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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.
RZ is based around the Riemann Zeta Function, a famous mathematical function, that is connected to the famous (or rather infamous) Riemann hypothesis. This function is predicted to only output a value of zero at negative multiples of 2, and for numbers in the form \(\frac{1}{2} + ti\) where \(i = \sqrt{-1}\), which is the value being passed into the Riemann Zeta function in the main equation. As you can see in the graph, the Riemann Zeta function is very chaotic (not using the formal definition) and varies wildly. Because the function is in the denominator, rhodot spikes massively at \(\zeta(t) = 0\)
$$\dot{\rho} = \frac{tc_1c_2w_1}{|\zeta(\frac{1}{2} + ti)|/2^b + 10^{-2}}$$
$$\dot{\delta}=w_1w_2w_3 \times |\zeta'(\frac{1}{2} + it)|^b$$
$$\zeta(s) = \sum^\infty_{n=1}n^{-s}$$
Here we see that \(\dot{\rho}\) is proportional to \(c_1c_2w_1t\). The presence of the zeta function in the denominator creates these spikes at zero. Notable, increasing b increases \(\dot{\rho}\) EXCEPT when \(\zeta(...)\) = 0 where the 0.01 term outcompetes.
For \(\delta\), it is proportional to \(w_1w_2w_3\) as well as the derivative of the zeta function. Also, it is effected by b, giving it multiple uses. Also, the only use of \(\delta\) as a currency is to purchase \(w_1\)
The final equation gives the Riemann Zeta function, although it is not the equation used in code (trust me you don't want) to be given what the code actually does.
And thus the variable breakdown
| \(c_1\) | Increases \(\dot{\rho}\) by TBA |
| \(c_2\) | Increases \(\dot{\rho}\) by 2x |
| \(w_1\) | Increases \(\dot{\delta}\) by TBA |
| \(w_2\) | Increases \(\dot{\delta}\) by 2x |
| \(w_3\) | Increases \(\dot{\delta}\) by 2x |
| \(b\) | Hard to describe. Increases \(\dot{\rho}\) by a bit and \(\dot{\delta}\) by alot (2-4x depending on \(\zeta'\)) |
Strategy in RZ is relatively simples, with classic doubling strats and coasting for \(c_{12}\) (possible for other variables as well in future). The main point is when to activate the black hole after unlocking it
| \(c_1\) | Always buy |
| \(c_2\) | Always buy |
| \(w_1\) | Always buy |
| \(w_2\) | Always buy |
| \(w_3\) | Always buy |
| \(b\) | Always buy |
| \(c_1\) | When \(\frac{1}{6}\) of \(c_2\) |
| \(c_2\) | Always buy |
| \(w_1\) | When \(\frac{1}{6}\) of \(w_2\) |
| \(w_2\) | Always buy |
| \(w_3\) | Always buy |
| \(b\) | Always buy |
If the strategy includes BH, set BH to auto-activate at the given t
If the strategy includes values of \(c_{12}\), deactivate \(c_{12}\) when they have reached that level
If the strategy includes MS, swap from using the \(w_2\) milestone to \(c_1\) exponent at the indicated rho
If the strategy is RZSpiralSwap, don't do it unless you like hyper-active strats for a negligible to non-existent gain
The below is a table of common good values of t to activate BH at. This was found using the theory sim. The rho values given are estimates only. This table is not intended to be a substitute to the theory sim and should not be used as such. For best results, we always recommend using theory simulator. There is overlap. The rho ranges are ranges where the target t may show up as the given t.
| \(\rho\) | t | \(\rho\) | t | \(\rho\) | t |
| 1e600 - 1e625 | 263.57 | 1e775 - 1e840 | 978.77 | 1e1065 - 1e1070 | 2139.38 |
| 1e625 - 1e640 | 353.49 | 1e800 - 1e850 | 1115.07 | 1e1070 - 1e1090 | 2864.91 |
| 1e640 - 1e660 | 388.85 | 1e805 - 1e880 | 1287.41 | 1e1090 - 1e1300 | 3797.85\(^{[1]}\) |
| 1e660 - 1e675 | 462.07 | 1e875 - 1e875 | 1413.84 | 1e1300 - 1e1425 | 5856.09\(^{[2]}\) |
| 1e675 - 1e700 | 498.58 | 1e880 - 1e920 | 1686.42 | 1e1425 - 1e1475 | 6554.19\(^{[3]}\) |
| 1e700 - 1e705 | 606.38 | 1e920 - 1e970 | 2139.38 | 1e1475 - 1e1500 | 11575.53 |
| 1e705 - 1e755 | 679.74 | 1e965 - 1e1000 | 2864.91 | ||
| 1e755 - 1e770 | 834.65 | 1e1000 - 1e1065 | 3797.85 |
\(^{[1]}\) Occasionally 5856.09 and 5438.49
\(^{[2]}\) Occasionally 6554.19 especially at 1400-1410
\(^{[3]}\) Occasionally 11575.53 and 7623.42