The short version of my question is as follows:
What is the best way to compute the probability of different hand ranks after redraw in poker? Can this easily generalise to a stacked (non-standard) deck?
Doomtown Reloaded is a trading card game in which combat is resolved by hands of poker. Each card has an associated suit and value. Deck construction requires a 52 card deck with up to 4 cards of each suit and value. The ability of your 'dudes' alters the way you construct your poker hand. Some 'dudes' are stud shooters they allow you to draw more cards. Some dudes are 'draw' shooters, they allow you to discard and redraw. You are also allowed to include an additional 2 jokers (which can be used as any suit and value for the purposes of forming poker hands)
Computing how adding stud shooters affects your draw hand probability is relatively easy, however I haven't been able to find a description of how to compute the probability of different hands after redraw.
I want to know how to compute the likelihood of the 10 poker hand ranks (high card -> 5 of a kind) given the deck construction, number of cards you initially draw and number of cards you discard and redraw.