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)@@ | = | … | = | … |
ℹ️ Coin prices come from CoinGecko.
Try successive upgrades until have profit
(🚨🚧 Work in progress 🚧🚨)@@N@@ | # wins | Gain | − | Cost | = | Profit | Probability | Cumulative prob. | Expectation | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
100% | = | = |
Fixed number @@N@@ of upgrades
(🚨🚧 Work in progress 🚧🚨)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 | ||||
---|---|---|---|---|---|---|---|---|---|---|
… | … | … | … | … | … | … | … | … | … | … |
Todo
- Probability of profit
- URL parameters to save data
- Think better and rebuild all
Links
- STEPN: Whitepaper / Game-Fi Elements / Gems and Sockets
- StepnFP
- STEPN Tools / Gem Types and Level (Pokey)
- Other STEPN resources
- My donate and referrals page
- Expected value (Wikipedia)
- Little explanation about one common error on probabilities: Probability to win at least once
- The JavaScript file used by this application: STEPN-gem-upgrade-expectation.js
- This application uses these other free softwares: