A ruling about cuting the deck?

[thysereivuth]

k so i was playing someone and lets say he activates TGW. Instead of cuting the deck i shuffle it. Can my opponent cut his deck afterward? Cuz i thought that me shuffling their deck was considered the cut and you couldnt re cut?

 

[PokePop]

If you cut, he can't recut.
But you didn't cut. You shuffled. So he get's the final cut then.