In bounty tournament, you find yourself in situation where, whilst you or an opponent is still 30-40BB deep; the bounty is worth more rhan the chips in the stack.

For example, in a pokerstars bounty builder, hero can be down to 1500 chip at 20/40 with a minimum bounty. Intheory, if this player shoved, the BB would have to call any 2 if it was folded to him/her, unless they knew it was only AA or KK.

So my question is, should hero have a shoving range here? If so, what should it look like from various positions? Would an optimal strategy involve some mixing with some normal opening and some shoving?

Also, given that we mostly see opening from players in these situations. How should opponents construct 3bettibg ranges/calling ranges from different positions?

These questions are very vague. I just want to open up a discussion and see where it goes.