Poker hands probability calculator for any number of suits and ranks (denominations)

After purchasing a 5 suited deck of cards and an 8 suited deck of cards, I decided to work out how the numbers of suits affect the probabilities of each poker hand.

Further, the following can calculate combinations and probabilities for any number of suits and any number of ranks (number of denominations).

You will notice;

at 5 suits a Flush overtakes a Full House,
at 6 suits a Flush overtakes a Four of a Kind, and
at 13 suits a Flush overtakes a Five of a Kind.

If you don’t believe the numbers, you are more than welcome to add them up and email me.

(thanks to CodeCogs for there LaTeX Engine)

Posted

12 June 2010

Random

MECTILE

Tags:

any, calculator, equations, poker, Probability, ranks, suits

Comments

12 responses to “Poker hands probability calculator for any number of suits and ranks (denominations)”

Brandon

9 August 2010

Very fun calculator. It looks like for decks with 13 or more ranks you calculate the number of straights where the Ace can be used as a low card (A,2,3,4,5). But in other decks this is not accounted for. Is this correct?

BTW I have found this calculator very useful and entertaining.

Reply
1. MECTILE
  
  9 August 2010
  
  yep, just the other way around.
  
  purely my thoughts when I was making this;
  
  A,2,3,4,5 always makes sense and with 13 ranks a King to Ace is normal, at the time I couldn’t image a Jack to Ace or Queen to Ace in a 11 and 12 rank deck being the norm.
  Though thinking about it now, I probably should have left it in, as it is all theoretical anyway.
  
  Reply
BJ

8 September 2010

looking for poker hand probabilty using a pinochle deck. can your calculator do that? i have tried 4*2 in suits and 6*2 in ranks but to no avail. dont know how else to put those numbers in to get accurate probabilites.

Reply
1. MECTILE
  
  8 September 2010
  
  interesting, never head about the pinochle deck until reading it on Wikipedia.
  The doubling up of cards (suit and rank) makes it not possible to use this calculator.
  
  Reply
Melissa

18 November 2010

I foud a great automatic poker odds calcultor, that helped me improve my poker strategy. They have a free beta trial, and I`m using it for 1 week. Helped me to win a lot of poker chips. Check it out: zpodds.com

Reply
Mark

10 September 2012

Would it be possible to calcuate probabilities with jokers or wildcards involved? Brilliant work Travis.

Reply
Jag

8 January 2017

Last week at Harrahs Casino in New Orleans a person was dealt Four on a kind twice in a row – what is possibility?

Reply
Dennis Myers

23 February 2019

Wildcards and larger hands. I need one for 6 card hands with a six suited deck. 3 wildcards optional. Which is better? 3 pair, or four of a kind?

Reply
C. Scott Davis

31 March 2020

I used your excellent calculator to work out the hand rankings for my 6-suit, 5-suit, and long suit decks. Thanks!
It would be interesting to also be able to see what effect wild cards would have. For example, if you were playing with a traditional 4-suit deck with 54 cards, but 2 of those cards the Jokers, which are wild and can be any rank. How would that affect the odds and hand rankings? It would make 5 of a Kind a possible hand (like when playing with more than 4 suits), but because the cards are wild, I’m assuming they would affect the odds differently.

Cheers,
C. Scott Davis

https://www.thegamecrafter.com/games/deck6
https://www.thegamecrafter.com/games/wild-suit-playing-cards
https://www.thegamecrafter.com/games/zero-mod-playing-cards

Reply
Johnathan

19 July 2020

Could you make this do probabilities for hands with more than 5 cards in them?

Reply
Rebekah Z

22 July 2021

Thank you so much! This calculator is exactly what I’ve been searching for. I’m trying to decide if it’s worth it to invent a 5-suit deck of cards with a single “god” face card and numbered cards 1-9 for each suit, plus two “Joker” equivalent wild cards. This is a big help!

Reply
Germain

26 August 2021

Great work!
I’d love to see this calculator for a 7-cards hand (texas hold’em)

Reply