In the last post, I covered two mathematical formulas useful for calculating advanced odds for poker hands – Texas Hold’em in particular. That post covered the basics. Let’s get in to some more details. (Please re-read the previous post before continuing, as the latter-half of this post is fairly math-dense.)
There are 10 categories of poker hands. They are, from highest value to lowest:
(1) Royal flush = Ace through 10 in the same suit)
(2) Straight flush = Five consecutive cards in the same suit
(3) Four of a kind = Four cards of the same value
(4) Full house = Three of a kind plus a pair
(5) Flush = Five consecutive cards in value, any suit
(6) Straight = Five cards of the same suit, no sequence necessary
(7) Three of a kind = Three cards of the same value, any suit
(8) Two pair = One pair of one card value, and another pair of another value.
(9) One pair = Two of a kind
(10) No pair
These are the poker hands that can be dealt from a single deck of 52 cards. These are just as applicable to Texas Hold’em as other forms of poker. Let’s have a look at some of the total possible unique hands for each category. Recall from the last post that there are 2,598,960 unique 5-card hands possible from a standard deck of 52, where order of cards does not matter.
Based on the definition, there can only be 4 possible royal flush hands because there are only four suits in a deck. These are very rare, obviously. The odds of being dealt 5 straight cards to form a flush are 4/2,598,960 =~ 1/650,000. [Note: these apply to the scenario where …