I am attempting to design a simplistic AI to play a trick taking card game known as Pfeffer. Unfortunately, my math skills are not quite up to the task it would seem. I am trying to find the probability that a card in a player's hand will take a trick if they win the bid and choose the trump suit.
The game is played with a 48 card pinochle deck. Players are dealt 11 cards each, and the remaining four cards go into a blind which the winner of the bid gets to trade cards from before the first trick is played. Cards are valued as follows: 9, 10, J, Q, K, A, 9 of Trump, 10 of Trump, Q of Trump, K of Trump, A of Trump, Left Bower, Right Bower. The Right Bower is the Jacks of the trump suit, and the Left Bower is the Jack of the same color as the trump suit (e.g. if spades is trump, then the Jack of Clubs is the Left Bower). The bidder starts the first trick by leading a card, and the other players must play one at a time, following suit. High card wins, and the winner would lead the next card.
Probability a card can win a trick with a trump suit - This question was very helpful, but it does not address the event where the player leads a trump card. It also doesn't consider whether or not an opponent's trump is "covered" by the player's.
What I am hoping to calculate is the probability that a card in a hand will win a trick, given that the player chooses the trump suit, receives the blind, and plays perfectly. I will then sum these to determine a rough number of tricks that the hand will take for a given trump suit.