thydzik’s technology blog

I recently purchased a 5 Dimension (5D) deck of playing cards from Canada for $5 (plus $5 shipping to Australia). Unlike a normal deck, the 5D deck has an extra suit, the star, plus a numeric 1 card (as opposed to an ace), a princess card and jokers, totalling 80 playing cards.

The cards are standard bridge size 2.25″ x 3.5″ (the thinner width making it easier to hold more cards), with a card width of 0.3 mm. The card material is of quite good quality, with no ruined corners yet.

So how does an extra suite and more denominations affect the probabilities of standard 5 card poker hands? With reference to Durango Bill’s Poker Probabilities, the probabilities in a 5 suit 13 denomination deck are as follows:

Poker Hand        Number of Combinations     Probability
--------------------------------------------------------
Royal Flush                         5        .0000006053
Five of a kind                     13        .0000015739
Straight Flush                     45        .0000054480
Four of a kind                  3,900        .0004721614
Flush                           6,385        .0007730129
Full House                      9,360        .0011331873
Straight                       31,200        .0037772909

Total                       8,259,888       1.0000000000

The biggest difference is a Full House is easier to be dealt then a Flush.

Now, how does adding a One and Princess denomination affect the probabilities.

Poker Hand        Number of Combinations     Probability
--------------------------------------------------------
Royal Flush                         5        .0000002897
Five of a kind                     15        .0000008691
Straight Flush                     55        .0000031867
Four of a kind                  5,250        .0003041822
Full House                     12,600        .0007300374
Flush                          14,955        .0008664849
Straight                       37,440        .0021692540

Total                      17,259,390       1.0000000000

A Flush goes back to having a higher probability than the Full House.

Tags: 5 Dimension, 5 suit, 5D, playing cards, poker hands, Probability, Star

This entry was posted on Saturday, August 16th, 2008 at 2:57 pm and is filed under Random. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.