Developing a 64 Card Poker Deck Variant - Curious About Probabilities

[Noah Tea]

Straight Variant:
The only difference is that the top rank can bridge the 1st rank to form a sequence. Think of it as if Q, K, A, 2, 3 was a legal straight. How is that calculated?

A More Complex Straight Variant:
This one gets trickier, I think.
In this variant, there are:

• 64 cards
• 4 suits
• 13 ranks
• Ranks 1-12 have 4 cards per rank
• However, rank 13 has 16 cards

Any rank 13 card would still have the bridging ability to make a straight connecting the top rank with the bottom rank.
How do you calculate that kind straight, where one rank has more cards than the others?

Flush Variant:
Similar to the previous, there are:

• 64 cards
• 4 suits
• 13 ranks
• Ranks 1-12 have 4 cards per rank
• Rank 13 has 16 cards
• Rank 13 cards have 2 suits
  • 4 rank 13 cards contain Hearts & Diamonds
  • 4 rank 13 cards contain Diamonds & Spades
  • 4 rank 13 cards contain Spades & Clubs
  • 4 rank 13 cards contain Clubs & Hearts

Is that in essence just 4 extra cards to draw from to get a flush?

"Full Court":
This deck has a "Court" system, which is pretty much like suits. I think of Suits running vertically down the ranks while Courts run horizontally.

• 64 cards
• 4 suits - hearts, diamonds, spades, clubs
• 4 courts - A, B, C, D (16 cards in each court)
  • Court A has ranks: 1, 4, 7, 10
  • Court B has ranks: 2, 5, 8, 11
  • Court C has ranks: 3, 6, 9, 12
  • Court D has all 16 cards in rank 13

To have a "Full Court" (5 cards of the same court), would that be the same as calculating a more traditional flush? Or am I missing something?

Cheers!

 

[fed2]

for the straight variant im going with 5^5 * 13 / combn( 64, 5) {=excel formula}. assign ranks in 13 posssible ways, and to each assign suites in 5^5 ways. (this includes 'flush'). Honestly these sort of counting problems can be tricky, so a computer will be your friend to check calcs. It always comes down to a matter of counting the unique combinations contributing to the event (straight, combo, etc). You can sort of infer the right answer from the wiki Straight, and thats probably the place to start.

 

[horsejack]

That sounds at least interesting!

 

[LiamLambert]

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