- Currency and Alpha in isolation -
To anyone lazy to read the whole "boring stuff", you can simply jump to the conclusions highlited in red 
Maths+Currency=915
Alpha=422
Assuming that you have 5 cities and can dedicate 20
per turn to building
or
:
- Currency brings 20 + 5
= 31 (assuming that you have libraries everywhere, which is not always the case) and pays for itself in 29.5 turns
- Alpha brings 20 and pays for itself in 21 turns
If you don't go for Monarchy, it's reasonable to assume that you can reach Alpha 10 turns earlier than Currency. Thus, we have:
T+0 = Alpha date
T+10 = Currency date
T+21 = date at which Alpha has paid for itself
T+41 = date at which Currency has paid for itself
This means that
Currency would only beat Alpha on T+77
Of course these figures can vary between games, but the basic thing is that
Alpha is far superior to Currency (in iso)
Wasn't obvious at first glance and can be a bit hard to fathom as we're so used to Currency being "superior" to Alpha in "normal" games.
Now, when should you tech Alpha in iso? That's a bit tougher.
- Building research means you're not building infrastructure. Now of course you don't need infrastructure during the iso part of the game, but later on you're better off when you don't have to whip it. However, the fact remains that it's usually better to build / and whip infra, because you can't whip /
- But the thing is you don't want to tech Alpha, be a single turn earlier to Optics - i.e. Astro - and having "wasted" 422 on paying for Alpha
To get an idea of the threshold that has to be reached for Alpha to be profitable, we can make the reasonable assumption that
1 spent on infrastructure equals 0.5. This is reasonable because whipping infra later is twice as efficient, but you always build
at the same rate.
Let's say that
1T earlier Astro=100 (a reasonable assumption because you'll be able to get the good res for gpt trades one turn earlier)
Now let's say you're averaging 100
per turn stable upon reaching Optics. This means that
if Alpha pays for itself+200, you'll be 2T earlier to Astro and gain the 200
that come with it, netting you a
400 total gain. On the other side, you'll only have "wasted" 622
=311
on slow-building infrastructure. So you already have a big net gain.
Considering all the above, it's safe to say that
it is worth it to tech Alphabet when isolated if you can generate an extra 600 by building science before you reach Optics.
Edit: Be careful about the definition of "extra" beakers. Working a grass mine and building
instead of working a grass cottage, over 30 turns, is only 40 "extra" beakers, even though you've generated 90
through hammers.
Hope it was clear enough
. So I am more worried about that.
)
