Caveat: I made this up but have never played it.
Sevendeck Poker Rules Summary
Sevendeck
Poker is played like regular poker, with a few adjustments. First, mere
pairs are of no value. Multiples of more than two have value; the pairs
contained in them don’t “cancel”. One consequence of this is that
there’s no Full House; a hand with three of one value and two of another
is just Three of a Kind.
Second, there are no flushes. Instead, there is a “Stretch”, which is
five cards with consecutive suits. Suits wrap around, as suggested by
the circle of suits on the box. So, for example,
Diamond-Violet-Cherry-Fire-Lemon would be a Stretch.
When a hand is both a Stretch and a multiple, the higher hand takes
precedence. There is no special hand category for Stretch-multiple
combinations. (Pairs in a Stretch do not cancel; they still contribute
their suit.) Straight Stretch is still a special hand, like the
Straight Flush in regular Poker. For a Straight Stretch, the values and
suits do not have to be in the same sequence.
Sevens can be low (zero) in a Straight. (Ones (“aces”) cannot be high.)
The order of the hands, from highest to lowest, is:
- Five of a Kind
- Straight Stretch
- Four of a Kind
- Straight
- Stretch
- Three of a Kind
- High Card
- Two Pair
- Pair
Notice how High Card beats Two Pair and Pair. High Card is always a
five-card hand, like a Straight or a Flush. (This might matter if you’re
playing a travesty like Guts where hands may be scored with fewer than
five cards.)
When breaking ties in Two Pair or Pair, use the non-paired “kickers”
first, then move on to the pairs as a last resort.
What follows is a math-geek-y discussion of where the above rules came from.
An Analysis of Poker with a Sevendeck
A
Sevendeck
is a deck of 49 cards, with seven suits and seven cards in each suit,
numbered 1 through 7. Unlike a regular deck of cards, the suits fall
into a well-defined sequence, based the number of angles in the symbol
as well as the spectrum order of the colours.
One question that this deck raises is how the game of Poker would work
on such a deck. The following is an attempt to answer that.
The most direct approach would be to simply use all the standard rules
of Poker, unmodified. The odds of being dealt a five-card hand of a
specific type are as follows:
|| Hand || Frequency || Probability ||
|| ---------------- || ---------------- || ------------------ ||
|| Five of a Kind || 147 || 0.000077 ||
|| Straight Flush || 28 || 0.000015 ||
|| Four of a Kind || 10290 || 0.005396 ||
|| Full House || 30870 || 0.016189 ||
|| Flush || 119 || 0.000062 ||
|| Straight || 67200 || 0.035241 ||
|| Three of a Kind || 180075 || 0.094434 ||
|| Two Pair || 324135 || 0.169981 ||
|| Pair || 1008420 || 0.528831 ||
|| High Card || 285600 || 0.149773 ||
This is sort of like playing a variant of Poker with wild cards, where
the probabiltites of different hands are no longer monotonically
increasing. We could instead re-order the values of the hands to put
them in probability order:
|| Hand || Frequency || Probability ||
|| ---------------- || ---------------- || ------------------ ||
|| Straight Flush || 28 || 0.000015 ||
|| Flush || 119 || 0.000062 ||
|| Five of a Kind || 147 || 0.000077 ||
|| Four of a Kind || 10290 || 0.005396 ||
|| Full House || 30870 || 0.016189 ||
|| Straight || 67200 || 0.035241 ||
|| Three of a Kind || 180075 || 0.094434 ||
|| High Card || 285600 || 0.149773 ||
|| Two Pair || 324135 || 0.169981 ||
|| Pair || 1008420 || 0.528831 ||
This has the interesting consequence of making flushes the most valuable
types of hands. However, it also makes them so rare that they are
nearly irrelevant to game play. This happens because in a Sevendeck, a
Flush is just like Five of a Kind, but with suits instead of numbers.
The fact that the Straight Flush splits this small set of hands into two
smaller subsets means that they are each more rare than Five of a Kind.
Also, notice that pairs are abundant. With only seven different numeric
values, there is more than a 50% chance that any set of five will be a
Pair. If all hands involving multiples are factored in, there is more
than an 81% chance of getting a hand with at least two of a single
value. This makes High Card more rare than Two Pair or Pair.
With the Sevendeck’s rich supply of novel suits, it seems like a waste
to make the suit-based hands so rare that they have basically no effect
on the game. Therefore, we need a new kind of suit-based hand that has
a better chance of coming up in a set of five cards.
