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===Probability===
===Probability===
[[File:PokéRadarShinyProbability.png|thumb|right|The formula for the probability of finding a Shiny Pokémon. N<sub>c</sub> is the number of Pokémon in the chain, up to 40. The chances are calculated so that any shaking patch found in or after a chain of 40 has a 1 in 200 probability of being Shiny.]]
[[File:PokéRadarShinyProbability.png|thumb|right|The formula for the probability of finding a Shiny Pokémon. N<sub>c</sub> is the number of Pokémon in the chain, up to 40.]]
The likelihood of encountering a shiny Pokémon increases gradually as the chain grows in number of encounters. The more Pokémon are knocked out (or captured), the greater the chance the next set of patches will contain a shiny. As per the formula in the image, we can calculate the following percentages:
The likelihood of encountering a Shiny Pokémon increases gradually as the chain grows in number of encounters. Based on the formula depicted at right, the probabilities can be approximated as 1/8000 for a chain of 1, 1/7800 for a chain of 2, and so on up to 1/200 for a chain of 40. However, due to in-game rounding errors, a more accurate list of probabilities is as follows:


{| class="roundy" style="background:#{{key items color}}; border: 3px solid #{{key items color dark}}"
{| class="roundy" style="background:#{{key items color}}; border: 3px solid #{{key items color dark}}"
|- style="background:#{{key items color light}}"
|- style="background:#{{key items color light}}"
! style="{{roundytl|5px}}" | Encounters
! style="{{roundytl|5px}}" | Chain length
! Shiny Chance (1 in ..)
! style="{{roundytr|5px}}" | Shiny Probability
! style="{{roundytr|5px}}" | Shiny Chance (%)
|- style="background:#fff"
|- style="background:#fff"
| 0
| 0
| 8,192
| 8/65536  (1/8192)
| 0.0122%
|- style="background:#fff"
|- style="background:#fff"
| 1
| 1
| 7,130
| 9/65536  (~1/7282)
| 0.0140%
|- style="background:#fff"
|- style="background:#fff"
| 2
| 2
| 6,970
| 9/65536  (~1/7282)
| 0.0143%
|- style="background:#fff"
|- style="background:#fff"
| 3
| 3
| 6,810
| 9/65536  (~1/7282)
| 0.0147%
|- style="background:#fff"
|- style="background:#fff"
| 4
| 4
| 6,649
| 9/65536  (~1/7282)
| 0.0150%
|- style="background:#fff"
|- style="background:#fff"
| 5
| 5
| 6,487
| 10/65536  (~1/6554)
| 0.0154%
|- style="background:#fff"
|- style="background:#fff"
| 6
| 6
| 6,324
| 10/65536  (~1/6554)
| 0.0158%
|- style="background:#fff"
|- style="background:#fff"
| 7
| 7
| 6,161
| 10/65536  (~1/6554)
| 0.0162%
|- style="background:#fff"
|- style="background:#fff"
| 8
| 8
| 5,996
| 10/65536  (~1/6554)
| 0.0167%
|- style="background:#fff"
|- style="background:#fff"
| 9
| 9
| 5,831
| 11/65536  (~1/5958)
| 0.0172%
|- style="background:#fff"
|- style="background:#fff"
| 10
| 10
| 5,664
| 11/65536  (~1/5958)
| 0.0177%
|- style="background:#fff"
|- style="background:#fff"
| 11
| 11
| 5,497
| 11/65536  (~1/5958)
| 0.0182%
|- style="background:#fff"
|- style="background:#fff"
| 12
| 12
| 5,328
| 12/65536  (~1/5461)
| 0.0188%
|- style="background:#fff"
|- style="background:#fff"
| 13
| 13
| 5,159
| 12/65536  (~1/5461)
| 0.0194%
|- style="background:#fff"
|- style="background:#fff"
| 14
| 14
| 4,989
| 13/65536  (~1/5041)
| 0.0200%
|- style="background:#fff"
|- style="background:#fff"
| 15
| 15
| 4,818
| 13/65536  (~1/5041)
| 0.0208%
|- style="background:#fff"
|- style="background:#fff"
| 16
| 16
| 4,646
| 14/65536  (~1/4681)
