I tried all the possible runs in the new year event and here are the best options
I created a program to test that. I didn't actually try all of them. Here are the results:
The columns are:
- run: the success probabilities chosen and then amount of times it needs to be selected
- steps: the number of steps necessary to get to the final stage
- inc_tot: the total increment of stages, based on the assumed success of the selection
- prob_sub: probability to get to the eng stage using the specified run
Assumptions: - every single attempt is independent from each other
Relevant info:
- I am not considering the sun shard bonus in the last 2 stages
- The inc_tot values that go above 10 may happen in the simulation because it is not considering the order of the selections as relevant, which doesn't change the total probability of success (assuming independence).
| run | steps | inc_tot | prob_suc |
|---|---|---|---|
| str | i64 | i64 | str |
| ---------------------------------- | ------- | --------- | ---------- |
| {0.9: 10} | 10 | 10 | 0.34868 |
| {0.8: 1, 0.9: 8} | 9 | 10 | 0.34437 |
| {0.8: 2, 0.9: 6} | 8 | 10 | 0.34012 |
| {0.8: 3, 0.9: 4} | 7 | 10 | 0.33592 |
| {0.7: 1, 0.9: 7} | 8 | 10 | 0.33481 |
| {0.8: 4, 0.9: 2} | 6 | 10 | 0.33178 |
| {0.7: 1, 0.8: 1, 0.9: 5} | 7 | 10 | 0.33067 |
| {0.8: 5} | 5 | 10 | 0.32768 |
| {0.7: 1, 0.8: 2, 0.9: 3} | 6 | 10 | 0.32659 |
| {0.7: 1, 0.8: 3, 0.9: 1} | 5 | 10 | 0.32256 |
| {0.7: 2, 0.9: 4} | 6 | 10 | 0.32149 |
| {0.7: 2, 0.8: 1, 0.9: 2} | 5 | 10 | 0.31752 |
| {0.7: 2, 0.8: 2} | 4 | 10 | 0.31360 |
| {0.8: 1, 0.9: 9} | 10 | 11 | 0.30994 |
| {0.7: 3, 0.9: 1} | 4 | 10 | 0.30870 |
| {0.8: 2, 0.9: 7} | 9 | 11 | 0.30611 |
| {0.8: 3, 0.9: 5} | 8 | 11 | 0.30233 |
| {0.8: 4, 0.9: 3} | 7 | 11 | 0.29860 |
| {0.7: 1, 0.8: 1, 0.9: 6} | 8 | 11 | 0.29761 |
| {0.8: 5, 0.9: 1} | 6 | 11 | 0.29491 |
| {0.7: 1, 0.8: 2, 0.9: 4} | 7 | 11 | 0.29393 |
| {0.7: 1, 0.8: 3, 0.9: 2} | 6 | 11 | 0.29030 |
| {0.7: 2, 0.9: 5} | 7 | 11 | 0.28934 |
| {0.7: 1, 0.8: 4} | 5 | 11 | 0.28672 |
| {0.7: 2, 0.8: 1, 0.9: 3} | 6 | 11 | 0.28577 |
| {0.7: 2, 0.8: 2, 0.9: 1} | 5 | 11 | 0.28224 |
| {0.7: 3, 0.9: 2} | 5 | 11 | 0.27783 |
| {0.7: 3, 0.8: 1} | 4 | 11 | 0.27440 |
| {0.7: 1, 0.8: 2, 0.9: 5} | 8 | 12 | 0.26454 |
| {0.7: 1, 0.8: 3, 0.9: 3} | 7 | 12 | 0.26127 |
| {0.7: 2, 0.9: 6} | 8 | 12 | 0.26041 |
| {0.7: 2, 0.8: 1, 0.9: 4} | 7 | 12 | 0.25719 |
| {0.7: 2, 0.8: 3} | 5 | 12 | 0.25088 |
| {0.7: 3, 0.8: 1, 0.9: 1} | 5 | 12 | 0.24696 |
| {0.5: 1, 0.9: 9} | 10 | 10 | 0.19371 |
| {0.5: 1, 0.8: 1, 0.9: 7} | 9 | 10 | 0.19132 |
| {0.5: 1, 0.8: 1, 0.9: 8} | 10 | 11 | 0.17219 |
| {0.15: 1} | 1 | 10 | 0.15000 |
| {0.2: 1, 0.9: 5} | 6 | 10 | 0.11810 |
| {0.5: 2, 0.9: 8} | 10 | 10 | 0.10762 |
| {0.2: 1, 0.8: 1, 0.9: 4} | 6 | 11 | 0.10498 |
| {0.2: 1, 0.8: 2, 0.9: 3} | 6 | 12 | 0.09331 |
| {0.2: 1, 0.7: 1, 0.9: 4} | 6 | 12 | 0.09185 |
| {0.2: 1, 0.8: 3, 0.9: 2} | 6 | 13 | 0.08294 |
| {0.2: 1, 0.7: 1, 0.8: 1, 0.9: 3} | 6 | 13 | 0.08165 |
| {0.2: 1, 0.8: 4, 0.9: 1} | 6 | 14 | 0.07373 |
| {0.2: 1, 0.7: 1, 0.8: 2, 0.9: 2} | 6 | 14 | 0.07258 |
| {0.2: 1, 0.7: 2, 0.9: 3} | 6 | 14 | 0.07144 |
Use that at your own risk, it doesn't guarantee anything it is just an expected behavior based on the assumptions.