June 2015 Academy vs Bulbing Discussion

beetle said:

That is not what Acken wrote. He is saying that it could take 120 turns for a GS to be worth planting rather than saving to bulb. So plant before T150.

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I did some calculations on a T130 Academy in the NC city. Assumed a T110 Education, T160 ST, T200 Plastics, T220 Atomic Theory, and a T270 SV finish. Also assumed Rationalism opener in T140s (this is does not affect the calculation by that much). And T180 Free Thought.

I am not sure if T220 Atomic Theory and T180 Free Thought are realistic, so calculation may be slightly off.

Also assumed 1 Bulb for ST and one bulb for Plastics.

Up until Plastics (T200) that academy has generated a total of ~1600-1700 Beakers (I included both bulbs, but did not factor any possible RAs).

Assuming 1-2 bulbs between Plastics and Atomic Theory, and a total of 12 GS over the course of the game, at T270 that academy will have generated a total of ~5500-5700 Beakers. This factors in the remaining 9 bulbs (which will generate ~2200-2300 beakers from that academy), but not any RA. I also did not consider the ISS bonus, nor the New Deal bonus.

I think an acceptable late game bulb would be ~8000 beakers, so saving the Scientist would give in the end more beakers.

There is also the discussion of how the science milestones are affected by the academy, but even in renaissance the academy gives 16.456 beakers, while ST costs ~1600 beakers. I don't think the absence of the academy delays ST and Plastics by more than 1-2 turns. But even by delaying plastics for 2 turns you still get the last tech earlier because of the extra scientist.

I don't really know how RAs will be affected by the academy, a bulb before Plastics, only gives on average 140-150 extra beakers because of the academy, so I expect a RA to give similar extra beakers early game. I think that with multiple RAs (eventually boosted by PT) an academy may provide extra beakers and give a faster win, but just by a couple of turns.

I think that even at t160 an academy may be worth it, since in the 30 lost turns, less than 500 beakers are lost, so at T270 the academy would amount to a total ~5000-5200 beakers.

A faster finish time (T250) would probably benefit more from an extra GS late game, so I think skipping the academy may be better, but if the assumed milestones are incorrect calculations may differ.

Sounds similar to what I had calculated in the past which underlines why I don't make academies at all.

My suggestion for 120 turns seems even too generous. But:

There is also the discussion of how the science milestones are affected by the academy, but even in renaissance the academy gives 16.456 beakers, while ST costs ~1600 beakers. I don't think the absence of the academy delays ST and Plastics by more than 1-2 turns. But even by delaying plastics for 2 turns you still get the last tech earlier because of the extra scientist.

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You have to remember the academy accelerates ST and plastics accross the whole distance. With similar benchmarks I get 650 beakers generated before ST and 880 before plastics. This is around 2 turns for each but at the benefit of 2 faster turns of schools and 2 faster turns of plastics. This could be valued in the 800ish area.

I don't really know how RAs will be affected by the academy, a bulb before Plastics, only gives on average 140-150 extra beakers because of the academy, so I expect a RA to give similar extra beakers early game. I think that with multiple RAs (eventually boosted by PT) an academy may provide extra beakers and give a faster win, but just by a couple of turns.

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RA are unchanged (unless you're the slower of the two partners but that's unlikely).

I think that even at t160 an academy may be worth it, since in the 30 lost turns, less than 500 beakers are lost, so at T270 the academy would amount to a total ~5000-5200 beakers.

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Weird conclusion considering the numbers no ?

Acken said:

Weird conclusion considering the numbers no ?

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Well I was considering that in the end a player would have more than 1000 BPT output. A T160 academy will lose 500 beakers compared to a T130 one. So in the end that may delay the finish time by at most one turn, but in some cases it may not delay it at all. Realistically panting a scientist right before ST means that ST will not be bulbed so this will delay ST and lose even more beakers. But theoretically if you have 2 scientists laying around, planting an academy before ST bulb may not delay the finish times in some cases.

What I did not factor in my calculations was a mountain capital. An Observatory, at say T150, may change the whole situation, and make planting worth it later in the game.

Would you plant more academies if your capital has an observatory?

Here is the calculation with the same milestones as before and a T140 Observatory:

1) Plant an academy on T130 in NC city. The academy would give 14.64 science (50% NC bonus, 33% University Bonus). For ten turns this amounts to 146.64 beakers

2) Have an observatory at T140, and also open Rationalism around that time. The academy gives 18.64 science, which compounded with the 10% Rationalism opener gives 20.504. For 20 turns this adds to 410.08 beakers

3) Bulb ST. The extra science from the academy would be 8 *20.504 = 164.032 beakers

4) ST at T160. This modifies the base yield of the academy by +2 so the academy now gives 25.63 science. For 20 turns that is 512.6 beakers

5) Free Thought at T180. This would increase the modifier for university, so the academy now gives 27.5 science (this is not really that important for this calculation, so turn time is not that relevant for this). For 20 turns that is 550 beakers

6) Bulb Plastics. The extra science from academy would be 8* 27.5= 220 beakers

Up until now the academy has yielded a total of: 2003.112 beakers. So I would average that at ~1900-2100 considering the turns for milestones may vary.

