Darkrai has the catch rate of maybe the lake pokemon( Azelf, Uxie, and Mesprit) seperate.
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A Pokemon's catch rate can range from 3 (hardest to catch) to 255 (easiest to catch). Hardest to catch (catch rate = 3): - Uxie - Mesprit - Azelf - Heatran - Regigigas - Giratina - Cresselia - Manaphy - Darkrai - Arceus Easier to catch (catch rate = 30): - Dialga (& Palkia) Easiest Sinnoh legendary to catch (catch rate = 45): - Shaymin
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Darkrai can be caught in any kind of Poke Ball, but Ultra Ball has 4x the catch rate by itself, which is pretty high.
The catch rate for the three legendary birds is 3 in all of the games, including Platinum.
In the Pastoria City Great Marsh, and on Route 212. The catch rate is 225, so that's good.