Special Upgrade (to step 5) Attempt Calculator
We can model the special upgrade process as a Markov chain with the given transition matrix. Since we want step 5 to be an absorbing state, step 5 is the last step in the chain. Steps 6 and 7 are not shown in the matrix since protective upgrade stones are typically used.
Transition Matrix (using Standard Anvil)
| Step 0 | Step 1 | Step 2 | Step 3 | Step 4 | Step 5 | |
|---|---|---|---|---|---|---|
| Step 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| Step 1 | 0.5 | 0 | 0.5 | 0 | 0 | 0 |
| Step 2 | 0 | 0.5 | 0 | 0.5 | 0 | 0 |
| Step 3 | 0 | 0 | 0.55 | 0 | 0.45 | 0 |
| Step 4 | 0 | 0 | 0 | 0.55 | 0 | 0.45 |
| Step 5 | 0 | 0 | 0 | 0 | 0 | 1 |
Transition Matrix (using Alban Anvil)
| Step 0 | Step 1 | Step 2 | Step 3 | Step 4 | Step 5 | |
|---|---|---|---|---|---|---|
| Step 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| Step 1 | 0.25 | 0 | 0.75 | 0 | 0 | 0 |
| Step 2 | 0 | 0.25 | 0 | 0.75 | 0 | 0 |
| Step 3 | 0 | 0 | 0.33 | 0 | 0.67 | 0 |
| Step 4 | 0 | 0 | 0 | 0.33 | 0 | 0.67 |
| Step 5 | 0 | 0 | 0 | 0 | 0 | 1 |