# Poker hand probabilities in Doomtown:Reloaded

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.

On the suggestion of mergatroid99 I've also asked this question at math.stackexchange.com here

• I don't really understand the deck construction rules. Is it a standard deck plus 2 jokers? Can you have 4 aces of hearts (as the deck construction sentence seems to imply)? – murgatroid99 Oct 23 '14 at 16:21
• The deck construction rules allow up to 4 cards of each suit and value. It's a trading card game where the cards have abilities but also function as cards when contributing to poker hands. You can have up to 4 ace of hearts for example, up to 16 cards of each value (4 Ah, 4 Ac, 4 As, 4 Ad) and up to 52 cards of each suit. A hand can have multiple cards with the same suit and value, so a hand of Ah, Ah, 2h, 3h, 5h is a flush. Ah, Ah, As, 2d, 2c is a full house. There are cards that punish cheatin' hands - hands where 2 or more cards share suit and value. But let's worry about that later. – MasterAir Oct 23 '14 at 16:29
• So you can have 4 of the exact same card (Ace of Hearts, for example)? In that case, if you can draw more than 5 cards to start, wouldn't the best hand be at least 6 of a kind (if you're considering identical suit and value) or N of a kind (if you're just considering identical value)? Also, are the Jokers in addition to the other cards or part of the 52? – murgatroid99 Oct 23 '14 at 16:32
• Yes, you can have 4 Ace of Hearts. No, the draw hand revealed is the best 5 card poker hand you can make from the hand you draw - as in e.g. Texas Hold em' - where you make a 5 card hand from the communal pool and your hole cards. Jokers are optional (but common) and are in addition to the 52. – MasterAir Oct 23 '14 at 16:37
• So these hands you're looking for are just the standard poker hands, plus 5 of a kind (which for obvious reasons is not a standard poker hand)? – murgatroid99 Oct 23 '14 at 16:40