Unlike in regular Poker, the Sevendeck has a well-defined relationship
among its suits. We can use this relationship to define a new type of
hand, called a Stretch, which consists of five cards with consecutive
suits. The sequence of suits wraps around, as suggested by the circle
of suits on the box and the spectral colouring of the suits. So, for
example, Diamond-Violet-Cherry-Fire-Lemon would be a Stretch.
Unlike the Flush, a Stretch is relatively easy to obtain in a set of
five cards. Also unlike the Flush, a Stretch is not mutually exclusive
with a multiple-value hand like Pair or Full House. To facilitate
computing odds, we can start with the “raw” frequences of all the
possible types of hands:
|| Hand || Frequency ||
|| ------------------------ || --------- ||
|| Five of a Kind Stretch || 49 ||
|| Five of a Kind || 98 ||
|| Four of a Kind Stretch || 1470 ||
|| Full House Stretch || 2940 ||
|| Straight Stretch || 3360 ||
|| Four of a Kind || 8820 ||
|| Stretch || 14280 ||
|| Three of a Kind Stretch || 14700 ||
|| Two Pair Stretch || 22050 ||
|| Full House || 27930 ||
|| Pair Stretch || 58800 ||
|| Straight || 63868 ||
|| Three of a Kind || 165375 ||
|| High Card || 271439 ||
|| Two Pair || 302085 ||
|| Pair || 949620 ||
One could simply attempt to play the game with these sixteen hands, but
the sequence is weird and hard to remember. It would be nice to have a
smaller set of distinct hands that have a simpler relationship.
A key aspect of the order of hands in Poker is that any hand that is
more constrained than another is worth more. For example, a Full House
beats Three of a Kind. The above sequence does not have this property.
Stretch beats Three of a Kind Stretch, Two Pair Stretch, and Pair
Stretch. As noted in the second “standard Poker” version above, High
Card still beats Two Pair and Pair. However, this latter condition is
kind of an interesting twist that seems worth keeping. After all, the
goal is to produce a game that is similar enough to Poker to still
resemble the game, yet different enough to be interesting.
However, the placement of Stretch in this sequence is awkward and calls
for improvement. The position of Pair at the bottom of the list
suggests a simple fix: “Pairs are worth nothing”. We can further
condense the list by declaring that for any hand that has the Stretch
property and a multiple value, it acts as the higher valued hand—there
is no special category for such a “combination” hand. We’ll keep the
Straight Stretch, though, because it parallels standard Poker well.
When we condense the list of hands in this manner, we get the following
simple sequence:
|| ‘‘‘Hand’’’ || ‘‘‘Frequency’’’ || ‘‘‘Probability’’’ ||
|| Five of a Kind || 147 || 0.000077 ||
|| Straight Stretch || 3360 || 0.001762 ||
|| Four of a Kind || 10290 || 0.005396 ||
|| Straight || 63868 || 0.033493 ||
|| Stretch || 112770 || 0.059138 ||
|| Three of a Kind || 193305 || 0.101372 ||
|| High Card || 271439 || 0.142347 ||
|| Two Pair || 302085 || 0.158418 ||
|| Pair || 949620 || 0.497996 ||
Note how a Stretch is more likely than a Straight, which is the opposite
of the relationship between Flush and Straight in regular Poker. This
arises because there are more possible starting points for the sequence.
With only one card value “wrapping around”, a Straight can only start at
four possible values. With total wraparound of suits, a Stretch has
seven possible starting points. Therefore, there are more possible
Stretch hands, even though a few are absorbed into Four of a Kind and Five of a Kind.
We still have the odd property that the less-constrained High Card hand
is rarer than Two Pair or Pair, but this quirk gives the game a nicely
different property than Standard Poker. If you like, think of High Card
as a hand consisting of five different values which are not sequential.
One more twist to make the game more “Sevendeck-y” is to allow 7 to be
low in a straight, instead of allowing 1 (the “Ace”) to be high. This
puts the specialness on the Seven, which seems appropriate for a deck
built around that number.
An open question is whether Two Pair and Pair should be lumped together
into a single group or not. What is clear is that when breaking ties
within those two groups, the pairs should take lower precedence. So
2-2-3-3-7 beats 4-4-5-5-6, for example. If the kickers match, then the
pairs can be used to break ties.
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