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STEPN gems upgrade expectationSTEPN gems upgrade expectation (🚨🚧🚧🚧 Work in progress 🚧🚧🚧🚨)
This (outdated 🚨) application computes the profit mathematical expectation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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| … | … | − | … | = | … | … | … |
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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 | ||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2022-08-13 12:10 |  Solana |  E | 0.02 SOL | 0.333 SOL | 2.18 SOL | 11.4 SOL | ||||
| 2022-08-13 12:10 | Solana |  L | 0.0298 SOL | 0.423 SOL | 2.89 SOL | 14.55 SOL | ||||
| 2022-08-13 12:10 | Solana |  C | 0.058 SOL | 0.584 SOL | 3.7 SOL | 16.95 SOL | ||||
| 2022-08-13 12:10 | Solana |  R | 0.01 SOL | 0.14 SOL | 1 SOL | 4.7 SOL | ||||
| 2022-08-13 12:10 |  BSC | E | 0.01 BNB | 0.058 BNB | 0.4 BNB | 2.2 BNB | ||||
| 2022-08-13 12:10 | BSC | L | 0.01 BNB | 0.088 BNB | 0.595 BNB | 3.29 BNB | ||||
| 2022-08-13 12:10 | BSC | C | 0.0129 BNB | 0.1018 BNB | 0.65 BNB | 3.47 BNB | ||||
| 2022-08-13 12:10 | BSC | R | 0.01 BNB | 0.023 BNB | 0.152 BNB | 0.88 BNB | ||||
| 2022-08-13 12:10 |  Ethereum | E | 0.00116 ETH | 0.13 ETH | 1.18 ETH | |||||
| 2022-08-13 12:10 | Ethereum | L | 0.001 ETH | 0.12 ETH | 1.24 ETH | |||||
| 2022-08-13 12:10 | Ethereum | C | 0.0178 ETH | 0.139 ETH | ||||||
| 2022-08-13 12:10 | Ethereum | R | 0.001 ETH | 0.11 ETH | ||||||
| 2022-07-31 11:20 | Solana | E | 0.0369 SOL | 0.458 SOL | 2.9 SOL | 14.46 SOL | ||||
| 2022-07-31 11:20 | Solana | L | 0.054 SOL | 0.615 SOL | 3.7 SOL | 15.5 SOL | ||||
| 2022-07-31 11:20 | Solana | C | 0.0446 SOL | 0.42 SOL | 2.718 SOL | 13.7 SOL | ||||
| 2022-07-31 11:20 | Solana | R | 0.01 SOL | 0.143 SOL | 1.03 SOL | 5 SOL | ||||
| 2022-07-31 11:20 | BSC | E | 0.01 BNB | 0.105 BNB | 0.62 BNB | 3.69 BNB | ||||
| 2022-07-31 11:20 | BSC | L | 0.012 BNB | 0.1138 BNB | 0.725 BNB | 3.5 BNB | ||||
| 2022-07-31 11:20 | BSC | C | 0.0109 BNB | 0.08 BNB | 0.5148 BNB | 2.68 BNB | ||||
| 2022-07-31 11:20 | BSC | R | 0.01 BNB | 0.0295 BNB | 0.222 BNB | 1.06 BNB | ||||
| 2022-07-31 11:20 | Ethereum | E | 0.03285 ETH | 1 ETH | 5.1 ETH | |||||
| 2022-07-31 11:20 | Ethereum | L | 0.0083 ETH | 0.86 ETH | 4.99 ETH | 13.45 ETH | ||||
| 2022-07-31 11:20 | Ethereum | C | 0.0485 ETH | 0.668 ETH | ||||||
| 2022-07-31 11:20 | Ethereum | R | 0.00191 ETH | 0.852 ETH | ||||||
| 2022-07-20 11:15 | Solana | E | 0.0375 SOL | 0.51 SOL | 3.2 SOL | 15.9 SOL | ||||
| 2022-07-20 11:15 | Solana | L | 0.04 SOL | 0.529 SOL | 3.45 SOL | 16.5 SOL | ||||
| 2022-07-20 11:15 | Solana | C | 0.0527 SOL | 0.53 SOL | 3.15 SOL | 14 SOL | ||||
| 2022-07-20 11:15 | Solana | R | 0.01 SOL | 0.15 SOL | 1.07 SOL | 5.35 SOL | ||||
| 2022-07-20 11:15 | BSC | E | 0.01 BNB | 0.102 BNB | 0.65 BNB | 3.36 BNB | ||||
| 2022-07-20 11:15 | BSC | L | 0.01 BNB | 0.1199 BNB | 0.7 BNB | 3.35 BNB | ||||
| 2022-07-20 11:15 | BSC | C | 0.0105 BNB | 0.1 BNB | 0.7 BNB | 3.99 BNB | ||||
| 2022-07-20 11:15 | BSC | R | 0.01 BNB | 0.0379 BNB | 0.319 BNB | 1.81 BNB | ||||
| 2022-07-20 11:15 | Ethereum | E | 0.21 ETH | |||||||
| 2022-07-20 11:15 | Ethereum | L | 0.95 ETH | |||||||
| 2022-07-20 11:15 | Ethereum | C | 0.749 ETH | |||||||
| 2022-07-20 11:15 | Ethereum | R | 0.24 ETH | |||||||
| 2022-07-10 18:10 | Solana | E | 0.09 SOL | 1.15 SOL | 6.9 SOL | 40 SOL | ||||
| 2022-07-10 18:10 | Solana | L | 0.066 SOL | 0.93 SOL | 5.85 SOL | 29 SOL | ||||
| 2022-07-10 18:10 | Solana | C | 0.0287 SOL | 0.54 SOL | 3.49 SOL | 18.19 SOL | ||||
| 2022-07-10 18:10 | Solana | R | 0.0104 SOL | 0.34 SOL | 2.8 SOL | 13 SOL | ||||
| 2022-07-10 18:10 | BSC | E | 0.027 BNB | 0.445 BNB | 5.5 BNB | 8.98 BNB | ||||
| 2022-07-10 18:10 | BSC | L | 0.01 BNB | 0.1396 BNB | 0.822 BNB | 4.5 BNB | ||||
| 2022-07-10 18:10 | BSC | C | 0.01 BNB | 0.12 BNB | 0.8 BNB | 3.89 BNB | ||||
| 2022-07-10 18:10 | BSC | R | 0.01 BNB | 0.0854 BNB | 0.5945 BNB | 2.77 BNB | ||||
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 page / 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: