RNG correlation (Generation I): Difference between revisions
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>Bbbbbbbbba (A lot of analysis that may not be easy to understand...) |
>Bbbbbbbbba (Added a graph to further confuse readers (hopefully not). Probably takes too much space (if only we have PDFEmbed, maybe I could have handled the size better), but everything below that is "for nerds" anyway. (Wait, aren't we all nerds?)) |
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# The last iteration of the rejection sampling, which must be in the range 0 ~ 45 to have a chance to catch the Tauros. |
# The last iteration of the rejection sampling, which must be in the range 0 ~ 45 to have a chance to catch the Tauros. |
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# The second random byte, which must be in the range 0 ~ 87 to actually catch the Tauros. |
# The second random byte, which must be in the range 0 ~ 87 to actually catch the Tauros. |
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Denoting those values as r<sub>1</sub>, r<sub>2</sub>, and r<sub>3</sub>, we have (r<sub>3</sub> - r<sub>2</sub>) - (r<sub>2</sub> - r<sub>1</sub>) = 93 or 94 (depending on the "sub-rDIV" value). However, those ranges are very "misaligned", |
Denoting those values as r<sub>1</sub>, r<sub>2</sub>, and r<sub>3</sub>, we have (r<sub>3</sub> - r<sub>2</sub>) - (r<sub>2</sub> - r<sub>1</sub>) = 93 or 94 (depending on the "sub-rDIV" value). However, those ranges are very "misaligned", as visualized in the graph below. |
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[[File:Tauros RNG correlation.png|center]] |
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From the graph, it can be seen that the only way for all three values to be in their respective ranges is that: |
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* r<sub>1</sub> must be in the range 151 ~ 184, |
* r<sub>1</sub> must be in the range 151 ~ 184, |
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* r<sub>2</sub> must be in the range (r<sub>1</sub> - 94) / 2 ~ 45. |
* r<sub>2</sub> must be in the range (r<sub>1</sub> - 94) / 2 ~ 45. |
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