2

From this link

The number of distinct 5-card poker hands that are possible from 7 cards is 4,824.

Does anyone have the break down of the 4,824?
A list of the 4824?
Better yet a program to generate the 4824?

  • I don't have any knowledge in poker, but maybe this can help you: stackoverflow.com/questions/2829883/7-card-poker-hand-evaluator :) – Kevin Apr 14 '17 at 18:43
  • 1
    This is a subset of the 7462 distinct 5-card hands. These 7462 are listed here: suffe.cool/poker/7462.html . You can find your 4824 by eliminating from this list the ones that aren't possible in 7 cards. – Lee Daniel Crocker Apr 14 '17 at 20:15
  • @LeeDanielCrocker Thanks I think that is what I am looking for – paparazzo Apr 14 '17 at 20:37
  • @LeeDanielCrocker If you have an answer, please post it below. Comments do not have the features of a proper answer, so nothing you say here can be vetted or improved. Thanks. – Robert Cartaino Apr 17 '17 at 18:18
  • @LeeDanielCrocker I will accept. – paparazzo Apr 17 '17 at 18:22
3

The hands that can't happen with seven cards are exactly the five card hands that improve no matter which two cards are added to them.

This basically means hands with low kickers.

A high card hand (think of very card as a kicker) like 7 5 4 3 2 is impossible because any cards added to it will improve it.

Some classes are easy to show that there are always two cards which can be added without improving it, and thus all of those hands are possible in 7 card poker:

  • A straight flush: Add any two cards of another suit
  • Four of a kind: Add two cards with the same rank as the kicker
  • Full house: Add two cards that don't match the ranks of the cards in the full house or each other
  • Flush: Add two cards of another suit and different ranks from the cards in the flush
  • Straight: Add two cards that don't extend the straight and are different ranks from the cards in the straight and each other and of a suit that avoids forming a flush

All of those hands can occur in 7 card poker. The hands below that all have some cases where there is no choice but to improve on the 5 card hand by adding two more. For example: Three of a Kind. If the kickers are both high enough there is a way to avoid improving the hand. Hands with at least one low kicker like AAAK2 or 44432 can only be improved though and thus can't occur in 7 card poker. AAAK3 also can't avoid being improved because we need to add two cards, and once we've added a 2 there is no second card that can be added. In most cases if there is a 2 or a 3 as a kicker the hand can't occur in 7 card poker, but there are a few cases where there doesn't need to be a 2 or a 3 either, like AAA45, where adding a 2 and 3 would form a straight.

The fourth column in the link that Lee Daniel Crocker posted is the number of ways for that hand to occur in 7-card poker. Anywhere that column has a non-zero is a hand that is possible. All 1609 hands that are straights or better are possible. Of the remaining 5853 hands 3215 are possible.

  • Nice info but I am going to not give the check mark hoping for a program code. Preferably C#. +1 – paparazzo Apr 19 '17 at 19:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.