Quote:
Originally Posted by tiger415
thanks! however i don't get why the non-pairs are double counted.
the way i see it,
(1) xx 2h 3c 4d 5d
(2) As xx 3c 4d 5d
(3) As 2h xx 4d 5d
(4) As 2h 3c xx 5d
(5) As 2h 3c 4d xx
(1)+As == (2)+2h == (3)+3c == (4)+4d == (5)+5d
i don't know what to make of this... i guess i don't get why this results in exactly double counting for the 36 non-pairs for the 5th card.
is there something obvious i'm overlooking?
Sorry I should have been clearer.
In your example (1), (2) & (3) are not badugis.
Goal: we want to create all 5-card unique hands with a 4 card badugi in them so that we can calculate
#five_card_hands_w_badugi/#five_card_hands
Fact 1: any 5-card hand with a badugi can be made by adding a card to 4-card badugi.
So if we add all possible cards to the set of 4-card hands we will have at least the set of 5-card hands with a badugi. There may however be multiple counting as I described.
Fact 2: when we add a card to a badugi this will pair one and only one suit. Which leads to 2 cases...
Case 1: card added pairs the badugi
The 5 cards will look like:
Ax By Cz Dw Ay
There is one and only one 4 card badugi in this hand.
Case 2: card added does not pair the badugi
The 5 cards will look like:
Ax By Cz Dw Ex
There is exactly 2 badugis:
-- By Cz Dw Ex
Ax By Cz Dw --
12 cards pair the badugi (four cards, three suits)
The remaining 36 cards do not but exactly double counts the 5-card hands they generate.