>>1115324gold key is 75% chance
silver keys are each 75% chance, but I need 2 to work
If I try with silver keys 3 times each attempt is an endependent event with 75% succes chance
3 keys fail: 0.25*0.25*0.25 = 0.015625
2 keys fail: 3 * 0.75*0.25*0.25 = 0.140625
1 key fails: 3*0.75*0.75*0.25 = 0.421875
no keys fail: 0.75*0.75*0.75 = 0.421875
now, silver keys will open it in the cases where either no key fails or one key fails
so the chance of opening witth silver keys is:
0.421875 + 0.421875 = 0.84375, which is higher than the chance with a gold key, so I use the silver keys
