I'm developing a 4 player Hearts game that has three AIs. So, I need some probabilities to do so.
Rules: Initially, 52 cards are distributed among all 4 players. Each of them has 13 random cards. One has to start, other has to play the same type card. If he hasn't that of type card, he can play any other card. Let's assume, if one has no card, then he plays a card that has a point (If he has point card, Ex. Hearts & Q of Spades). Cards sequence is 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A. 2 is lowest, A is Highest.
My Deck is: 7C, 8C, 9C, 10C, 7D, 8D, 9D, 10D, 7H, 8H, 9H, 10H, 7S
So, other players have 9 cards of Clubs, Diamonds, Hearts & 12 cards of Spades.
If I want to play 7C,
P(H1|N1) = ?
P(Q1|N1) = ?
P(L2) = ?
Hi be the i-th player has HEARTS
Qi be the i-th player has Q of Spades
Ni be the i-th player has no CLUBS
Li be the i-th player has lower CLUBS