Analysis of the Card Game "Declare"

Question

I was wondering if it would be possible (and feasible) to analyse a card game called "declare" which I recently discovered. Suppose there are 9 players playing with 4 decks of 52 cards and starting off with 9 cards in hand. If a person deems the sum of their cards small enough, they can show their cards (they win if it is indeed the smallest). Else, they pick up a card from a pile of hidden cards and throw one of their own cards. The other players can pick up a card either from the pile of hidden cards or the newly created pile of visible cards. If they have two or more of the same cards, they may throw all of them at once. I wanted to know if we could analyse when it would be reasonable to show your cards. The thing which crosses me is considering the unknown and known piles along with the fact that more than one card of the same number can be thrown at once. Is it even possible to estimate when it's favourable to show your cards and when it isn't without any experience and purely using probability? EDIT: Aces are counted as 1, and Jacks, Queens, and Kings are 11, 12, and 13 respectively.