7) T200 Plastics and Research Labs. The Academy now yields 33 beakers. For 20 turns that will add to 660 beakers

8) 1/2 bulbs while beelining atomic theory. Would produce 264/528 beakers

9) T220 Atomic Theory. This modifies the base yield of the academy by +2 so the academy now gives 39.6 science. For the rest of the game (lets' say T260 SV, so 40 more turns) this would give 1504 beakers.

10) The remaining 8/9 bulbs (assumed a total of 12 scientists throughout the game) would give 2217.6/2534.4 beakers

So in total that academy planted at T130, would give 130 turns later 6852.712/6905.512 beakers. We can approximate this at 6700-7000 Beakers, so almost as good as a late bulb. The fact that you get ST and Plastics earlier will probably compensate the missing beakers and the net result would be better.

As you can see planting at T140 or even T150 would not make that big of a difference, since the main science really comes after ST. But I would argue that bulbing ST would give good results since you get schools 7-8 turns earlier. So you need to keep a scientist for that.

My conclusion would be that you can plant as many academies as you can with observatory (keep one GS for the ST bulb), BUT the last one should be no later than 8 turns before you plan to bulb ST, otherwise you risk delaying the finish time. In theory you could get to plant two of them, but you need to time LToP after the second natural GS in order to plant 2 and still have one for the ST bulb. 100 turns before the estimated finish time, might be a good marker, but it seems like on the edge.

Without Observatory planting 120 turns before the estimated finish time like Acken said would be the absolute latest. The academy might break even, or it may not, so it may not be worth it to plant your first natural GS (at T110 Education, you should get the first GS in the T120s, any later than that and it is not worth it to plant in my opinion).

claudiupb said:

Well I was considering that in the end a player would have more than 1000 BPT output. A T160 academy will lose 500 beakers compared to a T130 one. So in the end that may delay the finish time by at most one turn, but in some cases it may not delay it at all. Realistically panting a scientist right before ST means that ST will not be bulbed so this will delay ST and lose even more beakers. But theoretically if you have 2 scientists laying around, planting an academy before ST bulb may not delay the finish times in some cases.

What I did not factor in my calculations was a mountain capital. An Observatory, at say T150, may change the whole situation, and make planting worth it later in the game.

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Well it's clear that waiting 30 turns is only a decrease of 500 beakers but doesn't your numbers already suggests a single academy is lower beakers than a late game bulb ?

Also:
When you factor inside the academy value the value of bulbing ST or plastics that scientist ALSO has potentially a lower beaker value than a late game bulb. If your scenario is:
Plant 1 bulb ST
you have to calculate the value of the bulb (or approximate it rather) and add the 7-8ish faster turns of schools (and labs) and compare it to
2 late game bulbs often in the 8000 (before satellites) and 10000 (final stretch)

I may be emphasising science too much/too long but I tend to get around 15000 for my late game scientists with 8 cities and around turn 210. Number of cities do factor heavily into the calculation as bulbing is stronger relative to planting the more cities you have. https://www.dropbox.com/s/000zp6dctqzjk46/2015-06-16_00004.jpg?dl=0

Acken said:

Well it's clear that waiting 30 turns is only a decrease of 500 beakers but doesn't your numbers already suggests a single academy is lower beakers than a late game bulb ?

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Yes, without an Observatory, an academy at T130 with a finish time at T270 seems to give a lower beaker output than a late game bulb. But what I was suggesting is that a T160 one is still comparable with a T130, since the total amount in lost beakers is roughly about half your BPT at the end game, so depending on the science overflow you get when researching last required tech those lost beakers might not even count. Of course those lost beakers early game will count more and other milestone are delayed, and this needs to be factored in for a complete conclusion.

Acken said:

When you factor inside the academy value the value of bulbing ST or plastics that scientist ALSO has potentially a lower beaker value than a late game bulb. If your scenario is:
Plant 1 bulb ST
you have to calculate the value of the bulb (or approximate it rather) and add the 7-8ish faster turns of schools (and labs) and compare it to
2 late game bulbs often in the 8000 (before satellites) and 10000 (final stretch)

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Yes, that would give the most correct estimate, but it is pretty hard to calculate all that, since there are so many variables. Currently I'm not sure how ST and Plastics would be delayed without an academy. 2 turns is an estimate, but can change situational, since you might get some lucky steals, or get very good timings for RAs, etc.

The 7-8 faster turns for schools and labs is even harder to estimate, since sometimes you are not able to build (or rush) them right away in all the cities. Also it is difficult to estimate how much the BPT will increase after those milestones, for schools you need to approximate the size of the cities, for labs you need to estimate the number of cities that already have observatory, and these may differ from game to game.

