Looking for an experienced mathematician with strong understanding of probability theory and statistics to discuss and answer several questions regarding a card game.
a) questions regarding use of Bayes' Theorem,
b) discussion of potential use of minimax algorithm and other optimization
c) discussion of expected-values
How the game is played:
1) The card game is Chinese Poker, a fairly simple zero-sum game.
2) It is played with a standard deck of 52 cards.
3) A player is dealt 13 cards (so 52 choose 13 combinations =~ 635 billion possible hands) and must form this into a "chinese hand", which consists of 3 sub-hands: a "front", a "middle", and a "back".
4) The front-hand contains exactly 3 cards, while the middle and back hands contain exactly 5 each (thus totaling the full 13 cards given at the start).
5) Standard poker grading applies to each hand (i.e. straight-flush > quads > full-house > flush > straight > trips > two-pair > pair > high-card).
6) By rule, a player's back-hand must be strictly greater (using standard poker grading) than his middle-hand, and similarly the middle-hand must be strictly greater than his front hand. So Back > Middle > Front. The front hand, being only 3 cards, has a maximum grade value of "trips" as flushes and straights are not applicable to a 3-card hand.