You can differentiate this enemy from normal elite enemies on the map by the flame effect behind their icon. The Emerald Key is earned by defeating a powered-up elite enemy. Keep in mind this will always be an option until the Key is taken, so wait until there isn't a more important Rest Site option to take, like recovering health or upgrading a crucial card. The keys that have already been collected can be seen in the upper left corner of the screen, and each key is found through a slightly different method: The Ruby Key is earned by choosing the Recall option at a Rest Site.
This is simply the number of unsigned integers 2^64 = 18446744073709551616, since each seed is a 64-bit integer.Once you've satisfied this first requirement, you'll be able to earn all three keys on a single run up the Spire in order to unlock Act IV. Let C be the number of cards available, and D be the starting deck size, then the answer is (applying multiplication rule): P(same) = 1/22 * (1/C)^(D) Apply the inverse rule again to find the probability that at least one seed exists: P(one seed) = 1 - (1 - P(same)))^NĬorollary 1: The inverse 1 / P(same) is the amount of seeds you would have to try to find at least one success on average (expectation of geometric variable).Ĭorollary 2: By multiplying the probability P(same) with the number of seeds N and the number of cards C (each card is independent), you get the expected total number of perfect seeds.Īll cards need to be the exact same specific card. Thus the probability that no seed exists is (1 - P(same))^N. For this to happen N times, multiply itself by N by applying the Multiplication Rule N times. The probability that all cards are not the same is 1 - P(same) by applying the Inverse Rule. Then, combine the two steps with the following proof:
That means the seed searching program must have searched a substantial fraction (1% or so) of the total seed space to find all the perfect seeds it found, showing the power of a GPU (and why 64 or even 80 bit keys are now insecure in crypto) Reasoning | Character | Perfect chance | Number of seeds | Trials | The following table details the chance there is at least one seed, the expected amount of them that exist, and the number of seeds you would have to try to find one by pure chance: +-+-+-+-+ The cause is the fact that adding one more card to the starting deck makes it 71 or 72 times less likely for a seed to succeed.įor the Silent, there's about a 22.7% chance any specific card has a perfect seed. (In fact, I believe the algorithm has already found most of the Defect and Watcher seeds, and has found a few of the Ironclad ones). For the Ironclad, Defect, and Watcher one very likely exists for every card.