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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.
CSR2 is based on a recurrence relation that computes sqrt(2), which is the following 2 sequences:
Where the next term (\(N_m\)) is the previous term (\(N_{m-1}\)) times 2 plus the term before that (\(N_{m-2}\)), for both N and D, that is
\((N/D)_m = 2(N/D)_{m-1} + (N/D)_{m-2}\)
Interestingly, if we take the quotient of corresponding terms in both series (\(\frac{N_m}{D_m}\)) (like 1/1, 3/2, 7/5, 17/12 ect.) as we get further along, it approaches \(\sqrt{2}\). Essentially, as m approaches infinity, (\(\frac{N_m}{D_m}\)) approaches \(\sqrt{2}\)
\(\dot{\rho} = q_1q_2q\)
\(\dot{q} = c_1c_2|\sqrt{2} - \frac{N_m}{D_m}|^{-1}\)
\(N_m = 2N_{m-1} + N_{m-2}, N_0 = 1, N_1 = 3\)
\(D_m = 2D_{m-1} + D_{m-2}, D_0 = 1, D_1 = 2\)
\(m = n + log_2(c_2)\)
The first line is the main equation, which shows that to increase ρ you want to increase q1, q2, and q
The second line is the equation for q, which shows that increase q you want to increase c1, c2, and get \(\frac{N_m}{D_m}\) closer to \(\sqrt{2}\)
The third line and forth line is the recurrence relation described above, which shows to get \(\frac{N_m}{D_m}\) closer to \(\sqrt{2}\), you want to increase m.
The fifth line is self explanatory
Therefore, \(q_{12}\) affect \(\rho\) directly and \(c_{12}\) and \(n\) affects q directly (and by extension \(\rho\) indirectly)
And thus we have the variable breakdown:
| \(q_1\) | Increases \(\dot{\rho}\) by approx. 7% |
| \(q_2\) | Increases \(\dot{\rho}\) by 2x |
| \(c_1\) | Increases \(\dot{q}\) by approx. 7% |
| \(n\) | Increases \(\dot{q}\) by 6x |
| \(c_2\) | Increases \(\dot{q}\) by 22x!! (with full milestones) |
Without full milestones \(c_2\) increases \(\dot{q}\) by about 11.5x
An increase in \(\dot{q}\) corresponds to an equivalent increase in \(\dot{\rho}\) over time
I've found it between 2 and 4.5 usually, but it varies
CSR2's strat is pretty simple, really heavy d strats. Because of the large variable disparity, doing active strats is especially beneficial
| \(q_1\) | 10x cheaper then \(min(q_2, n, c_2)\) |
| \(q_2\) | Always buy unless similar to \(n\) or \(c_2\) |
| \(q_1\) | 10x cheaper then \(min(q_2, n, c_2)\) |
| \(n\) | Always buy unless similar to \(c_2\) |
| \(c_2\) | Always buy |
There is a MS strat for CSR2. You can do CSR2XL x.xx explained here or you can just do one swap at the end of your pub, which is swapping form the usual milestone route of "0/1/0 -> 0/1/2 -> 3/1/2" to "3/0 -> 3/1/0 -> 3/1/2" at the end of your pub, wait a bit, and then publish and swap back.