CALCULATE THE CHANCES! (Math Geniuses!)
- Thread starter drvirus
- Start date
Orean
New Member
Math in a vacuum:
To rehash my calculation for landing an identical permutation of IV sets for a Pokemon, which was an eerily similar question asked in a recent thread
P), I'll cite this explanation of mine:
As Arnie stated, we would need to know the exact rate for the probability of encountering the Pokemon as well; however, to at least illustrate the formula if it helps enhance one's understanding on it, the odds of obtaining the exact-same set of IVs contingent on encountering the same Pokemon twice would be as follows:
(jigglypuff * 0.0000000009313225736)^2
Where jigglypuff = the encounter rate of the Pokemon-in-question, and ^2 exponentiates it to the second power—the formulaic representation of encountering the same Pokemon with the same set of IVs twice-consecutively, if that explains it understandably.
Complex RNG explanation:
While it does come across as an unimaginable longshot on-paper, it is even more primal to note that it's not really reflective of a "random" chance to land those IVs; nothing is computationally random, but the pattern behind PWO's RNG algorithm is even more predictable than standard attempts of emulating randomness on the medium of computers.
As also explained by Nikola in the aforementioned thread, PWO is very limited on the seed sets used for its RNG system. "Randomness" can only ever define the unpredictability of what outcome can happen, but it is even more so predictable in PWO with how its RNG algorithm behaves. The state of the RNG state only ever varies based on external factors, such as the time of the server's PC, the state of another number-randomizer, and so forth—factors that are very limited here, and thus there is not much variance. Due to the limitations on these parameters, the RNG state of some potential outcomes, such as a set of IVs for a Pokemon, infrequently shifts to a new state, so it is possible to land a Pokemon with those same IVs if it is timed correctly.
Considering the limited ranges of IVs for shinies, I would not be surprised if your shiny Jigglypuff was the first one caught after a server crash, and the second one was caught after yet another server crash; if that was the case, you probably just had great timing more than tremendous luck in landing those IVs. The levels may be different, but that's because the RNG state of the level-determination RNG was treated differently than the RNG state for the IV set itself, therefore having a different level didn't shift the RNG state of the IVs, necessarily.
Congratulations nonetheless~
To rehash my calculation for landing an identical permutation of IV sets for a Pokemon, which was an eerily similar question asked in a recent thread
P), I'll cite this explanation of mine:Naero said:For anyone who's really looking for the precise odds
To explain how I methodically calculated it, for anyone wondering about probability distribution:
1. I divided 1 by 32 - the exact probability of an IV landing on a particular value within the IV range; 32 is the denominator because 0 counts as an IV value too. That value is 0.03125, in decimal notation.
2. I exponentiated 0.03125 to the sixth power; in other words, I multiplied the probability of landing a single IV value by 6, to deduce the odds of landing particular IV values--the constituents of identical sets of IVs--in all six stats.
As Arnie stated, we would need to know the exact rate for the probability of encountering the Pokemon as well; however, to at least illustrate the formula if it helps enhance one's understanding on it, the odds of obtaining the exact-same set of IVs contingent on encountering the same Pokemon twice would be as follows:
(jigglypuff * 0.0000000009313225736)^2
Where jigglypuff = the encounter rate of the Pokemon-in-question, and ^2 exponentiates it to the second power—the formulaic representation of encountering the same Pokemon with the same set of IVs twice-consecutively, if that explains it understandably.
Complex RNG explanation:
While it does come across as an unimaginable longshot on-paper, it is even more primal to note that it's not really reflective of a "random" chance to land those IVs; nothing is computationally random, but the pattern behind PWO's RNG algorithm is even more predictable than standard attempts of emulating randomness on the medium of computers.
As also explained by Nikola in the aforementioned thread, PWO is very limited on the seed sets used for its RNG system. "Randomness" can only ever define the unpredictability of what outcome can happen, but it is even more so predictable in PWO with how its RNG algorithm behaves. The state of the RNG state only ever varies based on external factors, such as the time of the server's PC, the state of another number-randomizer, and so forth—factors that are very limited here, and thus there is not much variance. Due to the limitations on these parameters, the RNG state of some potential outcomes, such as a set of IVs for a Pokemon, infrequently shifts to a new state, so it is possible to land a Pokemon with those same IVs if it is timed correctly.
Considering the limited ranges of IVs for shinies, I would not be surprised if your shiny Jigglypuff was the first one caught after a server crash, and the second one was caught after yet another server crash; if that was the case, you probably just had great timing more than tremendous luck in landing those IVs.
The levels may be different, but that's because the RNG state of the level-determination RNG was treated differently than the RNG state for the IV set itself, therefore having a different level didn't shift the RNG state of the IVs, necessarily. Congratulations nonetheless~