I need help calculating the odds for a new custom playing card product. I'm the designer of the Bicycle Myriad Playing Card Set. It is an special 4 deck set of Bicycle playing cards in 4 different colors.
The 4 decks used together form a mega deck of 208 cards with 16 different suits. The suits are the 4 standard Spades, Diamonds, Clubs, and Hearts; each in the 4 colors of blue, purple, green, and red.
Here is the website for the set: MyriadCards.com
With this set there are 3 times as many ways to make a winning poker hand. There are 27 different ways to make a scoring hand, 18 more ways than the standard 9 poker hand ranks. This may seem complicated, but it simply adds the element of color matching to the standard poker ranks.
I would like to know the odds of drawing the 18 new 5 card poker hands. I probably won't change the order of the hands I have listed to keep the order simple, but I would like serious poker players to know the odds for these new combinations.
I am assuming the odds on the standard 9 poker hands won't change when using four decks together.
Here are links to 2 pages showing the poker hands: MyriadCards.com/playing-card-games-with-the-myriad-playing-card-set MyriadCards.com/myriad-poker-hand-ranks
Here is a link to the wikipedia page showing the odds for the 9 standard poker hands: Wikipedia.org - Poker Probability
Here are the poker hands for the set:
The new poker hands have asterisks *. These are the ones I need probabilities for.
* Royal Flush with Color Match
Straight Flush that ends or begins with an Ace, all the same color
Royal Flush
Straight Flush that ends or begins with an Ace
* Straight Flush with Color Match
5 cards in sequence, all of the same suit and the same color
Straight Flush
5 cards in sequence, all of the same suit
* Five Of A Kind (the odds of 5 of a Kind in this 4 card set are much better than a standard 1 deck with a wild card)
5 cards of one rank
* Four Of A Kind with Color Match
4 cards of one rank that are all the same color
Four Of A Kind
4 cards of 1 rank
* Full House with Full Color Match
3 matching cards of one rank and two matching cards of another rank with all 5 cards the same color
* Full House with 3 of a Kind Color Match
3 matching cards of one rank that are the same color and two matching cards of another rank
* Full House with Pair Color Match
3 matching cards of one rank and two matching cards of another rank that are the same color
Full House
3 matching cards of 1 rank and 2 matching cards of another rank
* Flush, Same Suit with Color Match
5 cards of the same suit, not in sequence that are all the same color
Flush
5 cards of the same suit, not in sequence
* Straight with Color Match
5 cards of sequential rank that are all the same color
Straight
5 cards of sequential rank
* Three Of A Kind with Color Match
3 cards of the same rank that are all the same color
Three Of A Kind
3 cards of the same rank
* Color Flush (same as a normal suit flush I presume?)
5 cards of the same color, not in sequence
* Two Pair with Full Color Match
2 cards of the same rank, plus another 2 cards of the same rank, all 4 cards the same color
* Two Pair with Two Color Matches
2 cards of the same rank that are the same color, plus another 2 cards of the same rank that are the same color
* Two Pair with One Pair Color Matched
2 cards of the same rank that are the same color, plus another 2 cards of the same rank
Two Pair
2 cards of the same rank, plus another 2 cards of the same rank
* 4 of a Color
4 cards of the same color, not in sequence
* One Pair with Color Match
2 cards of of the same rank that are the same color
One Pair
2 cards of the same rank
* 3 of a Color
3 cards of the same color, not in sequence
High Card
Highest ranked card (use Deck Rank Numbers)
I hope this is a relatively easy puzzle for a mathematician who knows how to determine probabilities.
I would appreciate your help,
Randy
The 4 decks used together form a mega deck of 208 cards with 16 different suits. The suits are the 4 standard Spades, Diamonds, Clubs, and Hearts; each in the 4 colors of blue, purple, green, and red.
Here is the website for the set: MyriadCards.com
With this set there are 3 times as many ways to make a winning poker hand. There are 27 different ways to make a scoring hand, 18 more ways than the standard 9 poker hand ranks. This may seem complicated, but it simply adds the element of color matching to the standard poker ranks.
I would like to know the odds of drawing the 18 new 5 card poker hands. I probably won't change the order of the hands I have listed to keep the order simple, but I would like serious poker players to know the odds for these new combinations.
I am assuming the odds on the standard 9 poker hands won't change when using four decks together.
Here are links to 2 pages showing the poker hands: MyriadCards.com/playing-card-games-with-the-myriad-playing-card-set MyriadCards.com/myriad-poker-hand-ranks
Here is a link to the wikipedia page showing the odds for the 9 standard poker hands: Wikipedia.org - Poker Probability
Here are the poker hands for the set:
The new poker hands have asterisks *. These are the ones I need probabilities for.
* Royal Flush with Color Match
Straight Flush that ends or begins with an Ace, all the same color
Royal Flush
Straight Flush that ends or begins with an Ace
* Straight Flush with Color Match
5 cards in sequence, all of the same suit and the same color
Straight Flush
5 cards in sequence, all of the same suit
* Five Of A Kind (the odds of 5 of a Kind in this 4 card set are much better than a standard 1 deck with a wild card)
5 cards of one rank
* Four Of A Kind with Color Match
4 cards of one rank that are all the same color
Four Of A Kind
4 cards of 1 rank
* Full House with Full Color Match
3 matching cards of one rank and two matching cards of another rank with all 5 cards the same color
* Full House with 3 of a Kind Color Match
3 matching cards of one rank that are the same color and two matching cards of another rank
* Full House with Pair Color Match
3 matching cards of one rank and two matching cards of another rank that are the same color
Full House
3 matching cards of 1 rank and 2 matching cards of another rank
* Flush, Same Suit with Color Match
5 cards of the same suit, not in sequence that are all the same color
Flush
5 cards of the same suit, not in sequence
* Straight with Color Match
5 cards of sequential rank that are all the same color
Straight
5 cards of sequential rank
* Three Of A Kind with Color Match
3 cards of the same rank that are all the same color
Three Of A Kind
3 cards of the same rank
* Color Flush (same as a normal suit flush I presume?)
5 cards of the same color, not in sequence
* Two Pair with Full Color Match
2 cards of the same rank, plus another 2 cards of the same rank, all 4 cards the same color
* Two Pair with Two Color Matches
2 cards of the same rank that are the same color, plus another 2 cards of the same rank that are the same color
* Two Pair with One Pair Color Matched
2 cards of the same rank that are the same color, plus another 2 cards of the same rank
Two Pair
2 cards of the same rank, plus another 2 cards of the same rank
* 4 of a Color
4 cards of the same color, not in sequence
* One Pair with Color Match
2 cards of of the same rank that are the same color
One Pair
2 cards of the same rank
* 3 of a Color
3 cards of the same color, not in sequence
High Card
Highest ranked card (use Deck Rank Numbers)
I hope this is a relatively easy puzzle for a mathematician who knows how to determine probabilities.
I would appreciate your help,
Randy