Previous: Theory 9 to Endgame
Disclaimer: This is a simplified version of the guide. The guide will skip over things, and is not completely optimal. Click here for a more polished, in-depth, and optimal guide.
When discussion strategy, this section may use more jargon then the rest of the guide. If you are confused, please check out the discord server and ask.
EF is based of eulers formula: \(e^{i\theta} = cos(\theta) + i sin(\theta)\), where \(i = \sqrt{-1}\), the imaginary unit
This means that as you increase θ, \(e^{i\theta}\) spirals around the origin (0, 0), always keeping a distance of 1. (and an angle of θ radians)
For those who don't know, a complex number is a number in the form a + bi. I won't fully explain complex number here, but it is in essence a 2d number, in the form a + bi instead of (x, y). if we set z = a + bi, then Re(z) = a, and Im(z) = b.
If you imagine the unit circle centered at the origin, then the value \(e^{i\theta}\) can be thought of a point 1 unit away from the origin and \(\theta\) radians around the circle
This formula will be used to generate 2 currencies, R and I, which are used to increase \(\rho\).
The equations in the theory have already expanded out eulers formula, and will be understandable if you have a good grasp of trigonometry, even if you don't understand complex numbers
Note that this theory's rho to tau rate is uniquely 1.6, this means that one must only reach 375 rho to max it out, and that tau increase 4 times faster with respect to rho, making this theory faster then it may seem when compared to the other CT's. This theory can feel extremely slow compared to other theories but it is actually one of the fastest
\(\dot{\rho} = a_1a_2a_3 \sqrt{tq^2 + R^2 + I^2}\)
\(G(t) = g_r + g_i\)
\(g_r = b_1b_2cos(t), g_i = c_1c_2sin(t)\)
\(\dot{q} = q_1q_2\)
\(\dot{R} = (g_r)^2, \dot{I} = -(g_i)^2\)
The first line is the main equation, which shows that to increase \(\rho\) you want to increase \(a_1\), \(a_2\), \(a_3\), t, and q (R and I are
effectively meaningless due to \(tq^2\) out competing them)
The second line is the graph, G(t) is the graph drawn on screen
The third line is Eulers formula, describing how \(g_r\) and \(g_i\) behave. Note that because they are squared below, negative values are fine
The forth line simple describes q
And the fifth line describes how R and I grow, based on the square of \(g_r\) and \(g_i\)
Note that even though R and I are meaningless in the main equation, they are used to buy \(b_{12}\), \(c_{12}\), and \(a_{23}\), making them quite important
And thus we have the variable breakdown:
| \(\dot{t}\) | Increases \(\dot{t}\) by +0.25 (max 1) |
| \(q_1\) | Increases \(\dot{q}\) by approx 7% |
| \(q_2\) | Increases \(\dot{q}\) by 2x |
| \(b_1\) | Increases \(\dot{R}\) by approx 14% |
| \(b_2\) | Increases \(\dot{R}\) by approx 21% |
| \(c_1\) | Increases \(\dot{I}\) by approx 20% |
| \(c_2\) | Increases \(\dot{I}\) by approx 21% |
| \(a_1\) | Increases \(\dot{\rho}\) by 2x |
| \(a_2\) | Increases \(\dot{\rho}\) by 2x, costs R |
| \(a_3\) | Increases \(\dot{\rho}\) by 2x, costs I |
TBA
EF strategy involves d strats with variable's that cost \(\rho\), and balancing between b/c upgrades and \(a_2/a_3\) upgrades with variable that cost R/I. Always buy \(\dot{t}\) as soon as you can
The idea with R and I are as follows: b/c upgrades increase R and I growth, but not \(\rho\). Early on, this is good because we need R and I to buy \(a_{23}\), but later into the pub they are less valuable, as their bonus takes a while to actually take effect. Therefore, later into the pub, we should buy b/c upgrades less
| var | Recovery | Tau gain |
|---|---|---|
| \(q_1\) | When \(\frac{1}{15}\) of \(q_2\) cost | When \(\frac{1}{15}\) of \(q_2\) cost |
| \(q_2\) | Always buy | Always buy |
| \(b_1\) | Always buy | When \(\frac{1}{5}\) of \(a_2\) cost |
| \(b_2\) | Always buy | When \(\frac{1}{5}\) of \(a_2\) cost |
| \(c_1\) | Always buy | When \(\frac{1}{5}\) of \(a_3\) cost |
| \(c_2\) | Always buy | When \(\frac{1}{5}\) of \(a_3\) cost |
| \(a_1\) | When \(\frac{1}{10}\) of \(q_2\) cost | When \(\frac{1}{10}\) of \(q_2\) cost |
| \(a_2\) | Always buy | Always buy |
| \(a_3\) | Always buy | Always buy |
The idle strat is EFSNAX not Autobuy All
✔️ - Always buy, ❌ - Never buy
| var | Recovery | Tau gain |
|---|---|---|
| \(q_1\) | ✔️ | ❌ |
| \(q_2\) | ✔️ | ✔️ |
| \(b_1\) | ✔️ | ❌ |
| \(b_2\) | ✔️ | ❌ |
| \(c_1\) | ✔️ | ❌ |
| \(c_2\) | ✔️ | ❌ |
| \(a_1\) | ✔️ | ✔️ |
| \(a_2\) | ✔️ | ✔️ |
| \(a_3\) | ✔️ | ✔️ |