So I just assumed that bulbing ST and Plastics is the best option, but again this may not be the case, so in the end, these calculations are rough estimates.

I'd say you should assume you can build the schools and labs otherwise there's no point in bulbing to begin with.

You also have to factor in that planting an Academy costs food/hammers. It's pretty minor, but it does add up.

Lately I've been thinking that planting is almost never right. Even if you get a GS early enough that planting an Academy seems to make sense, you may be better off simply using that GS for an extra midgame bulb.

I've started thinking about science victory more in terms of a race to a target beakers-per-turn level. I've been setting the target in the 1,700-1,800 range. What I've found is that getting your beakers up this high means that you really tear through the end of the tech tree, and you may not need many endgame GSes beyond what you get from Hubble/faithbuying. In contrast, if you're trying to win with only 1,200 or so beakers, you need to be very careful with GSes so that you don't come up short on science.

In games where my growth and science are very fast, I prefer to use bulbs to get started on late-game builds earlier -- in these situations, hammers are a significant constraint on your endgame, and you're more likely to be waiting for Hubble to finish than waiting for techs to research.

In games where midgame science growth is slower (generally due to few cities and/or few Observatories), I think there's merit to bulbing aggressively to get Fertilizer+Hospitals+Medical Labs ASAP. In these games, you can rush to get all of those up, then sit back and give yourself an extra 10-15 turns of turbo-growth to hit your beaker target before the endgame rush. Those extra turns of growth may make up for having one or two fewer GSes at the end.

But of course everything is situational. If you're a bit slower and playing on Deity, you may find that ideological unhappiness caps your population, preventing you from reaching the 1,700 bpt level. In those cases, you do need to be more careful with GSes. Deity also has strong research agreements, which mean that you may need less beakers from population anyway.

When you mathematical guys have resolved the issue, could you please tell us in simple language whether we should be bulbing or planting the first natural one? I appreciate the number crunching you're doing. You do us a service, sirs.

Well in the England game, I planted the Liberty GS on Iron Hills but since I aim on a DomV, science is not the end game.

Intuitively, planting is strictly short term benefit and saving up is long term investment

That's the other way around. Planting is typically a (very) long term investment.
Liberty GS has the advantage of coming earlier than any and at a time where the academy is a good chunk of your bpt. But even then, if the tech goal is extremely short like Machinery or Chivalry you're probably better off bulbing that tech with it than planting.

Well looked like that, then yes. But I meant when you save up all GSs for the endgame mass bulb they're worth a ton, can an Academy accumulate that many science to even it out?

stormtrooper412 said:

Well in the England game, I planted the Liberty GS on Iron Hills but since I aim on a DomV, science is not the end game.

Intuitively, planting is strictly short term benefit and saving up is long term investment

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Actually planting on a iron hill is probably a good option. Lets see you get 2 hammers from the hill, 1 from the iron and 1 from the forge so that's 4 in total.

I know this is largely irrelevant to the discussion above but I just want to throw out some numbers on how good an academy can be. But as the calculations above show by the time it you get the full benefits of the Academy its probably too late to be more valuable than a late game bulb.

8+2+2+4 (academy + ST + AT + Freedom) = 16 * 50 *50 * 50 *10 *50 (national college, observatory, university, rationalism, lab) 16 + 8 + 8 + 8 +1.6 + 8 = 49.6

8+2+2 (academy + ST + AT + Order) = 12 * 50 * 50 * 50 * 10 * 25 * 50 (national college, observatory, university, rationalism, Order, lab) 12 + 6 + 6 + 6 + 1.2 + 3 + 6 = 40.2

I don't know that looking at it in terms of total beaker output is ever going to get you anywhere definitive. Consider Great Scientist use in relation to the following question: How do you use Oxford?

Unambiguously, the beaker value of Oxford is maximized by saving it for a tech at the end of the tree. But it's pretty infrequent that Oxford is used like that. I would wager that, by far, the most common use of Oxford is for Radio. And I think that most experienced players agree that this is a fine play -- at least, it's agreed that you aren't totally blowing it by not saving Oxford for an endgame tech.

Given that analogy, I think it's safe to say that the action that gives the highest beaker output isn't automatically the best use of a Great Scientist.

Crap, I forgot about the Forge entirely

Manpanzee said:

You also have to factor in that planting an Academy costs food/hammers. It's pretty minor, but it does add up.

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Well regarding food if you plant an academy on a deer grassland tile you get 20 hammers from chopping/planting and you get 4 food (2 from grassland, 1 from deer, 1 from granary).

yeah, pretty good tradeoff

I suppose planting on bananas and non-river wheat can also work (particularly if you have sun god as that pantheon doesn't require a specific improvement).
If you have desert wheat you can have petra, sun god, granary and have a 4 food 1 hammer tile with academy on top.