What is the probability of a dealer winning in the below situation?

There is a new game where in a standard deck of 52 cards the dealer flips over a card. If that card is a 4 he would flip over 4 more cards. If at any point he flips over any of the 3 remaining 4s OR the Jack of Diamonds before he finishes flipping 4 cards, the dealer loses. The dealer wins if he flips over 4 cards and none of the remaining 4s nor the jack of diamonds are flipped over. Likewise if he flipped over an 8 as the first card he would flip 8 cards and if any of those 8 cards were 3 of the remaining 8s OR the Jack of Diamonds he loses, if he doesnt flip any 8s or the Jack of Diamonds, he wins. If 2s count for 2 flips, 3s for 3 flips, and so on...Jacks count for 11 flips, queens for 12, Kings for 13, and aces as 1 flip what are the odds the dealer will win in any given round (ie what is the dealer advantage in this game). (Note: if the jack of Diamonds is flipped up at any point, even as the very first card to determine how many flips there will be, the dealer loses) Thanks.