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When Shinato King of a Higher Plane attacks one of the opponent's Defense position monsters, the user can inflict damage to the opponent equal to half their Life Points

Team ChannelFireball broke the format at Pro Tour Paris with a little deck called Caw Blade

Consider its card type, any effects that modify when you could cast it (such as flash) and any other effects that stop you from casting it (such as from Meddling Mages ability) to determine if and when you can do this

Same goes for their ordinary versions

8, 2013 The most limiting factor of Pot of Dichotomy is that it must be activated at the start of Main Phase 1

Update: Revised with additional data from 10.5th Cola Cup