Multi bag is probably over-complicating things. You can take a note from TGM and just keep a running window of the last n pieces and reroll m times until you get one that wasn't in the window or run out of tries. I think n is usually 4 and m is usually 6. This works great, is easy to implement and doesn't feel too predictable (i.e. like single bag does.) Also you can preload the window with two S's and two Z's to lower the odds of getting those first, since that's annoying :)