New Odds
Regular poker has four suits and five cards per hand; there are exactly 2,598,960 distinct possible hands, excluding wild cards.
If we bump this up to six suits and seven cards, the odds change astronomically. Suddenly, there are 2,641,902,120 possible unique hands. That’s over 1,000 times as many!
In regular poker, the most likely hand you can be dealt is Junk, Nothing, No Pairs. If you want to be optimistic, you could call it “High Card” instead. 1,302,540 possible junk hands,over half of all hands!
But in six suit poker, you are actually more likely to get one pair than you are to get random junk!
ALL POSSIBLE HANDS IN 6-SUIT POKER (RANKED BY PROBABILITY)
To calculate these odds, I’ve used binomial coefficients, or “choose notation.” Given X items, of which you can choose Y of them, there are (X, Y) possibilities of what that combination could be.
One Pair: AABCDEF, there are (13,1) ways to pick the pair (13 values, pick 1), and (6,2) ways to pick its suit (6 values, pick 2). There are (12,5) ways to pick the remaining 5 values (12 values, pick any five), and (6,1)^5 ways to pick their suits. (13,1)x(6,2)x(12,5)x(6,1)^5 = 1,200,925,440
Two Pair: AABBCDE, (13,2)x(6,2)^2 for A and B, then (11,3)x(6,1)^3 for the rest = 625,482,000
Nothing: 478,120,440 In this version of poker, you’re more likely to get one or two pairs than you are to get nothing, so a pair is actually the least valuable hand. Junk beats one or two pairs, isn’t that odd?
Three-of-a-Kind: AAABCDE, there are (13,1) ways to choose the triple, and (6,3) ways to choose their suits. There are (12,4) ways to choose the remaining values, with (6,1)^4 ways to choose the suits. (13,1)x(6,3)x(12,4)x(6,1)^4 = 166,795,200
Three and Two: AABBBCD (13,1)x(6,2)x(12,1)x(6,3)x(11,2)x(6,1)^2 = 92,664,000
Three Pair: AABBCCD, (13,3)x(6,2)^3 for A, B and C, then (10,1)x(6,1) = 57,915,000
Four-of-a-Kind: AAAABCD, there are (13,1) ways to pick the quadruple, and (6,4) ways to pick its suit. There are (12,3) ways to pick the remaining values, with (6,1)^3 ways to pick their suits. (13,1)x(6,4)x(12,3)x(6,1)^3 = 9,266,400
Three, Two, Two: AAABBCC (13,2)x(6,2)^2 an (11,1)(6,3) = 3,861,000
Four and Two: AAAABBC (13,1)(6,4)(12,1)(6,2)(11,1)(6,1) = 2,316,600
Straight: 8x(6,1)^7 = 2,239,488 (includes straights and royals), minus 48 = 2,239,440
Two Three-of-a-Kinds: AAABBBC (13,2)x(6,3)^2(11,1)(6,1) = 2,059,200
Five-of-a-Kind: AAAAABC, (13,1)x(6,5)x(12,2)x(6,1)^2 = 185,328
Four and Three: AAAABBB (13,1(6,4)(12,1)(6,3) = 46,800
Five and Two: AAAAABB (13,1)(6,5)(12,1)(6,2) = 14,040
Flush: (6,1)x(13,7) = 10,296 (including straights and royals), minus 48 = 10,248
Six-of-a-Kind: AAAAAAB, (13,1)x(6,6)x(12,1)x(6,1) = 936
Straight Flush: 7x6 = 42
Royal Flush: 6
Not all of these hands have names, but I have a few proposals.
One Pair: double or two-of-a-kind
Two pairs: double double
Nothing: It’s not technically junk anymore, but I like the way it sounds, so I’m still gonna call it Junk.
Three-of-a-Kind: triple
Three and Two: What would you call three of a kind and a pair? In regular poker, this is a full house, but in 7 suit poker there are two additional cards that don’t match up with the three of a kind or the pair. I propose calling this an Empty House, or just a House
Three Pairs: I’d call it a Triple Double or a Senate
Four-of-a-Kind: Quadruple or Quad
Three Two Two: this is closer to what a Full House would be, but there are a few more hands that could also probably be called Full Houses, so I’d probably call this one just a House, with the Three-Two being an Empty House.
Four and Two: the name Full House implies a sold out stage production, so maybe these sorts of hands would be named after Opera seats. The best seats are Optima, but this would be up in the rafter, Balcony seats, or Gallery seats, up in the nosebleeds.
Straight: A straight is a straight no matter what
Two Three-of-a-Kinds: Two Triplets or a Double Triple
Five-of-a-Kind: Quintuple
Four and Three: Full House or Optima Seats
Five and Two: Full House or Front Row seats
Flush: Flush
Six-of-a-Kind: Sextuple or Hextuple, Hex
Straight Flush: Straight Flush
Royal Flush: Royal Flush
What do you guys think? If you want me to explain anything, just ask.