STEPN gems upgrade expectation

STEPN gems upgrade expectation (🚨🚧🚧🚧 Work in progress 🚧🚧🚧🚨)

This application compute the profit mathematical expectation of the fusion of 3 gems to upgrade to 1 gem of a better quality.
Chain:
Upgrade cost @@C@@ = =
@@P@@ = =
@@Q@@ = =
Ratio @@Q / P@@
Sell fees @@F@@
+ Gain if you win @@Q \left(1 - \frac{F}{100}\right)@@ = =
− Total upgrade cost @@3P + C@@ = =
= Profit if you win @@Q \left(1 - \frac{F}{100}\right) - (3P + C)@@ = =
Probability to win @@W@@ %
+ Gain expectation @@Q \left(1 - \frac{F}{100}\right) \frac{W}{100}@@ = =
− Total upgrade cost @@3P + C@@ = =
= Profit expectation @@Q \left(1 - \frac{F}{100}\right) \frac{W}{100} - (3P + C)@@ = =

Try successive upgrades until have profit

(🚧 Work in progress 🚧)
@@N@@# winsGainCost=ProfitProbabilityCumulative prob.Expectation
100%

Fixed number @@N@@ of upgrades

Gain expectation Total upgrades cost Profit expectation Probability of Profit and probability
@@N@@ @@Q \left(1 - \frac{F}{100}\right) \sum_{i=1}^N i \binom{N}{i} \left(\frac{W}{100}\right)^i \left(1 - \frac{W}{100}\right)^{N-i}@@ @@(3P + C) N@@ = positive profit for each number of success
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Gem price history

⚠️ Don’t trust these data. Check by yourself. And pay attention to the fact that maybe no one is buying.
Date Chain Gem Quality 1 Quality 2 Quality 3 Quality 4

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