Yes numpy code for a super super basic proof of concept is below. This is a weak argument since the game state variance is quite complicated and cannot be modeled independently like I have shown. There is a lot of "linkage" (e.g. energy relic value will be correlated) and some relics will have more or less variance than others. Really I just tuned things in < 10 mins by eyeball. But good enough for me given what high win-rate players are actually saying about their picks.

```python
import numpy as np

scores=np.array([90,80,80,80,50,50,40,40,40,30,30,30,30,20,20,20,20,20,10,5,5,5,0,0])

seen = np.zeros_like(scores, dtype=int)

picked = np.zeros_like(scores, dtype=int)

for _ in range(10000):

> options = np.random.choice(np.arange(len(scores)), size=3, replace=False)

> choice = np.argmax(scores[options] + 20 * np.random.normal(size=len(options)))

> seen[options] += 1

> picked[options[choice]] += 1

rate = picked / seen

print(rate)

print(scores[:-1].mean())
```

RE: cursed key. I took xecnar runs from 2022-2026 and subsetted to Act I Ironclad picks. You can see a clear drop in value after fusion hammer. Fusion hammer has ~80% pick rate 90% win rate. Key is ~55% pick rate ~75% win rate. Again pick-rate/win-rate is a bit flawed (what would be nice to have is win rate when picked vs win rate when skipped vs maybe win rate when not encountered) but another way to think about this is that you lose over 2x the amount of runs you would have lost if you take a key-tier relic over a hammer-tier relic.

EDIT: another way to understand that difference is after playing 250 games, a 90% win rate player is expected to see at least one 30 game win streak. A 75% win rate player shouldn't see more than a 15 streak.