Black Friday

Black Friday is a research with unique effect amongst other RP and DM researches. It decrease prices of particle upgrades and level ups.

Research cap: 50 (Each Vortex raises the cap by 1)

Initial price: 900 RP

Price formula: $$\color{Sepia} \pagecolor{Melon} 300 \times ((ResearchLevel+1)^2 + (ResearchLevel+1) \times 2)$$

Price formula for sum of first 'x' levels: $$\color{Sepia} \pagecolor{Melon} \frac{900}{18} \times \left (2x^3+9x^2+7x \right ) $$

Effect formula: $$\color{Sepia} \pagecolor{Melon} Price = baseCost \times (1.0870-0.0001 \times ResearchLevel)^{particleLevel}$$

Effect explanation: common particle level up price is $$\color{Sepia} \pagecolor{Melon} Lv.1cost \times 1.087^{particleLevel}$$. So every particle level multiplies cost by x1.087. Hovewer, Black Friday affect this multiplier, making higher particle levels much cheaper. For example, Alpha particle level up price from Lv.100 to Lv.101 will be $$\color{Sepia} \pagecolor{Melon}10 \times 1.087^{100} = 41,971.49$$, but with BF maxed at 50 it will be $$\color{Sepia} \pagecolor{Melon}10 \times 1.082^{100} = 26,468.30$$, which is only 63.06% of initial price. The higher particle level is, the higher BF effect will be. There is a table below to illustrate it:

Trivia

 * Black Friday is usually suggested to level up when you can reach particle levels 200 or 300, because at this point you should be able to afford it and in the same time make it worth the RP spent.
 * For particle upgrades formula is quite the same, but particleLevel is equal to upgrade level (10,25,50,75,100,150,200,300,500) and overall value multiplied by 5.