| 0.0215%
|- style="background:#fff"
|- style="background:#fff"
| 17
| 17
| 4,472
| 14/65536  (~1/4681)
| 0.0224%
|- style="background:#fff"
|- style="background:#fff"
| 18
| 18
| 4,298
| 15/65536  (~1/4369)
| 0.0233%
|- style="background:#fff"
|- style="background:#fff"
| 19
| 19
| 4,123
| 15/65536  (~1/4369)
| 0.0243%
|- style="background:#fff"
|- style="background:#fff"
| 20
| 20
| 3,947
| 16/65536  (1/4096)
| 0.0253%
|- style="background:#fff"
|- style="background:#fff"
| 21
| 21
| 3,770
| 17/65536  (~1/3855)
| 0.0265%
|- style="background:#fff"
|- style="background:#fff"
| 22
| 22
| 3,592
| 18/65536  (~1/3641)
| 0.0278%
|- style="background:#fff"
|- style="background:#fff"
| 23
| 23
| 3,413
| 19/65536  (~1/3449)
| 0.0293%
|- style="background:#fff"
|- style="background:#fff"
| 24
| 24
| 3,232
| 20/65536  (~1/3277)
| 0.0309%
|- style="background:#fff"
|- style="background:#fff"
| 25
| 25
| 3,051
| 21/65536  (~1/3121)
| 0.0328%
|- style="background:#fff"
|- style="background:#fff"
| 26
| 26
| 2,869
| 22/65536  (~1/2979)
| 0.0349%
|- style="background:#fff"
|- style="background:#fff"
| 27
| 27
| 2,685
| 24/65536  (~1/2731)
| 0.0372%
|- style="background:#fff"
|- style="background:#fff"
| 28
| 28
| 2,501
| 26/65536  (~1/2521)
| 0.0400%
|- style="background:#fff"
|- style="background:#fff"
| 29
| 29
| 2,315
| 28/65536  (~1/2341)
| 0.0432%
|- style="background:#fff"
|- style="background:#fff"
| 30
| 30
| 2,129
| 30/65536  (~1/2185)
| 0.0470%
|- style="background:#fff"
|- style="background:#fff"
| 31
| 31
| 1,941
| 33/65536  (~1/1986)
| 0.0515%
|- style="background:#fff"
|- style="background:#fff"
| 32
| 32
| 1,752
| 37/65536  (~1/1771)
| 0.0571%
|- style="background:#fff"
|- style="background:#fff"
| 33
| 33
| 1,562
| 41/65536  (~1/1598)
| 0.0640%
|- style="background:#fff"
|- style="background:#fff"
| 34
| 34
| 1,371
| 47/65536  (~1/1394)
| 0.0730%
|- style="background:#fff"
|- style="background:#fff"
| 35
| 35
| 1,178
| 55/65536  (~1/1192)
| 0.0849%
|- style="background:#fff"
|- style="background:#fff"
| 36
| 36
| 985
| 66/65536  (~1/993)
| 0.1015%
|- style="background:#fff"
|- style="background:#fff"
| 37
| 37
| 790
| 82/65536  (~1/799)
| 0.1265%
|- style="background:#fff"
|- style="background:#fff"
| 38
| 38
| 595
| 110/65536  (~1/596)
| 0.1682%
|- style="background:#fff"
|- style="background:#fff"
| 39
| 39
| 398
| 164/65536  (~1/400)
| 0.2515%
|- style="background:#fff"
|- style="background:#fff"
| style="{{roundybl|5px}}" | 40
| style="{{roundybl|5px}}" | 40
| 199
| style="{{roundybr|5px}}" | 328/65536  (~1/200)
| style="{{roundybr|5px}}" | 0.5015%
|}
|}
<small>Note: the formula ''only'' applies at 1 or more encounters; the row for 0 encounters is the standard chance of encountering a shiny and is included for completeness.</small>


Since the probability doesn't increase after 40, the player can simply keep recharging and resetting the radar continuously until a shiny patch is seen. The probability goes up very strongly near the end—going from 39 to 40 doubles it—meaning a chain doesn't start seriously paying off until it's well past 30.
Since the probability doesn't increase after 40, the player can simply keep recharging and resetting the radar continuously until a shiny patch is seen. The probability goes up very strongly near the end—going from 39 to 40 doubles it—meaning a chain doesn't start seriously paying off until it's well past 30.
Blueapple128
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