The Real Formula (Not +10% Per Key)
The game lies to you. Keys actually use a hyperbolic formula:
n / (n + 10)
This creates massive diminishing returns, but still gives insane value early on.
Chance: 50.00%
Formula: n / (n + 10)

Keys are way stronger, and way weirder than the description suggests. Here’s the true math behind free chests, how many Keys you actually need, and why Keys can scale your run incredibly hard.

The game lies to you. Keys actually use a hyperbolic formula:
n / (n + 10)
This creates massive diminishing returns, but still gives insane value early on.
| Keys | Chance |
|---|---|
| 1 | 9.09% |
| 2 | 16.67% |
| 3 | 23.08% |
| 4 | 28.57% |
| 5 | 33.33% |
| 6 | 37.50% |
| 7 | 41.18% |
| 8 | 44.44% |
| 9 | 47.37% |
| 10 | 50.00% |
| 11 | 52.38% |
| 12 | 54.55% |
| 13 | 56.52% |
| 14 | 58.33% |
| 15 | 60.00% |
| Keys | Chance |
|---|---|
| 16 | 61.54% |
| 17 | 62.96% |
| 18 | 64.29% |
| 19 | 65.52% |
| 20 | 66.67% |
| 21 | 67.74% |
| 22 | 68.75% |
| 23 | 69.70% |
| 24 | 70.59% |
| 25 | 71.43% |
| 26 | 72.22% |
| 27 | 72.97% |
| 28 | 73.68% |
| 29 | 74.36% |
| 30 | 75.00% |