities produce gets multiplied with the slider and the result is rounded down to a whole number

3. After adding the free beaker, the research from step 2 is multiplied by the prerequisite tech bonuses (here 1 tech for a bonus of 20%) and the result is round​

ed.

(there's also a bonus for techs known by other civs that you know, but you don't know anyone)

If you use binary research, there will be no losses in step 1 and 2, so binary research is usually the best.

In this case:

The 80% slider approach produces 3.6 gold/turn, of wich 0.6 gold is lost.
Because of this, the average slider is only 80% instead of 83.33% with binary research.

In step 2, the 14.4 beakers/turn from the 80% slider approach will get rounded down to 14 beakers, there will be no rounding with binary research, wich produces 15 beakers on average.

So after steps 1 and 2, binary is 1 beaker/turn ahead. This should become 1.2 beakers/turn after getting the 20% bonus but ......

In step 3, the free beaker, added to the 14 beakers from the 80% slider approach, will give a number divisible by 5, so you get no rounding when computing the 20% bonus, so you end up with 18 beakers/turn.

For the binary research, on the 100% slider turns, you will get 19 beakers after adding the free beaker, and 20% of this is 4.8, so you lose 0.8 beakers/turn on those turns, and you lose (5 * 0.8 + 0.2)/6 = 0.7 beakers/turn on average,
so you'll get 18.5 beakers/turn, wich is 3 extra beakers in 6 turns.

In this case however it is possible to get no rounding at all and do slightly better than binary.
With a 50% slider, you produce 9 beakers and 6 gold without roundoff in steps 1, and 2, and you'll get 10 beakers after adding the free beaker, so there's no roundoff in step 3 as well.

With 1 turn at 50% and 2 turns at 100%, you produce (12+2*22) = 56 beakers in 3 turns, of 18.67 beakers/turn, or 4 extra beakers in 6 turns.

 

[Killroyan]

So in short, binary research nets you in 3-5% extra research with a lot of micro. Is this correct?

 

[TheMeInTeam]

It doesn't take a lot of micro. In practice, it just takes some arithmetic, especially with any decent mod allowing 100% or 0% in 1 click. You put research on, and see if you can finish the tech before running out of money. If no, then turn it off until you can. That is not advanced math and should be able to do in a moment.

At the start of the game don't choose a tech at first; try to meet people and get the discount on higher levels in the opening turns. But after that, just spam 0% or 100% ---> finish tech, then back to 0%. If you are building lots of libraries or are close to an academy, it is OK to wait a moment before going to 100%.

Worker action tile micro is far more obnoxious due to the planning. So is swapping city tiles for each city, esp as empire grows. Binary is nothing by comparison.

 

[Pangaea]

True, it's not a massive pain in the butt compared with city and worker micro, but it adds another layer of time consumption for a fairly small reward. There are also cases where it postpones a new tech by a turn, which you may not want. Have been doing binary in my recent game until about 1000AD, but have just given up on the thing now. The benefit is there, albeit small, but I also like that when running at break-ish even you have an indicator of how well your economy is doing. If you break even at 20% it's not in great shape, but if you break even at 60-70% it's in pretty good shape.

Running binary at the very highest levels probably has a bigger effect, as you're more likely to get tech discounts and such, and you don't really want to research something others have anyway. At Monarch, which I'm playing right now, trying to get back into the swing of things, this isn't as big a deal.

 

[RJM]

...

At the start of the game don't choose a tech at first; try to meet people and get the discount on higher levels in the opening turns.

...

Presumably you don't actualy delay discovering your first tech, after all it is usually pretty important!

 

[kossin]

Presumably you don't actualy delay discovering your first tech, after all it is usually pretty important!

Just the first 5 turns (un-select the technology). On turn 5 you must assign a technology however... can't remember whether the beakers get lost or dumped in cheapest tech.

Might gain 1~3 beakers overall.

 

[TheMeInTeam]

They get dumped into what is usually a bad tech atty that point.

Number one reason for binary after opening turns is max trade abuse. Commit to the tech to broker when losing monopoly is least likely.

 

[lindsay40k]

Would an example of this be I'm Montezuma, on my fourth turn I encounter Isabel, and based on that I take the Polytheism route to my CoL Oracle since she's likely to go for Meditation and have it free to backfill come Alphabet?

 

[admtanaka]

Strict "binary" is that research is either on (1) or off (0). You therefore either bank beakers with the slider at 0% or run it at 100% to power through a tech. The advantage is that every turn you get a free beaker (minimal) but also that you can make a better decision as to what the AI is pursuing and what you can get trade value for. Also, effective tech costs decrease as more AIs learn techs, so you can gain some efficiency by deferring your selections.

 

[TheMeInTeam]

Would an example of this be I'm Montezuma, on my fourth turn I encounter Isabel, and based on that I take the Polytheism route to my CoL Oracle since she's likely to go for Meditation and have it free to backfill come Alphabet?

The less time it takes for you to tech something start-to-finish, the less likely an AI beats you to it and trades it first.

You should pick dynamically based on AI tendencies but also based on what you see that everyone has.

Each time you trade a tech for-value, you gain a 100% multiplicative boost to your research rate. While you can rarely get perfect for-value, you can easily get something like 250% by trading with 3 AI very often. There is absolutely nothing in the game that can come even close to touching this multiplier, and it's the reason tech trades and their descendent research agreements are the most brokenly overpowered aspect of economy management. Intelligent abuse of the post-everything multiplier has been one of the core centerpieces (along with war) for human dominance over high level AI in this game since trading was allowed. Yes, I mean that.

Also arguably, it removes strategy from the game and weakens the impact of all other choices with its massive impact scale. The exceptions to times you don't want to max your beaker returns relative to your opposition via tech trades are few and far between.

I've had a few games where I was able to tech forever using a couple vassals. Literally almost no research myself (~50 beakers/turn into the 1700's-1800's just running culture slider to mass draft) and stayed ahead (literally 1st) in tech SOLELY through trading something to one vassal for his monopoly tech, brokering that around for another, and just keeping the chain going. It's ridiculous.

 

[lindsay40k]

I've had good results in capitulating a number of AI and ordering them to research tech for me to broker between them. I've never heard of this multiplier effect though. I'd like to learn more, but Google's coming up blank...?

 

[maks]

I've had good results in capitulating a number of AI and ordering them to research tech for me to broker between them. I've never heard of this multiplier effect though. I'd like to learn more, but Google's coming up blank...?

I think the idea is that the first level of multipliers such as buildings, and civics add up, so that academy + library + free religion = 85% extra beakers. So if your city is producing 100 beakers, you will get 185. What makes the tech trading multiplier strong is that it's multiplicative with the other multipliers. So if you were able to get a tech worth 250% of what you're trading away you effectively get 100*1.85*3.5 = 647 beakers.

I'm sure this also applies to war, but it's not as clear, and I would be curious if someone could explain it.

 

[pepe26]

the multiplier effect is just an expression to convey that you research one monopoly tech for x beakers then broker it around at some point to gain 2-3 or even more techs with it... thus, you have spent x beakers to research one tech und have gained 3-4 techs with it (including the self-tech), multiplying the use of x beakers by 200-300%

 

[lindsay40k]

Okay, I understand now, the way I was reading the turn of phrase it made me think there was some kind of additional beaker multiplier that gets switched on after a tech trade!

 

[pepe26]

well it kinda is like that, right?